Electromagnetic Waves

JEE Main level, single correct, medium

14 of 165

Question 14 of 165

Match List - I with List - II.
List - IList - IIRelationLawA. ∮E⃗⋅dl→=−ddt∮B⃗⋅da→I. Ampere’s circuital lawB. ∮B⃗⋅dl→=μ0(I+ϵ0dϕEdt)II. Faraday’s laws ofelectromagnetic inductionC. ∮E⃗⋅da→=1ϵ0∫VρdvIII. Ampere - Maxwell lawD. ∮B⃗⋅dl→=μ0IIV. Gauss’s law of electrostatics\begin{array}{l} \text{List - I} & \text{List - II} \\ \text{Relation} & \text{Law} \\ \text{A. } \oint \vec{E} \cdot \overrightarrow{d l}=-\frac{d}{d t} \oint \vec{B} \cdot \overrightarrow{d a} & \text{I. Ampere's circuital law} \\ \text{B. } \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0}\left(I+\epsilon_{0} \frac{d \phi_{E}}{d t}\right) & \text{II. Faraday's laws of} \\ & \text{electromagnetic induction} \\ \text{C. } \oint \vec{E} \cdot \overrightarrow{d a}=\frac{1}{\epsilon_{0}} \int_{\mathrm{V}} \rho \mathrm{dv} & \text{III. Ampere - Maxwell law} \\ \text{D. } \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} I & \text{IV. Gauss's law of electrostatics} \end{array}
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Answer: (B) A-II, B-III, C-IV, D-I

Theoretical
A-II, B-III, C-IV, D-I

A. ∮E⃗⋅dl⃗=−ddt∮B⃗⋅da⃗\oint \vec{E} \cdot d\vec{l} = -\frac{d}{dt} \oint \vec{B} \cdot d\vec{a} → Faraday's law of electromagnetic induction (II)
B. ∮B⃗⋅dl⃗=μ0(I+ϵ0dΦEdt)\oint \vec{B} \cdot d\vec{l} = \mu_0 \left(I + \epsilon_0 \frac{d\Phi_E}{dt}\right) → Ampere-Maxwell law (III)
C. ∮E⃗⋅da⃗=1ϵ0∫ρ dv\oint \vec{E} \cdot d\vec{a} = \frac{1}{\epsilon_0} \int \rho \, dv → Gauss's law of electrostatics (IV)
D. ∮B⃗⋅dl⃗=μ0I\oint \vec{B} \cdot d\vec{l} = \mu_0 I → Ampere's circuital law (I)

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