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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.
- 40
- 80
- 120
- 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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