Physics · JEE Main, NEET

Electrostatics

311 practice questions with a worked solution for each. Tap an option to see instantly if you are right.

254MCQ57Numerical93With diagram
Start with question 1 Revise Electrostatics firstSee it move: Electric field lines
  1. 1An electric dipole of moment p⃗\vec{p} is placed in a uniform electric field E⃗\vec{E}. The torque acting on the dipole is maximum when the angle between p⃗\vec{p} and E⃗\vec{E} is:JEE Main/MCQ/Medium
  2. 2Two point charges +2 μC+2\,\mu\text{C} and +6 μC+6\,\mu\text{C} repel each other with force 12 N12\,\text{N}. If each is given −4 μC-4\,\mu\text{C}, new force is:NEET/MCQ/Medium
  3. 3Two concentric conducting spherical shells of radii R1R_1 and R2R_2 (R1<R2R_1 < R_2) carry charges q1q_1 and q2q_2. Electric field in region R1<r<R2R_1 < r < R_2 is:JEE Main/MCQ/Medium/With diagram
  4. 4A parallel plate capacitor with plate separation dd has capacitance C0C_0. A dielectric slab (K=4K=4, thickness t=d/2t=d/2) is placed inside. The new capacitance is:JEE Main/MCQ/Medium/With diagram
  5. 5Two concentric spherical shells of radii RR and 2R2R carry charges +Q+Q and +2Q+2Q. The electric potential at distance r=1.5Rr = 1.5R from center is:JEE Main/MCQ/Medium
  6. 6Two point charges q1=3 μCq_1=3\,\mu C and q2=−4 μCq_2=-4\,\mu C are placed at points (2i^+3j^+3k^)(2\hat{i}+3\hat{j}+3\hat{k}) and (i^+j^+k^)(\hat{i}+\hat{j}+\hat{k}) respectively. Force on charge q2q_2 is ________ N. (Take 14πϵ0=9×109 SI Units)\left(\text{Take } \dfrac{1}{4\pi\epsilon_0} = 9\times 10^9 \text{ SI Units}\right)JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  7. 7A point charge q=1μCq=1 \mu \mathrm{C} is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q=24μCQ=24 \mu \mathrm{C}, distributed uniformly along its length, as shown in figure. Force between qq and wire is ____\_\_\_\_ N. (Use : 14πϵo=9×109 N.m2/C2\frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^{9} \mathrm{~N}. \mathrm{m}^{2} / \mathrm{C}^{2})
    JEE Main/Numerical/Medium/Electric Charge and Coulomb's law/With diagram
  8. 8Two metal spheres of radius RR and 3R3 R have same surface charge density σ\sigma. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ1\sigma_1 and σ2\sigma_2, respectively. The ratio σ1σ2\frac{\sigma_1}{\sigma_2} is.JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  9. 9A small bob of mass 100 mg and charge +10μC+10 \mu \mathrm{C} is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density ' σ\sigma ' as shown in figure. If string subtends an angle of 45∘45^{\circ} with the sheet at equilibrium the charge density of sheet will be :
    (Given,     ε0=8.85×10−12 F m\varepsilon_0=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}} and acceleration due to gravity, g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^2)
    JEE Main/MCQ/Medium/Electric Charge and Coulomb's law/With diagram
  10. 10A small uncharged conducting sphere is placed in contact with an identical sphere but having 4×10−8C4 \times 10^{-8} \mathrm{C} charge and then removed to a distance such that the force of repulsion between them is 9×10−3 N9 \times 10^{-3} \mathrm{~N}. The distance between them is (Take 14πϵo\frac{1}{4 \pi \epsilon_{\mathrm{o}}} as 9×109inSI9 \times 10^9 \mathrm{in} \mathrm{SI} units)JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  11. 11A positive ion AA and a negative ion BB has charges 6.67×10−19C6.67 \times 10^{-19} \mathrm{C} and 9.6×10−10C9.6 \times 10^{-10} \mathrm{C}, and masses 19.2×10−27 kg19.2 \times 10^{-27} \mathrm{~kg} and 9×10−27 kg9 \times 10^{-27} \mathrm{~kg} respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is P×1045P \times 10^{45}, where the value of 10PP is \qquad
    (Take     14πε0=9×109Nm2C−1\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1} and universal gravitational constant as 6.67×10−11Nm2 kg−26.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2} )
    Assume that charge may not be an integral multiple of electrons.    JEE Main/Numerical/Medium/Electric Charge and Coulomb's law
  12. 12Two identical conducting spheres PP and SS with charge QQ on each, repel each other with a force 16 N16 \mathrm{~N}. A third identical uncharged conducting sphere RR is successively brought in contact with the two spheres. The new force of repulsion between P\mathrm{P} and S\mathrm{S} is :JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  13. 13The vehicles carrying inflammable fluids usually have metallic chains touching the ground :JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  14. 14Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle θ\theta with each other. When suspended in water the angle remains the same. If density of the material of the sphere is 1.5g/cc,1.5g/cc, the dielectric constant of water will be ______.
    (Take density of water     =1g/cc=1g/cc)    JEE Main/Numerical/Medium/Electric Charge and Coulomb's law
  15. 15Force between two point charges q1{q}_{1} and q2{q}_{2} placed in vacuum at rr cmcm apart is FF. Force between them when placed in a medium having dielectric K=5K=5 at r5\dfrac{r}{5} cmcm apart will be:JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  16. 16Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of 37∘37^{\circ} with each other. When suspended in a liquid of density 0.7gcm−30.7g{cm}^{-3}, the angle remains same. If density of material of the sphere is 1.4gcm−31.4g{cm}^{-3}, the dielectric constant of the liquid is _____ (tan⁡37∘=34)\left(\tan 37^{\circ}=\dfrac{3}{4}\right)JEE Main/Numerical/Medium/Electric Charge and Coulomb's law
  17. 17Three point charges q,−2qq,-2q and 2q2q are placed on xx axis at a distance x=0,x=34Rx=0,x=\dfrac{3}{4}R and x=Rx=R respectively from origin as shown. If q=2×10−6Cq=2\times {10}^{-6}C and R=2cmR=2cm, the magnitude of net force experienced by the charge −2q-2q is _____ NN.JEE Main/Numerical/Medium/Electric Charge and Coulomb's law/With diagram
  18. 18A 10μC10\mu C charge is divided into two parts and placed at 1cm1cm distance so that the repulsive force between them is maximum. The charges of the two parts are:JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  19. 19As shown in the figure, a configuration of two equal point charges (q0=+2μC)\left({q}_{0}=+2\mu C\right) is placed on an inclined plane. Mass of each point charge is 20g20g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height h=x×10−3mh=x\times {10}^{-3}m. The value ofxx is
    (Take14πϵ0=9×109Nm2C−2,g=10ms−2)\left(\text{Take}\dfrac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2},g=10m{s}^{-2}\right)
    JEE Main/Numerical/Medium/Electric Charge and Coulomb's law/With diagram
  20. 20Experimentally it is found that 12.8eV12.8eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is 9x×10−10m\dfrac{9}{x}\times {10}^{-10}m.
    The value of the     xx is: _____.
    (    1eV=1.6×10−19J,14πϵ0=9×109Nm2C21eV=1.6\times {10}^{-19}J,\dfrac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}\dfrac{{Nm}^{2}}{{C}^{2}} and electronic charge =1.6×10−19C=1.6\times {10}^{-19}C)    JEE Main/Numerical/Medium/Electric Charge and Coulomb's law
  21. 21A point charge q1=4q0{q}_{1}=4{q}_{0} is placed at origin. Another point charge q2=−q0{q}_{2}=-{q}_{0} is placed at x=12cmx=12cm. Charge of proton is q0{q}_{0}. The proton is placed on xx-axis so that the electrostatic force on the proton in zero. In this situation, the position of the proton from the origin is ______ cmcm.JEE Main/Numerical/Medium/Electric Charge and Coulomb's law
  22. 22If two charges q1{q}_{1}and q2{q}_{2} are separated with distance dd and placed in a medium of dielectric constant kk. What will be the equivalent distance between charges in air for the same electrostatic force?JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  23. 23Two identical metallic spheres AA and BB when placed at certain distance in air repel each other with a force of FF. Another identical uncharged sphere CC is first placed in contact with AA and then in contact with BB and finally placed at midpoint between spheres AAand BB. The force experienced by sphere CC will be :JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  24. 24A charge of 4μC4\mu C is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  25. 25Two identical positive charges QQ each are fixed at a distance of 2a2a apart from each other. Another point charge q0{q}_{0} with mass mm is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q0{q}_{0} executes SHM. The time period of oscillation of charge q0{q}_{0} will beJEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  26. 26Three point charges of magnitude 5μC,0.16μC5\mu C,0.16\mu C and 0.3μC0.3\mu C are located at the vertices A,B,CA,B,C of a right angled triangle whose sides are AB=3cmAB=3cm, BC=32cmBC=3\sqrt{2}cm and CA=3cmCA=3cm and point AA is the right angle corner. Charge at point AA experiences _____ NN of electrostatic force due to the other two charges.JEE Main/Numerical/Medium/Electric Charge and Coulomb's law
  27. 27Two point charges QQ each are placed at a distance dd apart. A third point charge qq is placed at a distance xx from mid-point on the perpendicular bisector. The value of xx at which charge qq will experience the maximum Coulomb's force is:JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  28. 28Three identical charged balls each of charge 2C2C are suspended from a common point PP by silk threads of 2m2m each (as shown in figure). They form an equilateral triangle of side 1m1m.
    The ratio of net force on a charged ball to the force between any two charged balls will be
    JEE Main/MCQ/Medium/Electric Charge and Coulomb's law/With diagram
  29. 29Sixty four conducting drops each of radius 0.02m0.02m and each carrying a charge of 5μC5\mu C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will beJEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  30. 30Two identical charged particles each having a mass 10g10g and charge 2.0×10−7C2.0\times {10}^{-7}C are placed on a horizontal table with a separation of LL between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.250.25, find the value of LL. [Use g=10ms−2g=10{ms}^{-2} ]JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  31. 31The relative permittivity of distilled water is 81.81. The velocity of light in it will be: ((Given μr=1)\left.{\mu }_{r}=1\right)JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  32. 32A particle of mass 1mg1mg and charge qq is lying at the mid-point of two stationary particles kept at a distance 2m2m when each is carrying same charge qq. If the free charged particle is displaced from its equilibrium position through distance xx (x<<1m)\left(x\lt \lt 1m\right). The particle executes SHM. Its angular frequency of oscillation will be _______ ×105rads−1\times {10}^{5}rad{s}^{-1} (if q2=10C2{q}^{2}=10{C}^{2})JEE Main/Numerical/Medium/Electric Charge and Coulomb's law
  33. 33A certain charge QQ is divided into two parts qq and (Q−q).(Q-q). How should the charges QQ and qq be divided so that qq and (Q−q)(Q-q) placed at a certain distance apart experience maximum electrostatic repulsion?JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  34. 34An infinite number of point charges, each carrying 1μC1\mu C charge, are placed along the y-axis at y=1m,2m,4m,8m....y=1m,2m,4m,8m....
    The total force on a     1C1C point charge, placed at the origin, is x×103Nx\times {10}^{3}N. The value of xx, to the nearest integer, is ___ .
    [Take     14πϵ0=9×109Nm2C−2\dfrac{1}{4\pi {ϵ}_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}]    JEE Main/Numerical/Medium/Electric Charge and Coulomb's law
  35. 35Two identical conducting spheres with negligible volume have 2.1nC2.1nC and −0.1nC-0.1nC charges, respectively. They are brought into contact and then separated by a distance of 0.5m0.5m. The electrostatic force acting between the spheres is ___×10−9N\times {10}^{-9}N.
    [Given :     4πϵ0=19×1094\pi {\epsilon }_{0}=\dfrac{1}{9\times {10}^{9}} SI unit]    JEE Main/Numerical/Medium/Electric Charge and Coulomb's law
  36. 36Two electrons each are fixed at a distance 2d.2d. A third charge proton placed at the midpoint is displaced slightly by a distance x(x≪d)x\left(x≪d\right) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency:
    (    m=m= mass of charged particle)    JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  37. 37Consider the force FF on a charge 'qq' due to a uniformly charged spherical shell of radius RR carrying charge QQ distributed uniformly over it. Which one of the following statements is true for FF, if 'qq' is placed at distance rr from the centre of the shell?JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  38. 38A solid sphere of radius RR carries a charge Q+qQ+q distributed uniformly over its volume. A very small point like piece of it of mass mm gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge qq. If it acquires a speed ν\nu when it has fallen through a vertical height yy (see figure), then (assume the remaining portion to be spherical)
    JEE Main/MCQ/Medium/Electric Charge and Coulomb's law/With diagram
  39. 39Two isolated conducting spheres S1{S}_{1} and S2{S}_{2} of radius 23R\dfrac{2}{3}R and 13R\dfrac{1}{3}R have 12μC12\mu C and −3μC-3\mu C charges, respectively, and are at a large distance from each other, They are now connected by a conducting wire. A long time after this is done the charges on S1{S}_{1} and S2{S}_{2} are respectively:JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  40. 40A charge Q is distributed over two concentric conducting thin spherical shells radii rr and R(R>r)R\left(R\gt r\right). If the surface charge densities on the two shells are equal, the electric potential at the common centre is :
    JEE Main/MCQ/Medium/Electric Charge and Coulomb's law/With diagram
  41. 41Charge is distributed within a sphere of radius RR with a volume charge density ρ(r)=Ar2e−2ra,\rho \left(r\right)=\dfrac{A}{{r}^{2}}{e}^{-\dfrac{2r}{a}}, where AA and aa are constants. If QQ is the total charge of this charge distribution, the radius RR is:JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  42. 42Three charges +Q,q,+Q+Q,q,+Q are placed respectively, at distance, 0,d/20,d/2 and dd from the origin, on the xx -axis. If the net force experienced by +Q,+Q, placed at x=0,x=0, is zero, then value of qq is:JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  43. 43Two identical conducting spheres AA and BB carry an equal charges. They are separated by a distance much larger than their diameters, and the force between them is FF. A third identical conducting sphere, CC, is uncharged. Sphere CC is first touched to AA, then to BB, and then removed. As a result, the force between AA and BB would be equal to:JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  44. 44A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is ρ\rho, how long will the charges take to travel a distance d\mathrm{d} ?JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  45. 45A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of 25.525.5 kVm−1\mathrm{kVm}^{-1}. The density of liquid is 1.26×103 kg m−31.26 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}. The radius of the drop is (neglect buoyancy).JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  46. 46Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential :JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  47. 47Two identical charged spheres suspended from a common point by two massless strings of length I are initially a distance d(d<<1)d(d\lt \lt 1) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity vv. Then as a function of distance xx between them,JEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  48. 48Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30∘30^{\circ} with each other. When suspended in a liquid of density 0.8 g cm−30.8 \mathrm{~g} \mathrm{~cm}^{-3}, the angle remains the same. If density of the material of the sphere is 16 g cm−316 \mathrm{~g} \mathrm{~cm}^{-3}, the dielectric constant of the liquid isJEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  49. 49If gE\mathrm{g}_{\mathrm{E}} and gm\mathrm{g}_{\mathrm{m}} are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio  electronic charge on the moon  electronic charge on the earth \frac{\text { electronic charge on the moon }}{\text { electronic charge on the earth }} to beJEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  50. 50Charges are placed on the vertices of a square as shown. Let E\mathrm{E} be the electric field and V\mathrm{V} the potential at the centre. If the charges on A\mathrm{A} and B\mathrm{B} are interchanged with those on D\mathrm{D} and C\mathrm{C} respectively, then
    JEE Main/MCQ/Medium/Electric Charge and Coulomb's law/With diagram
  51. 51Two point charges +8q+8 q and −2q-2 q are located at x=0x=0 and x=Lx=L respectively. The location of a point on the xx axis at which the net electric field due to these two point charges is zero isJEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  52. 52Two spherical conductor BB and CC having equal radii and carrying equal charges in them repel each other with a force FF when kept apart at some distance. A third spherical conductor having same radius as that of BB but uncharged brought in contact with BB, then brought in contact with C\mathrm{C} and finally removed away from both. The new force of repulsion, between BB and CC isJEE Main/MCQ/Medium/Electric Charge and Coulomb's law
  53. 53A thin half ring of radius 3535 cm is uniformly charged with a total charge of QQ coulomb. If the magnitude of the electric field at centre of the half ring is 100100 V/m, then the value of QQ is _______ nC. (ϵo=8.85×10−12\epsilon_o = 8.85 \times 10^{-12} C2^2/Nm2^2 and π=3.14\pi = 3.14)JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  54. 54A particle of charge qq and mass mm is projected from origin with an initial velocity v⃗=(v02x^+v02y^)\vec{v} = \left(\dfrac{v_0}{\sqrt{2}}\hat{x} + \dfrac{v_0}{\sqrt{2}}\hat{y}\right). There exists a uniform magnetic field B⃗=B0z^\vec{B} = B_0 \hat{z} and a space varying electric field E⃗=E0e−λxx^\vec{E} = E_0 e^{-\lambda x}\hat{x} within the region 0≤x≤L0 \leq x \leq L. After travelling a distance such that xx-coordinate has changed from x=0x=0 to x=Lx=L, the change in the kinetic energy is _______.JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  55. 55Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

    Assertion A: In electrostatics, a conductor does not store any net charge inside.

    Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.

    Choose the correct answer from the options given below    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  56. 56Two metal plates (A,B)(A, B) are kept horizontally with separation of (12π)\left(\dfrac{12}{\pi}\right) cm, with plate A on the top. An atomizer jet sprays oil (density 1.51.5 g/cm3^3) droplets of radius 11 mm horizontally. All oil droplets carry a charge 55 nC. The potentials VAV_A and VBV_B are required on plates A and B respectively in order to ensure the droplets do not descend. The values of VAV_A and VBV_B are _______.
    (Neglect the air resistance to the droplets and take     g=10g = 10 m/s2^2)    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  57. 57Identify the correct statements :
    A. Electrostatic field lines form closed loops.
    B. The electric field lines point radially outward when charge is greater than zero.
    C. The Gauss - Law is valid only for inverse - square force.
    D. The workdone in moving a charged particle in a static electric field around a closed path is zero.
    E. The motion of a particle under Coulomb's force must take place in a plane.
    Choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  58. 58A simple pendulum has a bob with mass mm and charge qq. The pendulum string has negligible mass. When a uniform and horizontal electric field E⃗\vec{E} is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ____\_\_\_\_. (g: acceleration due to gravity)JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  59. 59Six point charges are kept 60∘60^{\circ} apart from each other on the circumference of a circle of radius RR as shown in figure. The net electric field at the center of the circle is ____\_\_\_\_. (ϵ0\epsilon_{0} is permittivity of free space)
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  60. 60An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' −σ-\sigma '. The rate of change of de-Broglie wave length associated with the electron varies inversely as nth \mathrm{n}^{\text {th }} power of time. The numerical value of nn is ________.JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  61. 61Electric charge is transferred to an irregular metallic disk as shown in figure. If σ1,σ2,σ3\sigma_1, \sigma_2, \sigma_3 and σ4\sigma_4 are charge densities at given points then, choose the correct answer from the options given below:

    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  62. 62Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : The outer body of an air craft is made of metal which protects persons sitting inside from lightning-strikes.
    Reason (R) : The electric field inside the cavity enclosed by a conductor is zero.
    In the light of the above statements, chose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  63. 63Two infinite identical charged sheets and a charged spherical body of charge density ' ρ\rho ' are arranged as shown in figure. Then the correct relation between the electrical fields at A,B,C\mathrm{A}, \mathrm{B}, \mathrm{C} and D points is :
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  64. 64Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density +σ+\sigma and −2σ-2 \sigma. The force experienced by a point charge +q placed at the mid point between two plates will be :
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  65. 65A point charge +q is placed at the origin. A second point charge +9 q is placed at (d,0,0)(\mathrm{d}, 0,0) in Cartesian coordinate system. The point in between them where the electric field vanishes is :JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  66. 66A particle of mass ' mm ' and charge ' qq ' is fastened to one end ' AA ' of a massless string having equilibrium length ll, whose other end is fixed at point ' OO '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x -axis is
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  67. 67An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity 106 m/s10^6 \mathrm{~m} / \mathrm{s}. If the magnitude of the electric field between the plates is 9.1 V/cm9.1 \mathrm{~V} / \mathrm{cm}, then the vertical component of velocity of electron is (mass of electron =9.1×10−31 kg=9.1 \times 10^{-31} \mathrm{~kg} and charge of electron =1.6×10−19C=1.6 \times 10^{-19} \mathrm{C} )JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  68. 68If the net electric field at point P\mathrm{P} along Y\mathrm{Y} axis is zero, then the ratio of ∣q2q3∣\left|\frac{q_2}{q_3}\right| is 85x\frac{8}{5 \sqrt{x}}, where x=x= _____.
    JEE Main/Numerical/Medium/Electric Field and Electric Field Lines/With diagram
  69. 69Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point PP is xσϵo\frac{x \sigma}{\epsilon_o}. The value of xx is _______ (all quantities are measured in SI units).
    JEE Main/Numerical/Medium/Electric Field and Electric Field Lines/With diagram
  70. 70An infinite plane sheet of charge having uniform surface charge density +σsC/m2+\sigma_s \mathrm{C} / \mathrm{m}^2 is placed on x−yx-y plane. Another infinitely long line charge having uniform linear charge density +λeC/m+\lambda_e \mathrm{C} / \mathrm{m} is placed at z=4 mz=4 \mathrm{~m} plane and parallel to yy-axis. If the magnitude values ∣σs∣=2∣λe∣\left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right| then at point (0,0,2)(0,0,2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is πn:1\pi \sqrt{n}: 1. The value of nn is_______.JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  71. 71An infinitely long positively charged straight thread has a linear charge density λCm−1\lambda \mathrm{Cm}^{-1}. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  72. 72Suppose a uniformly charged wall provides a uniform electric field of 2×104NC−12\times {10}^{4}N{C}^{-1} normally. A charged particle of mass 2g2g being suspended through a silk thread of length 20cm20cm and remain stayed at a distance of 10cm10cm from the wall. Then the charge on the particle will be 1xμC\dfrac{1}{\sqrt{x}}\mu C where x=x= ________ [use g=10ms−2g=10m{s}^{-2}]JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  73. 73Two charges qq and 3q3q are separated by a distance ‘rr’ in air. At a distance xx from charge qq, the resultant electric field is zero. The value of xx is :JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  74. 74A particle of charge −q-q and mass mm moves in a circle of radius rr around an infinitely long line charge of linear density +λ+\lambda. Then time period will be given as:
    (Consider     kk as Coulomb's constant)    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  75. 75An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet SS having surface charge density +σ+\sigma. The electron at t=0t=0 is at a distance of 1m1m from SS and has a speed of 1ms−11m{s}^{-1}. The maximum value of σ\sigma, if the electron strikes SS at t=1st=1s is α[mϵ0e]Cm2\alpha \left[\dfrac{m{ϵ}_{0}}{e}\right]\dfrac{C}{{m}^{2}}. The value of α\alpha is _____.JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  76. 76Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason(R)
    Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
    Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces.
    In the light of the above statements, choose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  77. 77A thin metallic wire having cross sectional area of 10−4m2{10}^{-4}{m}^{2} is used to make a ring of radius 30cm30cm. A positive charge of 2πC2\pi C is uniformly distributed over the ring, while another positive charge of 30pC30pC is kept at the centre of the ring. The tension in the ring is _______N; provided that the ring does not get deformed (neglect the influence of gravity).
    (Given,     14πϵ0=9×109\dfrac{1}{4\pi {ϵ}_{0}}=9\times {10}^{9} SI units)    JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  78. 78A thin infinite sheet charge and an infinite line charge of respective charge densities +σ+\sigma and +λ+\lambda are placed parallel at 5m5m distance from each other. Points PP and QQ are at 3πm\dfrac{3}{\pi }m and 4πm\dfrac{4}{\pi }m perpendicular distances from line charge towards sheet charge, respectively. Ep{E}_{p} and Eq{E}_{q} are the magnitudes of resultant electric field intensities at point PP and QQ respectively. If EPEQ=4a\dfrac{{E}_{P}}{{E}_{Q}}=\dfrac{4}{a} for 2∣σ∣=∣λ∣,2|\sigma |=|\lambda |, then the value of aa is _____.JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  79. 79An electron revolves around an infinite cylindrical wire having uniform linear charge density 2×10−82\times {10}^{-8} Cm−1C{m}^{-1} in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ______________ ×106ms−1\times {10}^{6}m{s}^{-1}. Given mass of electron =9×10−31kg=9\times {10}^{-31}kg
    JEE Main/Numerical/Medium/Electric Field and Electric Field Lines/With diagram
  80. 80Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R,R,with distance rr from the centre OO is represented by:
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  81. 81A cubical volume is bounded by the surfaces x=0,x=a,y=0,y=a,z=0,z=ax=0,x=a,y=0,y=a,z=0,z=a. The electric field in the region is given by E⃗=E0xi^\vec{E}={E}_{0}x\hat{i}. Where E0=4×104NC−1m−1{E}_{0}=4\times {10}^{4}{NC}^{-1}{m}^{-1}. If a=2cma=2cm, the charge contained in the cubical volume is Q×10–14CQ\times {10}^{–14}C. The value of QQ is ______.
    (Take     ϵ0=9×10−12C2N−1m−2{ϵ}_{0}=9\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2})    JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  82. 82Two equal positive point charges are separated by a distance 2a2a. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge q0{q}_{0} becomes maximum is ax\dfrac{a}{\sqrt{x}}. The value of xx is ______.JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  83. 83Considering a group of positive charges, which of the following statements is correct?JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  84. 84As shown in the figure, a point charge QQ is placed at the centre of conducting spherical shell of inner radius aa and outer radius bb. The electric field due to charge QQ in three different regions I,IIandIIII,II\text{and}III is given by : (I:r<a,II:a<r<b,III:r>b)(I:r\lt a,II:a\lt r\lt b,III:r\gt b)
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  85. 85A point charge of 10µC10µC is placed at the origin. At what location on the XX-axis should a point charge of 40µC40µC be placed so that the net electric field is zero at x=2cmx=2cm on the XX-axis ?JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  86. 86A uniform electric field of 10NC−110N{C}^{-1} is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5eV.0.5eV. The length of each plate is 10cm10cm. The angle (θ)(\theta ) of deviation of the path of electron as it comes out of the field is ______(in degree).
    JEE Main/Numerical/Medium/Electric Field and Electric Field Lines/With diagram
  87. 87A stream of a positively charged particles having qm=2×1011Ckg−1\dfrac{q}{m}=2\times {10}^{11}C{kg}^{-1} and velocity v⃗0=3×107i^ms−1{\vec{v}}_{0}=3\times {10}^{7}\hat{i}m{s}^{-1} is deflected by an electric field 1.8j^kVm−11.8\hat{j}kV{m}^{-1}. The electric field exists in a region of 10cm10cm along xx direction. Due to the electric field, the deflection of the charge particles in the yy direction is _____ mmmm.JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  88. 88A spherically symmetric charge distribution is considered with charge density varying as
    ρ(r)={ρ0(34−rR)forr≤RZeroforr>R\rho \left(r\right)=\left\{\begin{matrix}{\rho }_{0}\left(\dfrac{3}{4}-\dfrac{r}{R}\right) & \text{for}r\leq R \\ Zero & & & forr\gt R\end{matrix}\right.

    Where,     r(r<R)r\left(r\lt R\right) is the distance from the centre OO (as shown in figure). The electric field at point PP will be :
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  89. 89A uniform electric field E=(8me)Vm−1E=\left(\dfrac{8m}{e}\right)V{m}^{-1} is created between two parallel plates of length 1m1m as shown in figure, (where m=m= mass of electron and e=e= charge of electron). An electron enters the field symmetrically between the plates with a speed of 2ms−12m{s}^{-1}. The angle of the deviation (θ)\left(\theta \right) of the path of the electron as it comes out of the field will be _____ .
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  90. 90A 1m1m long copper wire carries a current of 1A1A. If the cross section of the wire is 2.0mm22.0{mm}^{2} and the resistivity of copper is 1.7×10−8Ωm1.7\times {10}^{-8}\Omega m. The force experienced by moving electron in the wire is _____×10−23N\times {10}^{-23}N
    (Charge of electron    =1.6×10−19C=1.6\times {10}^{-19}C )    JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  91. 91A positive charge particle of 100mg100mg is thrown in opposite direction to a uniform electric field of strength 1×105NC−11\times {10}^{5}N{C}^{-1}. If the charge on the particle is 40μC40\mu C and the initial velocity is 200ms−1200{ms}^{-1}, how much distance it will travel before coming to the rest momentarilyJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  92. 92Two point charges AA and BB of magnitude +8×10−6C+8\times {10}^{-6}C and −8×10−6C-8\times {10}^{-6}C respectively are placed at a distance dd apart. The electric field at the middle point OO between the charges is 6.4×104NC−16.4\times {10}^{4}N{C}^{-1}. The distance 'dd' between the point charges AA and BB isJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  93. 93The three charges q2,q\dfrac{q}{2},q and q2\dfrac{q}{2} are placed at the corners A,DA,D and CC of a square of side aa as shown in figure. The magnitude of electric field (E)\left(E\right) at the corner BB of the square, is
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  94. 94Statement-I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.
    Statement-II : An electric dipole is placed in a uniform electric field. The net electric force on the dipole will not be zero.    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  95. 95In the figure, a very large plane sheet of positive charge is shown. P1{P}_{1} and P2{P}_{2} are two points at distance ll and 2l2l from the charge distribution. If σ\sigma is the surface charge density, then the magnitude of electric fields E1{E}_{1} and E2{E}_{2} at P1{P}_{1} and P2{P}_{2} respectively are
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  96. 96A long cylindrical volume contains a uniformly distributed charge of density ρ\rho. The radius of cylindrical volume is RR. A charge particle (q)\left(q\right) revolves around the cylinder in a circular path. The kinetic energy of the particle is :JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  97. 97A vertical electric field of magnitude 4.9×105NC−14.9\times {10}^{5}N{C}^{-1} just prevents a water droplet of a mass 0.1g0.1g from falling. The value of charge on the droplet will be : (Given g=9.8ms−2g=9.8m{s}^{-2})JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  98. 98Choose the incorrect statement:
    (a) The electric lines of force entering into a Gaussian surface provide negative flux.
    (b) A charge     qq is placed at the centre of a cube. The flux through all the faces will be the same.
    (c) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.
    (d) When an electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.
    Choose the most appropriate answer from the options given below:    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  99. 99Two particles AA and BB having charges 20μC20\mu C and −5μC-5\mu C respectively are held fixed with a separation of 5cm5cm At what position a third charged particle should be placed so that it does not experience a net electric force ?
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  100. 100Figure shows a rod ABAB, which is bent in a 120∘120^{\circ} circular arc of radius RR. A charge(−Q)(-Q) is uniformly distributed over rod ABAB. What is the electric filed E⃗\vec{E} at the centre of curvature OO ?
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  101. 101A uniformly charged disc of radius RR having surface charge density σ\sigma is placed in the xyxy plane with its center at the origin. Find the electric field intensity along the zz-axis at a distance ZZ from origin:JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  102. 102What will be the magnitude of the electric field at point OO as shown in the figure? Each side of the figure is ll and perpendicular to the other?
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  103. 103A simple pendulum of mass ' mm ', length ' ll ' and charge ′+q′'+{q}^{'} suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  104. 104Given below are two statements
    Statement     II : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere.
    Statement     IIII : If RR is the radius of a solid metallic sphere and QQ be the total charge on it. The electric field at any point on the spherical surface of radius r(<R)r\left(\lt R\right) is zero but the electric flux passing through this closed spherical surface of radius rr is not
    In the light of the above statements, choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  105. 105Find the electric field at point PP (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length LL carrying a charge QQ. The distance of the point PP from the centre of the rod is a=32La=\dfrac{\sqrt{3}}{2}L
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  106. 106Two small spheres each of mass 10mg10mg are suspended from a point by threads 0.5m0.5m long. They are equally charged and repel each other to a distance of 0.20m0.20m. The charge on each of the sphere is a21×10−8C.\dfrac{a}{21}\times {10}^{-8}C. The value of aa will be ___.[Given g=10ms−2g=10m{s}^{-2}]JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  107. 107The peak electric field produced by the radiation coming from the 8W8W bulb at a distance of 10m10m is x10μ0cπVm−1\dfrac{x}{10}\sqrt{\dfrac{{\mu }_{0}c}{\pi }}V{m}^{-1}. The efficiency of the bulb is 1010% and it is a point source. The value of xx is,JEE Main/Numerical/Medium/Electric Field and Electric Field Lines
  108. 108A cube of side aa has point charges +Q+Q located at each of its vertices except at the origin where the charge is −Q.-Q. The electric field at the centre of cube is:
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  109. 109Charges Q1{Q}_{1} and Q2{Q}_{2} are at points AA and BB of a right-angled triangle OABOAB. The resultant electric field at point OO is perpendicular to the hypotenuse, then Q1/Q2{Q}_{1}/{Q}_{2} is proportional to:
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  110. 110Two charged thin infinite plane sheets of uniform charge density σ+{\sigma }_{+} and σ−{\sigma }_{-}, where ∣σ+∣>∣σ−∣\left|{\sigma }_{+}\right|\gt \left|{\sigma }_{-}\right|, intersect at the right angle. Which of the following best represents the electric field lines for the system:JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  111. 111Consider a sphere of radius RR which carries a uniform charge density ρ\rho . If a sphere of radius R2\dfrac{R}{2} is carved out of it, as shown, the ratio ∣EA⃗∣∣EB⃗∣\dfrac{\left|\vec{{E}_{A}}\right|}{\left|\vec{{E}_{B}}\right|} of magnitude of electric field EA⃗\vec{{E}_{A}} and EB⃗\vec{{E}_{B}} , respectively, at points AA and BB due to the remaining portion is:

    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  112. 112Three charged particles A,B\text{A}, \text{B} and C\text{C} with charges −4q,2q-4q,2q and −2q-2q are present on the circumference of a circle of radius d.d. The charged particles A,C\text{A}, \text{C} and centre O\text{O} of the circle formed an equilateral triangle as shown in the figure. The electric field at the point O\text{O} is

    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  113. 113A particle of mass mm and charge qq has an initial velocity v⃗=v0j^\vec{v}={v}_{0}\hat{j} . If an electric field E⃗=E0i^\vec{E}={E}_{0}\hat{i} and magnetic field B⃗=B0i^\vec{B}={B}_{0}\hat{i} act on the particle, its speed will double after a timeJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  114. 114Two infinite planes each with uniform surface charge density +σ+\sigma are kept in such a way that the angle between them is 30o{30}^{o} . The electric field in the region shown between them is given by:
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  115. 115A simple pendulum of length LL is placed between the plates of a parallel plate capacitor having electric field EE , as shown in figure. Its bob has mass mm and charge qq . The time period of the pendulum is given by:
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  116. 116Four point charges −q,+q,+q-q,+q,+q and −q-q are placed on y-axis at y=−2d,y=−d,y=-2d,y=-d, and y=+2d,y=+2d, respectively. The magnitude of the electric field EE at a point on the x-axis at x=D,x=D, with D≫d,D≫d, will behave as:JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  117. 117A positive point charge is released from rest at a distance r0{r}_{0} from a positive line charge with uniform charge density. The speed (v)(v) of the point charge, as a function of instantaneous distance rr from line charge, is proportional to
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  118. 118The bob of a simple pendulum has mass 2g2g and a charge of 5.0μC.5.0\mu C. It is at rest in a uniform horizontal electric field of intensity 2000V/m2000V/m At equilibrium, the angle that the pendulum makes with the vertical is:
    (takeg=10m/s2)\left(takeg=10m/{s}^{2}\right)    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  119. 119A parallel plate capacitor with plates of area 1m21{m}^{2} each, are at a separation of 0.1m.0.1m. If the electric field between the plates is 100N/C,100 N/C, the magnitude of charge on each plate is: (Take∈0=8.85×10−12C2N-m2)(\text{Take} {\in }_{0}=8.85\times {10}^{-12}\dfrac{{C}^{2}}{N\text{-}{m}^{2}})JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  120. 120Two point charges q1(10μC){q}_{1}\left(\sqrt{10}\mu C\right) and q2(−25μC){q}_{2}\left(-25\mu C\right) are placed on the xx -axis at x=1mx=1m and x=4mx=4m respectively. The electric field (inV/m)\left(\text{in}V/m\right) at a point y=3my=3m on yy-axis is,

    [Take14πϵ0=9×109Nm2C−2]\left[\text{Take}\dfrac{1}{4\pi {ϵ}_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}\right]    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  121. 121For a uniformly charged ring of radius R,R, the electric field on its axis has the largest magnitude at a distance hh from its centre. Then value of hh is:JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  122. 122[12]
    A solid ball of radius     R\mathrm{R} has a charge density ρ\rho given by ρ=ρ0(1−rR)\rho=\rho_0\left(1-\frac{r}{R}\right) for 0≤r≤R0 \leq r \leq R. The electric field outside the ball is:    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  123. 123A body of mass MM and charge qq is connected to a spring of spring constant kk. It is oscillating along x\mathrm{x}-direction about its equilibrium position, taken to be at x=0x=0, with an amplitude AA. An electric field EE is applied along the x\mathrm{x}-direction. Which of the following statements is correct?JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  124. 124A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is:JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  125. 125The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density ρ=Ar\rho =\dfrac{A}{r} , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  126. 126A wire of length L=20cmL=20cm is bent into a semi-circular arc and the two equal halves of the arc are uniformly charged with charges +Q+Q and −Q-Q as shown in the figure. The magnitude of the charge on each half is ∣Q∣=103ϵ0\left|Q\right|={10}^{3}{\epsilon }_{0}, where ϵ0{\epsilon }_{0} is the permittivity of free the space. The net electric field at the centre OO is

    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  127. 127A thin disc of radius b=2ab=2a has a concentric hole of radius aa in it (see figure). It carries uniform surface charge σ\sigma on it. If the electric field on its axis at a height h(h<<a)\text{h}\left(\text{h}\lt \lt \text{a}\right) from its centre is given as Ch\text{C}\text{h} then the value of CC is

    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  128. 128Shown in the figure are two point charges +Q+Q and −Q-Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If σ1{\sigma }_{1} is the surface charge on the inner surface and Q1{Q}_{1} net charge on it and σ2{\sigma }_{2} the surface charge on the outer surface and Q2{Q}_{2} net charge on it then:

    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  129. 129A long cylindrical shell carries positive surface charge σ\sigma in the upper half and negative surface charge –σ–\sigma in the lower half. The electric field lines around the cylinder will look like figure given in:

    (figures are schematic and not drawn to scale)    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  130. 130

    Two long currents carrying thin wires, both with current     II, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle ' θ\theta ' with the vertical. If wires have a mass λ\lambda per unit length then the value of II is:
    (    g=g= gravitational acceleration)    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  131. 131A spherically symmetric charge distribution is characterised by a charge density having the following variations:
    ρ(r)=ρo(1−rR)\rho(r)=\rho_o\left(1-\frac{r}{R}\right) for r<Rr \lt R
    ρ(r)=0\rho(\mathrm{r})=0 for r≥Rr \geq \mathrm{R}
    Where     rr is the distance from the centre of the charge distribution ρo\rho_{\mathrm{o}} is a constant. The electric field at an internal point (r<R)(r \lt R) is:    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  132. 132The surface charge density of a thin charged disc of radius R\mathrm{R} is σ\sigma. The value of the electric field at the centre of the disc is σ2∈0\frac{\sigma}{2 \in_0}. With respect to the field at the centre, the electric field along the axis at a distance R\mathrm{R} from the centre of the disc:JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  133. 133Two small equal point charges of magnitude qq are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle θ\theta from the vertical. If the mass of each charge is mm, then the electrostatic potential at the centre of line joining them will be
    (14π∈0=k). \left(\frac{1}{4 \pi \in_0}=k\right) \text {. }    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  134. 134Two balls of same mass and carrying equal charge are hung from a fixed support of length ll. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, xx between the balls is proportional to :JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  135. 135Three positive charges of equal value qq are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as inJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  136. 136In a uniformly charged sphere of total charge QQ and radius RR, the electric field EE is plotted as a function of distance from the centre. The graph which would correspond to the above will beJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  137. 137Let there be a spherically symmetric charge distribution with charge density varying as ρ(r)=ρ0(54−rR)\rho(r)=\rho_0\left(\frac{5}{4}-\frac{r}{R}\right) upto r=Rr=R, and ρ(r)=0\rho(r)=0 for r>Rr\gt R, where rr is the distance from the origin. The electric field at a distance r(r<R)r(r \lt R) from the origin is given byJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  138. 138A thin semi-circular ring of radius rr has a positive charge qq distributed uniformly over it. The net field E⃗\vec{E} at the centre OO is
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  139. 139A charge QQ is placed at each of the opposite corners of a square. A charge qq is placed at each of the other two corners. If the net electrical force on QQ is zero, then the Q/qQ / q equalsJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  140. 140Let P(r)=QπR4rP(r)=\frac{Q}{\pi R^4} r be the charge density distribution for a solid sphere of radius RR and total charge QQ. for a point ' pp ' inside the sphere at distance r1r_1 from the centre of the sphere, the magnitude of electric field isJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  141. 141A thin spherical shell of radius RR has charge QQ spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r)E(r) produced by the shell in the range 0≤0 \leq r<∞r \lt \infty, where rr is the distance from the centre of the shell?JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  142. 142Two spherical conductors AA and BB of radii 1 mm1 \mathrm{~mm} and 2 mm2 \mathrm{~mm} are separated by a distance of 5 cm5 \mathrm{~cm} and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres AA and BB isJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  143. 143A charged ball B hangs from a silk thread SS which makes an angle θ\theta with a large charged conducting sheet P\mathrm{P}, as show in the figure. The surface charge density σ\sigma of the sheet is proportional to
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  144. 144A charged oil drop is suspended in a uniform field of 3×104 V/m3 \times 10^4 \mathrm{~V} / \mathrm{m} so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge =9.9×10−15 kg=9.9 \times 10^{-15} \mathrm{~kg} and g=\mathrm{g}= 10 m/s210 \mathrm{~m} / \mathrm{s}^2 )JEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  145. 145Four charges equal to −Q-Q are placed at the four corners of a square and a charge qq is at its centre. If the system is in equilibrium the value of qq isJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  146. 146Three charges −q1,+q2-q_1,+q_2 and −q3-q_3 are placed as shown in the figure. The xx-component of the force on −q1-q_1 is proportional to
    JEE Main/MCQ/Medium/Electric Field and Electric Field Lines/With diagram
  147. 147If a charge qq is placed at the centre of the line joining two equal charges QQ such that the system is in equilibrium then the value of qq isJEE Main/MCQ/Medium/Electric Field and Electric Field Lines
  148. 148The electric potential as a function of x,yx, y is given by V=5(x2−y2)V = 5(x^2 - y^2) V. The electric field at a point (2,3)(2, 3) m is __________ V/m.JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  149. 149A three coulomb charge moves from the point (0,−2,−5)(0, -2, -5) to the point (5,1,2)(5, 1, 2) in an electric field expressed as E⃗=2xi^+3y2j^+4k^\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k} N/C. The work done in moving the charge is _______ J.JEE Main/Numerical/Medium/Electric Potential and Potential Energy
  150. 150Two charged conducting spheres S1S_1 and S2S_2 of radii 88 cm and 1818 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S1S_1 and S2S_2 spheres are ES1E_{S_1} and ES2E_{S_2} respectively. The value of ES1ES2\dfrac{E_{S_1}}{E_{S_2}} is _______.JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  151. 151Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is ____\_\_\_\_ μJ\mu \mathrm{J}.
    14πϵ0=9×109 N.m2/C2\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{~N}. \mathrm{m}^{2} / \mathrm{C}^{2}    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  152. 152The electrostatic potential in a charged spherical region of radius rr varies as V=ar3+bV=a r^{3}+b, where aa and bb are constants. The total charge in the sphere of unit radius is α×πa∈o\alpha \times \pi a \in_{\mathrm{o}}. The value of α\alpha is ____\_\_\_\_.
    (permittivity of vacuum is     ϵ0\epsilon_{0})    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  153. 153There are three co-centric conducting spherical shells A,BA, B and CC of radii a,ba, b and cc respectively (c>b>a)(c\gt b\gt a) and they are charged with charge q1,q2q_{1}, q_{2} and q3q_{3} respectively. The potentials of the spheres A,BA, B and CC respectively, are :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  154. 154Two charges 7μC7 \mu \mathrm{C} and −2μC-2 \mu \mathrm{C} are placed at (−9,0,0)cm(-9,0,0) \mathrm{cm} and (9,0,0)cm(9,0,0) \mathrm{cm} respectively in an external field E=Ar2r^E=\frac{\mathrm{A}}{r^{2}} \hat{r}, where A=9×105 N/C.m2A=9 \times 10^{5} \mathrm{~N} / \mathrm{C}. \mathrm{m}^{2}. Considering the potential at infinity is 0, the electrostatic energy of the configuration is ____\_\_\_\_ J.JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  155. 155Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  156. 156Five positive charges each having charge qq are placed at the vertices of a pentagon as shown in the figure. The electric potential (V)(V) and the electric field (E⃗)(\vec{E}) at the center OO of the pentagon due to these five positive charges are:
    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  157. 157Electric field in a region is given by E⃗=Axi^+Byj^\vec{E}=A x \hat{i}+B y \hat{j}, where A=10 V/m2A=10 \mathrm{~V} / \mathrm{m}^{2} and B=5 V/m2B=5 \mathrm{~V} / \mathrm{m}^{2}. If the electric potential at a point (10,20)(10,20) is 500 V, then the electric potential at origin is ____\_\_\_\_ V.JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  158. 158Consider two identical metallic spheres of radius RR each having charge QQ and mass mm. Their centers have an initial separation of 4R4 R. Both the spheres are given an initial speed of uu towards each other. The minimum value of uu, so that they can just touch each other is :
    (Take     k=14πϵ0k=\frac{1}{4 \pi \epsilon_{0}} and assume kQ2>Gm2k Q^{2}\gt G m^{2} where GG is the Gravitational constant)    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  159. 159A point charge of 10−8C10^{-8} \mathrm{C} is placed at origin. The work done in moving a point charge 2μC2 \mu \mathrm{C} from point A(4,4,2)mA(4,4,2) \mathrm{m} to B(2,2,1)mB(2,2,1) \mathrm{m} is ____\_\_\_\_ J. (14πϵo=9×109\left(\frac{1}{4 \pi \epsilon_{o}}=9 \times 10^{9}\right. in SI units ))JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  160. 160Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R\mathrm{R} Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.
    Reason     R\mathrm{R} : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  161. 161Two charges q1\mathrm{q}_1 and q2\mathrm{q}_2 are separated by a distance of 30 cm. A third charge q3q_3 initially at ' C ' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of q3q_3 from CC to DD is given by q3 K4πϵ0\frac{\mathrm{q}_3 \mathrm{~K}}{4 \pi \epsilon_0}, the value of K is :
    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  162. 162A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc⁡AB\operatorname{arc} \mathrm{AB} to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?
    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  163. 163Two small spherical balls of mass 10 g each with charges −2μC-2 \mu \mathrm{C} and 2μC2 \mu \mathrm{C}, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of 100μC/m2100 \mu \mathrm{C} / \mathrm{m}^2 such that length of rod makes an angle of 30∘30^{\circ} with electric field generated by charge sheet. Net torque acting on the rod is:
    (Take     ε0:8.85×10−12C2/Nm2\varepsilon_0: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2)    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  164. 164The electrostatic potential on the surface of uniformly charged spherical shell of radius R=10 cm\mathrm{R}=10 \mathrm{~cm} is 120 V. The potential at the centre of shell, at a distance r=5 cm\mathrm{r}=5 \mathrm{~cm} from centre, and at a distance r=15 cm\mathrm{r}=15 \mathrm{~cm} from the centre of the shell respectively, are :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  165. 165Consider a circular loop that is uniformly charged and has a radius a2\mathrm{a} \sqrt{2}. Find the position along the positive z -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  166. 166Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is VV. The potential difference between the points A and B (shown in the figure) is :
    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  167. 167Match List - I with List - II.
    \(\begin{array}{l|l}
    \text { List - I } & \text { List - II } \\
    \hline \text { (A) }\begin{array}{l}
    \text { Electric field inside (distance } r>0 \text { from center) } \\
    \text { of a uniformly charged spherical shell with } \\
    \text { surface charge density } \sigma \text {, and radius R. }
    \end{array} & \text { (I) } \begin{array}{l}
    \sigma / \epsilon_0
    \end{array} \\
    \text { (B) } \begin{array}{l}
    \text { Electric field at distance r>0 from a uniformly } \\
    \text { charged infinite plane sheet with surface } \\
    \text { charge density } \sigma .
    \end{array} & \text { (II) } \sigma / 2 \epsilon_0 \\
    \text { (C) } \begin{array}{l}
    \text { Electric field outside (distance r>0 from center) } \\
    \text { of a uniformly charged spherical shell with } \\
    \text { surface charge density } \sigma \text {, and radius R. }
    \end{array} & \text { (III) } 0 \\
    \text { (D) } \begin{array}{l}
    \text { Electric field between } 2 \text { oppositely charged } \\
    \text { infinite plane parallel sheets with uniform } \\
    \text { surface charge density } \sigma .
    \end{array} & \text { (IV) } \frac{\sigma R^2}{\epsilon_0 r^2}
    \end{array}\)
    Choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  168. 168Three infinitely long wires with linear charge density λ\lambda are placed along the x−axis,yx-a x i s, y-axis and z−z- axis respectively. Which of the following denotes an equipotential surface?JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  169. 169
    In the first configuration (1) as shown in the figure, four identical charges \(\left(q_0\right)\) are kept at the corners \(A, B, C\) and \(D\) of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points \(\mathrm{G}, \mathrm{E}, \mathrm{H}\) and F, of the square, If \(\mathrm{K}=\frac{1}{4 \pi \varepsilon_0}\), the difference between the potential energies of configuration (2) and (1) is given by :    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  170. 170Two charges 7μc7 \mu \mathrm{c} and −4μc-4 \mu \mathrm{c} are placed at (−7 cm,0,0)(-7 \mathrm{~cm}, 0,0) and (7 cm,0,0)(7 \mathrm{~cm}, 0,0) respectively. Given, ϵ0=8.85×10−12C2 N−1 m−2\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}, the electrostatic potential energy of the charge configuration is :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  171. 171At the centre of a half ring of radius R=10 cm\mathrm{R}=10 \mathrm{~cm} and linear charge density 4nCm−14 \mathrm{n} \mathrm{C} \mathrm{m}^{-1}, the potential is xπVx \pi \mathrm{V}. The value of xx is _______JEE Main/Numerical/Medium/Electric Potential and Potential Energy
  172. 172Two charged conducting spheres of radii aa and bb are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  173. 173The distance between charges +q+q and −q-q is 2l2l and between +2q+2q and −2q-2q is 4l4l. The electrostatic potential at point PP at a distance rr from centre OO is −α[qlr2]×109V-\alpha \left[\dfrac{ql}{{r}^{2}}\right]\times {10}^{9}V, where the value of α\alpha is ______. (Use 14πϵ0=9×109Nm2C−2\dfrac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2})JEE Main/Numerical/Medium/Electric Potential and Potential Energy/With diagram
  174. 174The electrostatic potential due to an electric dipole at a distance rr varies as :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  175. 175The electric potential at the surface of an atomic nucleus (Z=50)(Z=50) of radius 9×10−13cm9\times {10}^{-13}cm is α×106V\alpha \times {10}^{6}V. What is the value of α\alpha?
    (Charge of proton     1.6×10−19C1.6\times {10}^{-19}C)    JEE Main/Numerical/Medium/Electric Potential and Potential Energy
  176. 176An electric charge 10−6μC{10}^{-6}\mu C is placed at origin (0,0)(0,0) mm of X−YX-Y co-ordinate system. Two points PP and QQ are situated at (3,3)m(\sqrt{3},\sqrt{3})m and (6,0)m(\sqrt{6},0)m respectively. The potential difference between the points PP and QQ will be :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  177. 177If VV is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be:JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  178. 178Three concentric spherical metallic shells X,YX,Y and ZZ of radius a,ba,b and cc respectively [a<b<c]\left[a\lt b\lt c\right] have surface charge densities σ,–σ\sigma ,–\sigma and σ\sigma, respectively. The shells XX and ZZ are at same potential. If the radii of X&Y are 2cm2cm and 3cm3cm, respectively. The radius of shell ZZ is _____cmcm.JEE Main/Numerical/Medium/Electric Potential and Potential Energy
  179. 179Electric potential at a point PP due to a point charge of 5×10−9C5\times {10}^{-9}C is 50V50V. The distance of PP from the point charge is:
    (Assume,     14πϵ0=9×109Nm2C−2\dfrac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2})    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  180. 180For a uniformly charged thin spherical shell, the electric potential (V)\left(V\right) radially away from the centre (O)\left(O\right) of shell can be graphically represented as
    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  181. 181Which of the following correctly represents the variation of electric potential (V)(V) of a charged spherical conductor of radius (R)(R) with radial distance (r)(r) from the centre?JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  182. 182Two isolated metallic solid spheres of radii RR and 2R2R are charged such that both have same charge density σ\sigma . The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is σ′{\sigma }^{'}. The ratio σ′σ\dfrac{{\sigma }^{'}}{\sigma } is :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  183. 183For a charged spherical ball, electrostatic potential inside the ball varies with rr as V=2ar2+bV=2a{r}^{2}+b.
    Here,     aa and bb are constant and rr is the distance from the center. The volume charge density inside the ball is −λaϵ-\lambda a\epsilon. The value of λ\lambda is ______.
    ϵ=\epsilon = permittivity of medium.    JEE Main/Numerical/Medium/Electric Potential and Potential Energy
  184. 184A point charge 2×10–2C2\times {10}^{–2}C is moved from PP to SS in a uniform electric field of 30NC–130N{C}^{–1} directed along positive xx-axis. If coordinates of PP and SS are (1,2,0)mand(0,0,0)m(1,2,0)m\text{and}(0,0,0)m respectively, the work done by electric field will beJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  185. 185The electric potential at the centre of two concentric half rings of radii R1{R}_{1} and R2{R}_{2}, having same linear charge density λ\lambda is
    .    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  186. 186Given below are two statements.
    Statement I : Electric potential is constant within and at the surface of each conductor.
    Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
    In the light of the above statements, choose the most appropriate answer from the options give below.    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  187. 187Two uniformly charged spherical conductors AA and BB of radii 5mm5mm and 10mm10mm are separated by a distance of 2cm2cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere AA and BB will beJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  188. 188If the electric potential at any point (x,y,z)m\left(x,y,z\right)m in space is given by V=3x2V=3{x}^{2} volt. The electric field at the point (1,0,3)m\left(1,0,3\right)m will be :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  189. 1892727 identical drops are charged at 22V22V each. They combine to form a bigger drop. The potential of the bigger drop will be _____ VV.JEE Main/Numerical/Medium/Electric Potential and Potential Energy
  190. 190The two thin coaxial rings, each of radius aa and having charges +Q+Q and −Q-Q respectively are separated by a distance of ss. The potential difference between the centres of the two rings is :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  191. 1912727 similar drops of mercury are maintained at 10V10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ___________ times that of a smaller drop.JEE Main/Numerical/Medium/Electric Potential and Potential Energy
  192. 192In an electrical circuit, a battery is connected to pass 20C20C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15V15V. The workdone by the battery is _______ JJJEE Main/Numerical/Medium/Electric Potential and Potential Energy
  193. 193512512 identical drops of mercury are charged to a potential of 2V2V each. The drops are joined to form a single drop. The potential of this drop is VV in Volt.JEE Main/Numerical/Medium/Electric Potential and Potential Energy
  194. 194Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges1,3,5,7,91,3,5,7,9 have charge (+q)(+q) each, while 2,4,6,8,102,4,6,8,10 have charge (–q)(–q) each. The potential V and the electric field E at the centre of the circle are respectively : (TakeV=0V=0 at infinity)JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  195. 195A two point charges 4q4q and –q–q are fixed on the xx -axis at x=−d2x=\dfrac{-d}{2} and x=d2x=\dfrac{d}{2}, respectively. If the third point charge ‘qq ’ is taken from the origin to x=dx=d along the semicircle as shown in the figure, the energy of the charge will:
    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  196. 196Concentric metallic hollow spheres of radii R and 4R hold charges Q1{Q}_{1} and Q2{Q}_{2} respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R)−V(4R)V\left(R\right)-V(4R) is:JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  197. 197Consider two charged metallic spheres S1{S}_{1} and S2{S}_{2} of radii R1{R}_{1} and R2,{R}_{2}, respectively. The electric fields E1{E}_{1} (on S1{S}_{1} ) and E2{E}_{2} (on S2{S}_{2} ) on their surfaces are such that E1E2=R1R2.\dfrac{{E}_{1}}{{E}_{2}}=\dfrac{{R}_{1}}{{R}_{2}}. Then the ratio V1{V}_{1} (on S1{S}_{1} )//V2{V}_{2} (on S2{S}_{2} ) of the electrostatic potentials on each sphere is:JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  198. 198In free space, a particle AA of charge 1μC1\mu C is held fixed at point PP . Another particle BB of the same charge and mass 4μg4\mu g is kept at a distance of 1mm1mm from P.P. If BB is released, then its velocity at a distance of 9mm9mm from PP is:
    [Take     14πϵ0=9×109Nm2C−2\dfrac{1}{4\pi {ϵ}_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2} ]    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  199. 199A uniformly charged ring of radius 3a3a and total charge qq is placed in x‐yx‐y plane centred at origin. A point charge qq is moving towards the ring along the z−z- axis and has speed vv at z=4az=4a . The minimum value of vv such that it crosses the origin is:JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  200. 200A system of three charges are placed as shown in the figure:

    If     D>>d,D\gt \gt d, the potential energy of the system is best given by:    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  201. 201The electric field in a region is given by E⃗=(Ax+B)i^,\vec{E}=\left(Ax+B\right)\hat{i}, where EE is in NC−1N{C}^{-1} and xx is in metres. The values of constants are A=20SIA=20SI unit and B=10SIB=10SI unit. If the potential at x=1x=1 is V1{V}_{1} and that at x=−5x=-5 is V2,{V}_{2}, then V1−V2{V}_{1}-{V}_{2} isJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  202. 202A solid conducting sphere, having a charge Q,Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V.V. If the shell is now given a charge of –4Q,–4Q, the new potential difference between the same two surfaces is:JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  203. 203There is a uniform spherically symmetric surface charge density at a distance R0{R}_{0} from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t))V\left(R\left(t\right)\right) of the distribution as a function of its instantaneous radius R(t)R\left(t\right) is:JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  204. 204Three charges Q,+yQ,+y and +q+q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q\mathrm{Q} is

    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  205. 205The given graph shows variation (with distancer from centre) of:

    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  206. 206Four equal point charges QQ each are placed in the xyxy plane at (0,2),(4,2),(4,−2)\left(0, 2\right),\left(4, 2\right),\left(4, -2\right) and (0,−2)\left(0, -2\right) . The work required to put a fifth charge QQ at the origin of the coordinate system will be:JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  207. 207Charges −q-q and +q+q, located at AA and BB, respectively, constitute an electric dipole. Distance AB=2aAB=2a, OO is the mid point of the dipole and OPOP is perpendicular to ABAB. A charge QQ is placed at PP where OP=yOP=y and y≫2ay≫2a. The charge QQ experiences an electrostatic force FF. If QQ is now moved along the equatorial line to P′P' such that OP′=(y3)OP'=\left(\dfrac{y}{3}\right) the force on QQ will be close to(y3≪2a)\left(\dfrac{y}{3}≪2a\right)
    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  208. 208A charge QQ is distributed over three concentric spherical shells of radii a,b,c(a<b<c)a,b,c\left(a\lt b\lt c\right) such that their surface charge densities are equal to one another.

    The total potential at a point at distance     rr from their common centre, where r<a,r\lt a, would be:    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  209. 209Three concentric metal shells A,BA,B and CC of respective radii a,ba,b and c(a<b<c)c(a\lt b\lt c) have surface charge densities <c) charge="" densities="" have="" math="" surface=""> +σ,−σ+\sigma ,-\sigma and +σ+\sigma respectively. The potential of shell BB is:</c)>JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  210. 210The energy stored in the electric field produced by a metal sphere is 4.5J4.5J. If the sphere contains 4μC4\mu C charge, its radius will be: [Take:14π∈0=9×109Nm2C−2]\left[Take:\dfrac{1}{4\pi {\in }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}\right]JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  211. 211There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at PP, in the region, is found to vary between the limits 589.0V589.0V to 589.8V589.8V. What is the potential at a point on the sphere whose radius vector makes an angle of 60∘60^{\circ} with the direction of the field?JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  212. 212Within a spherical charge distribution of charge density ρ(r),\rho \left(r\right), N equipotential surfaces of potential V0,V0+∆V,V0+2∆V,…V0+N∆V(∆V>0),{V}_{0},{V}_{0}+∆V,{V}_{0}+2∆V,\ldots {V}_{0}+N∆V\left(∆V\gt 0\right), are drawn and have increasing radii r0,r1,r2,…rN,{r}_{0},{r}_{1},{r}_{2},\ldots {r}_{N}, respectively. If the difference in the radii of the surfaces is constant for all values of V0and∆V{V}_{0}and∆V then :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  213. 213The potential (in volts) of a charge distribution is given by

    V(z)=30−5z2V\left(z\right)=30-5{z}^{2} for ∣z∣≤1m\left|z\right|\leq 1m

    V(z)=35−10∣z∣V\left(z\right)=35-10\left|z\right| for ∣z∣≥1m\left|z\right|\geq 1m .

    V(z)V\left(z\right) does not depend on x and y. If this potential is generated by a constant charge per unit volume ρ0{\rho }_{0} (in units of ϵ0{ϵ}_{0} ) which is spread over a certain region, then choose the correct statement.    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  214. 214An electric field E⃗=(25i^+30j^)NC−1\vec{E}=\left(25\hat{i}+30\hat{j}\right)N{C}^{-1} exists in a region of space. If the potential at the origin is taken to be zero then the potential at x=2mx=2m, y=2my=2m is:JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  215. 215A uniformly charged solid sphere of radius R has potential V0{V}_{0} (measured with respect to ∞\infty ) on its surface. For this sphere the equipotential surfaces with potential 3V02,5V04,3V04\dfrac{3{V}_{0}}{2},\dfrac{5{V}_{0}}{4},\dfrac{3{V}_{0}}{4} and V04\dfrac{{V}_{0}}{4} have radius R1{R}_{1} , R2,R3{R}_{2},{R}_{3} and R4{R}_{4} respectively. Then
    Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  216. 216Assume that an electric field E⃗=30x⁡2i⁡^\vec{\text{E}}=30{x⁡}^{2}\hat{i⁡} exists in space. Then the potential difference VA−VO{\text{V}}_{\text{A}}-{\text{V}}_{\text{O}} , where VO is the potential at the origin and VA the potential at x = 2 m is :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  217. 217The gravitational field in a region is given by: E⃗=(5N/kg)i^+(12N/kg)j^\vec{E}=(5 N / k g) \hat{i}+(12 N / k g) \hat{j}
    If the potential at the origin is taken to be zero, then the ratio of the potential at the points     (12 m,0)(12 \mathrm{~m}, 0) and (0,5 m)(0,5 \mathrm{~m}) is :    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  218. 218This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.

    Statement 1: No work is required to be done to move a test charge between any two points on an equipotential surface.
    Statement 2 : Electric lines of force at the equipotential surfaces are mutually perpendicular to each other.    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  219. 219A point charge of magnitude +1μC+1 \mu \mathrm{C} is fixed at (0(0, 0,0)0,0). An isolated uncharged spherical conductor, is fixed with its center at (4,0,0)(4,0,0). The potential and the induced electric field at the centre of the sphere is :JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  220. 220A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :

    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  221. 221A charge of total amount QQ is distributed over two concentric hollow spheres of radii rr and R(RR(R >r\gt r ) such that the surface charge densities on the two spheres are equal. The electric potential at the common centre isJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  222. 222The electric potential V(x)V(x) in a region around the origin is given by V(x)=4x2V(x)=4 x^2 volts. The electric charge enclosed in a cube of 1 m1 \mathrm{~m} side with its centre at the origin is (in coulomb)JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  223. 223This question has statement 11 and statement 22 . Of the four choices given after the statements, choose the one that best describes the two statements.
    An insulating solid sphere of radius     R\mathrm{R} has a uniformly positive charge density ρ\rho. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.
    Statement     11: When a charge qq is taken from the centre to the surface of the sphere, its potential energy changes by qp3ε0\frac{\mathrm{qp}}{3 \varepsilon_0}
    Statement     22: The electric field at a distance r(r<R)r(r \lt R) from the centre of the sphere is ρr3ε0\frac{\rho r}{3 \varepsilon_0}    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  224. 224The electrostatic potential inside a charged spherical ball is given by ϕ=αρ2+b\phi=\alpha \rho^2+b where rr is the distance from the centre; a,ba, b are constants. Then the charge density inside ball isJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  225. 225Two points PP and QQ are maintained at the potentials of 10 V10 \mathrm{~V} and −4 V-4 \mathrm{~V} respectively. The work done in moving 100 electrons from PP to QQ isJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  226. 226This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
    Statement - 1: For a charged particle moving from point     PP to point QQ, the net work done by an electrostatic field on the particle is independent of the path connecting point PP to point QQ.
    Statement-2: The net work done by a conservative force on an object moving along a closed loop is zero    JEE Main/MCQ/Medium/Electric Potential and Potential Energy
  227. 227The potential at a point xx (measured in μm\mu \mathrm{m} ) due to some charges situated on the x\mathrm{x}-axis is given by V(x)=20/(x2−4) Volts\mathrm{V(x)=20 /\left(x^2-4\right)} \mathrm{~Volts}. The electric field E\mathrm{E} at x=4 μm\mathrm{x=4 ~\mu m} is given byJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  228. 228An electric charge 10−3μC10^{-3} \mu \mathrm{C} is placed at the origin (0,0)(0,0) of X−YX-Y co-ordinate system. Two points AA and B\mathrm{B} are situated at (2,2)(\sqrt{2}, \sqrt{2}) and (2,0)(2,0) respectively. The potential difference between the points AA and BB will beJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  229. 229Two insulating plates are both uniformly charged in such a way that the potential difference between them is V2−V1=20 VV_2-V_1=20 \mathrm{~V}. (i.e. plate 2 is at a higher potential). The plates are separated by d=0.1 md=0.1 \mathrm{~m} and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1 . What is its speed when it hits plate 2?2 ?
    (e=1.6×10−19C,me=9.11×10−31 kg)\left(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}, \mathrm{m}_{\mathrm{e}}=9.11 \times 10^{-31} \mathrm{~kg}\right)
    JEE Main/MCQ/Medium/Electric Potential and Potential Energy/With diagram
  230. 230Two thin wires rings each having a radius RR are placed at a distance dd apart with their axes coinciding. The charges on the two rings are +q+q and −q-q. The potential difference between the centres of the two rings isJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  231. 231An α\alpha-particle of energy 5MeV5 \mathrm{MeV} is scattered through 180∘180^{\circ} by a fixed uranium nucleus. The distance of the closest approach is of the order ofJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  232. 232A charged particle qq is shot towards another charged particle QQ which is fixed, with a speed vv it approaches QQ upto a closest distance rr and then returns. If qq were given a speed 2v2 v, the closest distances of approach would beJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  233. 233A thin spherical conducting shell of radius R\mathrm{R} has a charge q\mathrm{q}. Another charge Q\mathrm{Q} is placed at the centre of the shell. The electrostatic potential at a point P\mathrm{P} a distance R2\frac{\mathrm{R}}{2} from the centre of the shell isJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  234. 234On moving a charge of 20 coulombs by 2 cm,2 J2 \mathrm{~cm}, 2 \mathrm{~J} of work is done, then the potential difference between the points isJEE Main/MCQ/Medium/Electric Potential and Potential Energy
  235. 235A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field E⃗1=E0x^\vec{E}_1=E_0\hat{x}. If another electric field E⃗2=2E0(y^+z^)\vec{E}_2=2E_0(\hat{y}+\hat{z}) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?JEE Main/MCQ/Medium/Electric Dipole
  236. 236Two short electric dipoles AA and BB having dipole moment p1p_1 and p2p_2 respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point xx is making an angle of 60°60° with the line joining points OO and xx. The ratio of the dipole moments p2/p1p_2/p_1 is _______.
    JEE Main/MCQ/Medium/Electric Dipole/With diagram
  237. 237Three charges +2q,+3q+2 q,+3 q and −4q-4 q are situated at (0,−3a),(2a,0)(0,-3 a),(2 a, 0) and (−2a,0)(-2 a, 0) respectively in the xyx y plane. The resultant dipole moment about origin is ____\_\_\_\_.JEE Main/MCQ/Medium/Electric Dipole
  238. 238Two shorts dipoles (A,B),A(A, B), A having charges ±2μC\pm 2 \mu \mathrm{C} and length 1 cm and BB having charges ±4μC\pm 4 \mu \mathrm{C} and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point PP, equi-distant from the centres of both dipoles is ____\_\_\_\_ N/C.
    JEE Main/MCQ/Medium/Electric Dipole/With diagram
  239. 239A dipole with two electric charges of 2μC2 \mu \mathrm{C} magnitude each, with separation distance 0.5μ m0.5 \mu \mathrm{~m}, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30∘30^{\circ} from the axis, it tends to realign in the direction due to a torque. The value of torque is :JEE Main/MCQ/Medium/Electric Dipole
  240. 240Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.
    Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.
    In the light of the above statements, choose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Electric Dipole
  241. 241An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density σo\sigma_{\mathrm{o}}. Choose the correct option from the following.
    JEE Main/MCQ/Medium/Electric Dipole/With diagram
  242. 242An electric dipole of mass m, charge q, and length \(l\) is placed in a uniform electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:JEE Main/MCQ/Medium/Electric Dipole
  243. 243An electric dipole of dipole moment 6×10−6Cm6 \times 10^{-6} \mathrm{Cm} is placed in uniform electric field of magnitude 106 V/m10^6 \mathrm{~V} / \mathrm{m}. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.JEE Main/Numerical/Medium/Electric Dipole
  244. 244Two point charges −4μc-4 \mu c and 4μc4 \mu c, constituting an electric dipole, are placed at (−9,0,0)cm(-9,0,0) \mathrm{cm} and (9,0,0)cm(9,0,0) \mathrm{cm} in a uniform electric field of strength 104NC−110^4 \mathrm{NC}^{-1}. The work done on the dipole in rotating it from the equilibrium through 180∘180^{\circ} is :JEE Main/MCQ/Medium/Electric Dipole
  245. 245A point particle of charge QQ is located at PP along the axis of an electric dipole 1 at a distance rr as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r . The dipoles are made of opposite charge q separated by a distance 2a2 a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?
    JEE Main/MCQ/Medium/Electric Dipole/With diagram
  246. 246For a short dipole placed at origin OO, the dipole moment PP is along xx-axis, as shown in the figure. If the electric potential and electric field at A are V0\mathrm{V}_0 and E0\mathrm{E}_0, respectively, then the correct combination of the electric potential and electric field, respectively, at point BB on the yy-axis is given by

    JEE Main/MCQ/Medium/Electric Dipole/With diagram
  247. 247The electric field at point p\mathrm{p} due to an electric dipole is E\mathrm{E}. The electric field at point R\mathrm{R} on equitorial line will be Ex\frac{\mathrm{E}}{x}. The value of xx :
    JEE Main/Numerical/Medium/Electric Dipole/With diagram
  248. 248Two charges of −4μC-4\mu C and +4μC+4\mu C are placed at the points A(1,0,4)mA(1,0,4)m and B(2,−1,5)mB(2,-1,5)m located in an electric field E⃗=0.20i^Vcm−1\vec{E}=0.20\hat{i}V{cm}^{-1}. The magnitude of the torque acting on the dipole is 8α×10−5Nm8\sqrt{\alpha }\times {10}^{-5}Nm, where α=\alpha =_________.JEE Main/Numerical/Medium/Electric Dipole
  249. 249The electric field due to a short electric dipole at a large distance (r)\left(r\right) from center of dipole on the equatorial plane varies with distance as :JEE Main/MCQ/Medium/Electric Dipole
  250. 250Two charges of each magnitude 0.01C0.01C and separated by a distance of 0.4mm0.4mm constitute an electric dipole. If the dipole is placed in an uniform electric field E⃗\vec{E} of 10dyne⋅C−110dyne\cdot {C}^{-1} making 30∘{30}^{^{\circ}} angle with E⃗,\vec{E}, the magnitude of torque acting on dipole is:JEE Main/MCQ/Medium/Electric Dipole
  251. 251Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
    Assertion A : If an electric dipole of dipole moment     30×10–5Cm30\times {10}^{–5}Cm is enclosed by a closed surface, the net flux coming out of the surface will be zero.
    Reason R : Electric dipole consists of two equal and opposite charges.
    In the light of above, statements, choose the correct answer from the options given below.    JEE Main/MCQ/Medium/Electric Dipole
  252. 252An electric dipole of dipole moment is 6.0×10−6Cm6.0\times {10}^{-6}Cm placed in a uniform electric field of 1.5×103NC−11.5\times {10}^{3}N{C}^{-1} in such a way that dipole moment is along electric field. The work done in rotating dipole by 180∘180^{\circ}in this field will be_______mJmJ.JEE Main/Numerical/Medium/Electric Dipole
  253. 253A dipole comprises of two charged particles of identical magnitude qq and opposite in nature. The mass mm of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance ll . If the dipole is placed in a uniform electric field E⃗\vec{E}; in such a way that dipole axis makes a very small angle with the electric field, E⃗\vec{E}. The angular frequency of the oscillations of the dipole when released is given by:JEE Main/MCQ/Medium/Electric Dipole
  254. 254Two electric dipoles of dipole moments 1.2×10−30cm1.2\times {10}^{-30}cm and 2.4×10−30cm2.4\times {10}^{-30}cm are placed in two difference uniform electric fields of strengths 5×104NC−15\times {10}^{4}N{C}^{-1} and 15×104NC−115\times {10}^{4}N{C}^{-1} respectively. The ratio of maximum torque experienced by the electric dipoles will be 1x\dfrac{1}{x}. The value of xx is _____ .JEE Main/Numerical/Medium/Electric Dipole
  255. 255Two ideal electric dipoles AA and BB, having their dipole moment p1{p}_{1} and p2{p}_{2} respectively are placed on a plane with their centres at OO as shown in the figure. At point CC on the axis of dipole AA, the resultant electric field is making an angle of 37∘37^{\circ} with the axis. The ratio of the dipole moment of AA and B,p1p2B,\dfrac{{p}_{1}}{{p}_{2}} is:(:( take sin⁡37∘=35)\left.\sin 37^{\circ}=\dfrac{3}{5}\right)
    JEE Main/MCQ/Medium/Electric Dipole/With diagram
  256. 256An electric dipole is placed on x−x-axis in proximity to a line charge of linear charge density 3.0×10−6Cm−1.3.0\times {10}^{-6}C{m}^{-1}. Line charge is placed on z−z-axis and positive and negative charge of dipole is at a distance of 10mm10mm and 12mm12mm from the origin respectively. If total force of 4N4N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.JEE Main/MCQ/Medium/Electric Dipole
  257. 257Two identical electric point dipoles have dipole have dipole moments p⃗1=pi^{\vec{p}}_{1}=p\hat{i} and p⃗2=−pi^{\vec{p}}_{2}=-p\hat{i} and are held on the xx-axis at distance 'aa' from each other. When released, they move along the xx-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'mm', their speed when they are infinitely far apart is :JEE Main/MCQ/Medium/Electric Dipole
  258. 258An electric dipole of moment p⃗=(−i^−3j^+2k^)×10−29C m\vec{\text{p}}=\left(-\hat{i}-3\hat{j}+2\hat{k}\right)\times {10}^{-29}\text{C m} at the origin (0,0,0)\left(0,0,0\right) . The electric field due to this dipole at r⃗=+i^+3j^+5k^\vec{\text{r}}=+\hat{i}+3\hat{j}+5\hat{k} (note that r⃗∙p⃗=0\vec{r}∙\vec{p}=0 ) is parallel to:JEE Main/MCQ/Medium/Electric Dipole
  259. 259A Point dipole p⃗=−p0x^\vec{p}=-{p}_{0}\hat{x} is kept at the origin. The potential and electric field due to this dipole on the y−axisy-axis at a distance dd are, respectively: (Taken V=0V=0 at infinity)JEE Main/MCQ/Medium/Electric Dipole
  260. 260An electric dipole is formed by two equal and opposite charges qq with separation dd . The charges have same mass m. It is kept in a uniform electric field E.E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ω\omega is:JEE Main/MCQ/Medium/Electric Dipole
  261. 261Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

    JEE Main/MCQ/Medium/Electric Dipole/With diagram
  262. 262An electric field of 1000 V/m1000 \mathrm{~V} / \mathrm{m} is applied to an electric dipole at angle of 45∘45^{\circ}. The value of electric dipole moment is 10−29C⋅m.10^{-29} \mathrm{C} \cdot \mathrm{m} . What is the potential energy of the electric dipole?JEE Main/MCQ/Medium/Electric Dipole
  263. 263Two electric dipoles, A,A, BB with respective dipole moments dA⃗=−4qai^\vec{{d}_{A}}=-4qa\hat{i} and dB⃗=−2qai^\vec{{d}_{B}}=-2qa\hat{i} are placed on the xx -axis with a separation R,R, as shown in the figure



    The distance from     AA at which both of them produce the same potential is:    JEE Main/MCQ/Medium/Electric Dipole/With diagram
  264. 264An electric dipole has fixed dipole moment p⃗\vec{p}, which makes angle θ\theta with respect to x−x-axis. When subjected to an electric field E⃗1=Ei^,{\vec{E}}_{1}=E\hat{i}, it experiences a torque T⃗1=τk^{\vec{T}}_{1}=\tau \hat{k}. When subjected to another electric field E⃗2=3E1j^{\vec{E}}_{2}=\sqrt{3}{E}_{1}\hat{j} it experiences a torque T⃗2=−T⃗1{\vec{T}}_{2}=-{\vec{T}}_{1} . The angle θ\theta is:JEE Main/MCQ/Medium/Electric Dipole
  265. 265Two point dipoles of dipole moment p⃗1\vec{p}_1 and p⃗2\vec{p}_2 are at a distance xx from each other and p⃗1∣∣p⃗2\vec{p}_1 || \vec{p}_2.
    The force between the dipoles is :    JEE Main/MCQ/Medium/Electric Dipole
  266. 266A electric dipole is placed at an angle of 30∘30^{\circ} to a non-uniform electric field. The dipole will experienceJEE Main/MCQ/Medium/Electric Dipole
  267. 267Two point charges 8 μC8 \, \mu C and −2 μC-2 \, \mu C are located at x=2x = 2 cm and x=4x = 4 cm, respectively on the xx-axis. The ratio of electric flux due to these charges through two spheres of radii 33 cm and 55 cm with their centers at the origin is _______.JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  268. 268Two point charges 2q2 q and qq are placed at vertex AA and centre of face CDEFC D E F of the cube as shown in figure. The electric flux passing through the cube is :
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  269. 269An infinitely long wire has uniform linear charge density λ=2nC/m\lambda=2 \mathrm{nC} / \mathrm{m}. The net flux through a Gaussian cube of side length 3 cm\sqrt{3} \mathrm{~cm}, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be xNm2C−1\mathrm{xNm}^2 \mathrm{C}^{-1}, where x is :
    [Neglect any edge effects and use     14πε0=9×109\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 SI units]    JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  270. 270The electric field in a region is given by E→=(2i^+4j^+6k^)×103 N/C\overrightarrow{\mathrm{E}}=(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) \times 10^3 \mathrm{~N} / \mathrm{C}. The flux of the field through a rectangular surface parallel to x−zx-z plane is 6.0Nm2C−16.0 \mathrm{Nm}^2 \mathrm{C}^{-1}. The area of the surface is ________ cm2\mathrm{cm}^2.JEE Main/Numerical/Medium/Electric Flux and Gauss Law
  271. 271A point charge causes an electric flux of −2×104Nm2C−1-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1} to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :
    (Given     ϵ0=8.85×10−12C2 N−1 m−2\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2} )    JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  272. 272A square loop of sides a=1 ma=1 \mathrm{~m} is held normally in front of a point charge q=1C\mathrm{q}=1 \mathrm{C}. The flux of the electric field through the shaded region is 5p×1ε0Nm2C\frac{5}{\mathrm{p}} \times \frac{1}{\varepsilon_0} \frac{\mathrm{Nm}^2}{\mathrm{C}}, where the value of p is _____.
    JEE Main/Numerical/Medium/Electric Flux and Gauss Law/With diagram
  273. 273A line charge of length  ’ a ’ 2\frac{\text { ' } a \text { ' }}{2} is kept at the center of an edge BCB C of a cube ABCDEFGHA B C D E F G H having edge length ' aa ' as shown in the figure. If the density of line charge is λ\lambda C per unit length, then the total electric flux through all the faces of the cube will be _______. (Take, ϵ0\epsilon_0 as the free space permittivity)

    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  274. 274An electric field E⃗=(2xi^)NC−1\vec{E}=(2 x \hat{i}) N C^{-1} exists in space. A cube of side 2 m2 \mathrm{~m} is placed in the space as per figure given below. The electric flux through the cube is ______ Nm2/C\mathrm{Nm}^2 / \mathrm{C}.
    JEE Main/Numerical/Medium/Electric Flux and Gauss Law/With diagram
  275. 275Five charges +q,+5q,−2q,+3q+q,+5 q,-2 q,+3 q and −4q-4 q are situated as shown in the figure. The electric flux due to this configuration through the surface SS is :
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  276. 276An electric field, E→=2i^+6j^+8k^6\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}} passes through the surface of 4 m24 \mathrm{~m}^2 area having unit vector n^=(2i^+j^+k^6)\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right). The electric flux for that surface is ______ Vm\mathrm{Vm}.JEE Main/Numerical/Medium/Electric Flux and Gauss Law
  277. 277Ques:
    σ\sigma is the uniform surface charge density of a thin spherical shell of radius RR. The electric field at any point on the surface of the spherical shell is :    JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  278. 278A charge qq is placed at the center of one of the surface of a cube. The flux linked with the cube is:JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  279. 279C1{C}_{1} and C2{C}_{2} are two hollow concentric cubes enclosing charges 2Q2Q and 3Q3Q respectively as shown in figure. The ratio of electric flux passing through C1{C}_{1} and C2{C}_{2} is:JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  280. 280An electric field is given by (6i^+5j^+3k^)NC−1(6\hat{i}+5\hat{j}+3\hat{k})N{C}^{-1}. The electric flux through a surface area 30i^m230\hat{i}{m}^{2} lying in YZ-plane(in SI unit) is:JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  281. 281Match List I with List II

    Chose the correct answer from the options given below    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  282. 282Two charges of 5Q5Q and −2Q-2Q are situated at the points (3a,0)(3a,0) and (−5a,0)(-5a,0) respectively. The electric flux through a sphere of radius 4a4a having centre at origin is:JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  283. 283Let σ\sigma be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region EI,EII{E}_{I},{E}_{II} and EIII{E}_{III}
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  284. 284Expression for an electric field is given by E⃗=4000x2i^Vm−1\vec{E}=4000{x}^{2}\hat{i}V{m}^{-1}. The electric flux through the cube of side 20cm20cm when placed in electric field (as shown in the figure) is ______ VcmVcm.JEE Main/Numerical/Medium/Electric Flux and Gauss Law/With diagram
  285. 285As shown in figure, a cuboid lies in a region with electric field E=2x2i^−4yj^+6k^NC−1E=2{x}^{2}\hat{i}-4y\hat{j}+6\hat{k}N{C}^{-1}. The magnitude of charge within the cuboid is nϵ0Cn{\epsilon }_{0}C.
    The value of     nn is ______ (if dimension of cuboid is 1×2×3m31\times 2\times 3{m}^{3})
    JEE Main/Numerical/Medium/Electric Flux and Gauss Law/With diagram
  286. 286In a cuboid of dimension 2L×2L×L2L\times 2L\times L , a charge qq is placed at the centre of the surface SS having area of 4L24{L}^{2} . The flux through the opposite surface to SS is given byJEE Main/MCQ/Medium/Electric Flux and Gauss Law
  287. 287A long cylindrical volume contains a uniformly distributed charge of density ρCm−3\rho C{m}^{-3}. The electric field inside the cylindrical volume at a distance x=2ϵ0ρmx=\dfrac{2{\epsilon }_{0}}{\rho }m from its axis is _____ Vm−1V{m}^{-1}.
    JEE Main/Numerical/Medium/Electric Flux and Gauss Law/With diagram
  288. 288The volume charge density of a sphere of radius 6m6m is 2μCcm−32\mu C{cm}^{-3}. The number of lines of force per unit surface area coming out from the surface of the sphere is _____ ×1010NC−1.\times {10}^{10}N{C}^{-1}.
    [Given : Permittivity of vacuum     ϵ0=8.85×10−12C2N−1−m−2{ϵ}_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}-{m}^{-2}]    JEE Main/Numerical/Medium/Electric Flux and Gauss Law
  289. 289If a charge qq is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  290. 290A cube is placed inside an electric field, E⃗=150y2j^\vec{E}=150{y}^{2}\hat{j} The side of the cube is 0.5m0.5m and is placed in the field as shown in the given figure. The charge inside the cube is:
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  291. 291A solid metal sphere of radius RR having charge qq is enclosed inside the concentric spherical shell of inner radius aa and outer radius bb as shown in the figure. The approximate variation electric field E⃗\vec{E}, as a function of distance rr, from centre OO, is given by:
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  292. 292The total charge enclosed in an incremental volume of 2×10−9m32\times {10}^{-9}{m}^{3} located at the origin is nC,nC, if electric flux density of its field is found asD=e−xsin⁡yi^−e−xcosyj^+2zk^Cm−2D={e}^{-x}\sin y\hat{i}-{e}^{-x}cosy\hat{j}+2z\hat{k}C{m}^{-2}JEE Main/Numerical/Medium/Electric Flux and Gauss Law
  293. 293The electric field in a region is given by E⃗=25E0i^+35E0j^\vec{E}=\dfrac{2}{5}{E}_{0}\hat{i}+\dfrac{3}{5}{E}_{0}\hat{j} with E0=4.0×103NC−1.{E}_{0}=4.0\times {10}^{3}N{C}^{-1}. The flux of this field through a rectangular surface, area 0.4m20.4{m}^{2} parallel to the Y−ZY-Z plane is _______ Nm2C−1N{m}^{2}{C}^{-1}.JEE Main/Numerical/Medium/Electric Flux and Gauss Law
  294. 294The electric field intensity is produced by the radiation coming from a 100W100W bulb at a distance of 3m3m is EE. The electric field intensity produced by the radiation coming from 60W60W at the same distance is x5E\sqrt{\dfrac{x}{5}}E. Where the value of x=x=_________ .JEE Main/Numerical/Medium/Electric Flux and Gauss Law
  295. 295Find out the surface charge density at the intersection of point x=3mx=3m plane and xx-axis, in the region of uniform line charge of 8nCm−18nC{m}^{-1} lying along the zz-axis in free space.JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  296. 296A charge qq is placed at one corner of a cube as shown in figure. The flux of electrostatic field E⃗\vec{E} through the shaded area is:
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  297. 297The electric field in a region is given by E⃗=(35E0i^+45E0j^)NC−1\vec{E}=\left(\dfrac{3}{5}{E}_{0}\hat{i}+\dfrac{4}{5}{E}_{0}\hat{j}\right)N{C}^{-1}. The ratio of flux of reported field through the rectangular surface of area 0.2m20.2{m}^{2} (parallel to y−zy-z plane) to that of the surface of area 0.3m20.3{m}^{2} (parallel to x−zx-z plane) is a:b=a:2,a:b=a:2, where a=?a=? [Here i^,j^\hat{i},\hat{j} and k^\hat{k} are unit vectors along x,yx,y and zz -axes respectively]JEE Main/Numerical/Medium/Electric Flux and Gauss Law
  298. 298A point charge of +12μC+12\mu C is at a distance 6cm6cm vertically above the centre of a square of side 12cm12cm as shown in figure. The magnitude of the electric flux through the square will be _______ ×103Nm2C−1.\times {10}^{3}N{m}^{2}{C}^{-1}.
    JEE Main/Numerical/Medium/Electric Flux and Gauss Law/With diagram
  299. 299An electric field E⃗=4xi^−(y2+1)j^N/C\vec{E}=4x\hat{i}-\left({y}^{2}+1\right)\hat{j}N/C passes through the box shown in figure. The flux of the electric field through surfaces ABCDABCD and BCGFBCGF are marked as ϕI{\phi }_{\text{I}} and ϕII{\phi }_{\text{II}} respectively. The difference between (ϕI−ϕII)\left({\phi }_{I}-{\phi }_{II}\right) is (in Nm2/CN{m}^{2}/C ) ____________.

    JEE Main/Numerical/Medium/Electric Flux and Gauss Law/With diagram
  300. 300In finding the electric field using Gauss law the formula ∣E⃗∣=qencϵ0∣A∣\left|\vec{E}\right|=\dfrac{{q}_{enc}}{{\epsilon }_{0}\left|A\right|} is applicable. In the formula ϵ0{\epsilon }_{0} is permittivity of free space, AA is the area of Gaussian surface and qenc{q}_{enc} is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  301. 301Let a total charge 2Q2Q be distributed in a sphere of radius R,R, with the charge density given by ρ(r)=kr,\rho (r)=kr, where rr is the distance from the centre. Two charges AA and BB , of −Q-Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If AA and BB do not experience any force, then:JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  302. 302Shown in the figure is a shell made of a conductor. It has inner radius aa and outer radius bb, and carries charge QQ . At its centre a dipole p⃗\vec{p} is placed as shown then:
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  303. 303A charge QQ is placed at a distance a2\dfrac{a}{2} above the centre of a square surface of side length aa. The electric flux through the square surface due to the charge would be?
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  304. 304A charge QQ is placed at a distance a/2\mathrm{a} / 2 above the centre of the square surface of edge a as shown in the figure. The electric flux through the square surface is:
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  305. 305Four closed surfaces and corresponding charge distributions are shown below.



    Let the respective electric fluxes through the surfaces be     ϕ1,ϕ2,ϕ3{\phi }_{1},{\phi }_{2},{\phi }_{3} and ϕ4{\phi }_{4}. Then:    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  306. 306The electric field in a region of space is given by, E⃗=E0i^+2E0j^\vec{E}={E}_{0}\hat{i}+2{E}_{0}\hat{j} where E0=100NC−1{E}_{0}=100N{C}^{-1}. The flux of this field through a circular surface of radius 0.02m0.02m parallel to the Y‐ZY‐Z plane is nearlyJEE Main/MCQ/Medium/Electric Flux and Gauss Law
  307. 307A cone of base radius RR and height hh is located in a uniform electric field E→\overrightarrow{\mathrm{E}} parallel to its base. The electric flux entering the cone is:JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  308. 308The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about 150N/C150N/C, directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be : [Given : ∈O=8.85×10−12C2/N-m2,RE=6.37×106m{\in }_{\text{O}}=\text{8.85}\times 1{0}^{-12}{\text{C}}^{2}/{\text{N-m}}^{2}\text{,}{\text{R}}_{\text{E}}=\text{6.37}\times 1{0}^{6}\text{m}]JEE Main/MCQ/Medium/Electric Flux and Gauss Law
  309. 309The flat base of a hemisphere of radius a with no charge inside it lies in a horizontal plane. A uniform electric field E⃗\vec{E} is applied at an angle π4\frac{\pi}{4} with the vertical direction. The electric flux through the curved surface of the hemisphere is
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram
  310. 310If the electric flux entering and leaving an enclosed surface respectively is ϕ1\phi_1 and ϕ2\phi_2, the electric charge inside the surface will beJEE Main/MCQ/Medium/Electric Flux and Gauss Law
  311. 311A charged particle qq is placed at the centre OO of cube of length LL (A B C D E F G H). Another same charge qq is placed at a distance LL from OO. Then the electric flux through ABCDA B C D is
    JEE Main/MCQ/Medium/Electric Flux and Gauss Law/With diagram

NEET question paper PDF

This chapter includes NEET questions. Open a year to read the full paper, or download the PDF.

NEET 2025 question paper (Code 45)

Open Download PDF

Opening paper…

JEE Main question paper PDF

This chapter includes JEE Main questions. Open a shift to read the paper, or download the PDF.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Other Physics chapters

Current Electricity 380Kinematics 308Ray Optics 295Rotational Motion 280Magnetic Effects & Magnetism 276Atoms & Nuclei 239Gravitation 223Laws of Motion 210Semiconductors 209Dual Nature of Matter 200Oscillations 194Fluid Mechanics 192Wave Optics 191Alternating Current 190Thermodynamics 190Work Energy Power 183Capacitors 180Kinetic Theory 168Electromagnetic Waves 165Electromagnetic Induction 153Units & Dimensions 149Waves 142Center of Mass, Momentum & Collision 130Thermal Properties of Matter 126Mathematics in Physics 121Mechanical Properties of Solids 118Experimental Physics 70Magnetic Properties of Matter 57Modern Physics 5

Stuck on a Electrostatics question from your book?

Snap it and get a whiteboard video that solves it step by step. Your first video needs no login.

Scan a doubtView plans