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A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is

  1. 4.8π μV
  2. 0.8π μV
  3. 1.6π μV
  4. 3.2π μV

Correct answer: 1.6π μV

Solution

The induced emf is calculated using Faraday's law of electromagnetic induction: emf = |dΦ/dt|, where Φ = B × A. Here, A = πr², and dA/dt = 2πr(dr/dt). Substituting B = 0.04 T, r = 0.02 m, and dr/dt = -0.002 m/s, we get emf = |0.04 × 2π × 0.02 × (-0.002)| = 1.6π μV.

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