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Electromagnetic Induction · Class 12 · CBSE · Science Physics

A circular loop of radius r is placed in a uniform magnetic field B perpendicular to the plane of the loop. If the radius of the loop starts shrinkin…

Practice question from Electromagnetic Induction (Class 12 · CBSE · Science Physics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-B264BE

A circular loop of radius rr is placed in a uniform magnetic field BB perpendicular to the plane of the loop. If the radius of the loop starts shrinking at a constant rate dr/dt=vdr/dt = v, then the induced emf in the loop at that instant is:

  1. A.2\pi BrvCorrect answer
  2. B.\pi Brv
  3. C.Brv
  4. D.0

Solution

The magnetic flux Φ=B⋅A=B(πr2)\Phi = B \cdot A = B(\pi r^2). The induced emf is given by Faraday's law: e=−dΦdt=−Bπddt(r2)=−Bπ(2rdrdt)e = -\frac{d\Phi}{dt} = -B\pi \frac{d}{dt}(r^2) = -B\pi (2r \frac{dr}{dt}). Substituting drdt=v\frac{dr}{dt} = v, the magnitude of the induced emf is 2πBrv2\pi Brv.

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