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JEE Main 2023 (25 Jan, Shift 2) · Displacement Current, Maxwell's Equations & Production

Displacement Current, Maxwell's Equations & Production question from JEE Main 2023 (25 Jan, Shift 2)

Q9JEE Main 2023 · 25 JAN · SHIFT 2Easy

Displacement Current, Maxwell's Equations & Production

Match List I with List II

Choose the correct answer from the options given below:

List IList II
A.Gauss's Law in ElectrostaticsI.∮E⃗⋅dl⃗=−dϕBdt\oint \vec{E} \cdot \vec{dl} = -\frac{d\phi_B}{dt}
B.Faraday's LawII.∮B⃗⋅dA→=0\oint \vec{B} \cdot \overrightarrow{dA} = 0
C.Gauss's Law in MagnetismIII.∮B⃗⋅dl⃗=μ0ic+μ0ϵ0dϕEdt\oint \vec{B} \cdot \vec{dl} = \mu_0 i_c + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}
D.Ampere-Maxwell LawIV.∮E⃗⋅ds⃗=qϵ0\oint \vec{E} \cdot \vec{ds} = \frac{q}{\epsilon_0}
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Answer: (c)

  1. Gauss's law in electrostatics: ∮E⃗⋅ds⃗=q/ϵ0\oint \vec{E}\cdot\vec{ds} = q/\epsilon_0, so A-IV.
  2. Faraday's law: ∮E⃗⋅dl⃗=−dϕB/dt\oint \vec{E}\cdot\vec{dl} = -d\phi_B/dt, so B-I.
  3. Gauss's law in magnetism: ∮B⃗⋅dA⃗=0\oint \vec{B}\cdot\vec{dA} = 0, so C-II.
  4. Ampere-Maxwell law: ∮B⃗⋅dl⃗=μ0ic+μ0ϵ0dϕE/dt\oint \vec{B}\cdot\vec{dl} = \mu_0 i_c + \mu_0\epsilon_0 d\phi_E/dt, so D-III.
  5. So the answer is (c).
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