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A thin conducting circular loop of area 3.5 * 10⁻³ m² and resistance 10 ohm is placed perpendicular to a uniform time-varying magnetic field B(t) = (0.4 T) sin(50*pi*t). Find the net charge that flows through the loop between t = 0 and t = 10 ms.
- 0.14 mC
- 0.21 mC
- 0.06 mC
- 0.07 mC
Correct answer: 0.14 mC
Solution
Charge is the change in flux divided by resistance. B goes from 0 (t=0) to 0.4 T (t=10 ms, since sin(pi/2)=1). delta(flux) = A*delta(B) = 3.5e-3 * 0.4 = 1.4e-3 Wb. q = 1.4e-3/10 = 1.4e-4 C = 0.14 mC.
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