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A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mm s⁻¹. The induced e.m.f. when the radius is 2 cm is
- 2πμV
- πμV
- π/2 μV
- 2μV
Correct answer: πμV
Solution
The induced emf is given by Faraday's law: emf = -dΦ/dt, where Φ = B × A. Here, A = πr², so dΦ/dt = B × dA/dt. Since dA/dt = 2πr × dr/dt, substituting B = 0.025 T, r = 0.02 m, and dr/dt = -0.001 m/s, we get emf = πμV.
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