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Electrostatics: concepts, formulas & solved PYQ-style examples

Electrostatics carries heavy weight in both JEE and NEET and connects straight into capacitors and current electricity. The questions look different every year but test a small set of ideas: superposition, potential energy, Gauss’s law and charge sharing between capacitors.

Work with vectors for fields and scalars for potential — mixing the two is the most common source of wrong answers.

Also for AP Physics 2Also for AP Physics C: E&MAlso for A-level Physics
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Key concepts

Coulomb’s law and superposition

Net force or field is the vector sum of each charge’s contribution.

Electric potential

A scalar — add algebraically with signs; field is the negative gradient of potential.

Gauss’s law

Flux through a closed surface depends only on enclosed charge; use symmetry for spheres, lines and sheets.

Capacitors

Series and parallel combinations, dielectrics, energy stored and energy lost on sharing charge.

Conductors

Field inside is zero; charge sits on the outer surface; the whole conductor is one equipotential.

Formula sheet

Coulomb’s law

F=14πε0q1q2r2F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r^2}

Field and potential of a point charge

E=kqr2,V=kqrE = \dfrac{kq}{r^2},\quad V = \dfrac{kq}{r}

Gauss’s law

∮E⃗⋅dA⃗=qencε0\oint \vec E\cdot d\vec A = \dfrac{q_{enc}}{\varepsilon_0}

Capacitance and energy

C=ε0Ad,U=12CV2=Q22CC = \dfrac{\varepsilon_0 A}{d},\quad U = \tfrac12 CV^2 = \dfrac{Q^2}{2C}

Common potential on sharing

V=C1V1+C2V2C1+C2V = \dfrac{C_1V_1 + C_2V_2}{C_1 + C_2}

What PYQs keep asking

Patterns that repeat across previous-year JEE and NEET papers for this chapter.

  • Finding the point on a line where the net field (or potential) of two charges is zero.
  • Energy lost when a charged capacitor is connected to an uncharged one.
  • Gauss’s law for spherical shells and infinite sheets — field inside vs outside.
  • Effect of inserting a dielectric slab with the battery connected vs disconnected.

Solved examples

Example 1

Charges +2 μC and −8 μC are 30 cm apart. Where on the line joining them is the electric field zero?

  1. 1Between unlike charges the fields add, so the zero point is outside — on the side of the smaller charge (+2 μC).
  2. 2Let it be xx from +2 μC: 2x2=8(x+0.3)2\dfrac{2}{x^2} = \dfrac{8}{(x+0.3)^2}.
  3. 3Taking square roots: x+0.3x=2⇒x=0.3\dfrac{x+0.3}{x} = 2 \Rightarrow x = 0.3 m.
Answer: 30 cm from the +2 μC charge, on the side away from the −8 μC charge
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Example 2

A 10 μF capacitor charged to 100 V is connected across an identical uncharged capacitor. Find the common voltage and the energy lost.

  1. 1Charge is conserved: V=10×100+10×010+10=50V = \dfrac{10 \times 100 + 10 \times 0}{10 + 10} = 50 V.
  2. 2Initial energy: 12(10×10−6)(100)2=0.05\tfrac12 (10\times10^{-6})(100)^2 = 0.05 J.
  3. 3Final energy: 12(20×10−6)(50)2=0.025\tfrac12 (20\times10^{-6})(50)^2 = 0.025 J, so 0.025 J is lost as heat and radiation.
Answer: 50 V; energy lost = 0.025 J (half the initial energy)
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Common traps

  • Adding field magnitudes without directions — always draw the field vectors first.
  • Looking for the zero-field point between unlike charges, where it can never be.
  • Assuming charge stays the same after inserting a dielectric while the battery is still connected (then V stays fixed).

Practise with

Current ElectricityModern PhysicsRotational MotionElectric field lines simulationCapacitors, dielectrics and RC circuits simulation311 Electrostatics practice questionsVideo solutions

FAQ

Why is energy lost when two capacitors share charge?

Charge flows through the connecting wires until the voltages are equal; the lost energy appears as heat and electromagnetic radiation, independent of wire resistance.

Where is the electric field zero for two charges?

For like charges, between them (closer to the smaller one). For unlike charges, outside the pair, on the side of the smaller charge.

Is Gauss’s law asked in NEET?

Yes, mainly as direct applications: field of a charged sphere, shell, wire or sheet and the flux through a closed surface.

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