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JEE Main 2024 (30 Jan, Shift 2) · Lenz's Law, Eddy Currents & Induced Electric Field

Lenz's Law, Eddy Currents & Induced Electric Field question from JEE Main 2024 (30 Jan, Shift 2)

Q12JEE Main 2024 · 30 JAN · SHIFT 2Easy

Lenz's Law, Eddy Currents & Induced Electric Field

Match List I with List II

Choose the correct answer from the options given below:

List IList II
(A)Gauss's law of magnetostatics(I)∮E⃗⋅da⃗=1ε0∫ρ dV\oint \vec{E} \cdot d\vec{a} = \frac{1}{\varepsilon_0}\int \rho\, dV
(B)Faraday's law of electromagnetic induction(II)∮B⃗⋅da⃗=0\oint \vec{B} \cdot d\vec{a} = 0
(C)Ampere's law(III)∫E⃗⋅dl⃗=−ddt∫B⃗⋅da⃗\int \vec{E} \cdot d\vec{l} = \frac{-d}{dt}\int \vec{B} \cdot d\vec{a}
(D)Gauss's law of electrostatics(IV)∮B⃗⋅dl⃗=μ0I\oint \vec{B} \cdot d\vec{l} = \mu_0 I
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Answer: (c)

  1. Gauss's law of magnetostatics: ∮B⃗⋅da⃗=0\oint \vec{B}\cdot d\vec{a} = 0 → A-II.
  2. Faraday's law: ∮E⃗⋅dl⃗=−ddt∫B⃗⋅da⃗\oint \vec{E}\cdot d\vec{l} = -\dfrac{d}{dt}\int \vec{B}\cdot d\vec{a} → B-III.
  3. Ampere's law: ∮B⃗⋅dl⃗=μ0I\oint \vec{B}\cdot d\vec{l} = \mu_0 I → C-IV; Gauss's law of electrostatics: ∮E⃗⋅da⃗=1ε0∫ρ dV\oint \vec{E}\cdot d\vec{a} = \dfrac{1}{\varepsilon_0}\int \rho\,dV → D-I.
  4. So the answer is (c) A-II, B-III, C-IV, D-I.
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