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A circular conducting loop of radius 1 m lies in the X-Y plane. A magnetic field B = (3t³ j-hat + 3t² k-hat) tesla (SI units) is present. The induced emf in the loop at t = 2 s equals n*pi volt. Determine n.

1. 12
2. 6
3. 24
4. 3

Correct answer: 12

Solution

The j-hat component is in the plane of the loop and produces no flux. Only the k-hat (z) component links the loop. Flux = B_z * (pi r²) = 3t² * pi * 1². The emf is the time derivative of this flux, evaluated at t = 2 s.

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