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A circular conducting loop of radius 1 m is placed in a uniform magnetic field B directed perpendicular to its plane. The loop has resistance 2 microohm. The field is gradually reduced according to B = (4/pi) * 10⁻³ (1 - t/100) T, where t is in seconds, until it reaches zero. Determine the total heat (in mJ) generated in the loop during the entire process of switching off the field.

1. 40
2. 80
3. 120
4. 160

Correct answer: 80

Solution

Because dB/dt is constant, the induced EMF and hence the power are constant throughout. The field reaches zero at t = 100 s, and the steady power multiplied by this time gives the total heat.

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