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JEE Main 2023 (13 Apr, Shift 1) · Displacement Current, Maxwell's Equations & Production

Displacement Current, Maxwell's Equations & Production question from JEE Main 2023 (13 Apr, Shift 1)

Q8JEE Main 2023 · 13 APR · SHIFT 1Easy

Displacement Current, Maxwell's Equations & Production

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions:

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Answer: (c)

  1. In static conditions ϕB\phi_B is constant, so the circulation of E⃗\vec{E} is ∮E⃗⋅dl⃗=0\oint \vec{E}\cdot\vec{dl} = 0; (a) holds only for statics.
  2. (b) misses displacement current, so it also holds only for steady conditions; (d) is Gauss's law, valid always.
  3. Faraday's law ∮E⃗⋅dl⃗=−∂ϕB∂t\oint \vec{E}\cdot\vec{dl} = -\dfrac{\partial \phi_B}{\partial t} is the form that describes time-varying fields.
  4. So the answer is (c).
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