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A conducting circular loop made of a thin wire has area 3.5 × 10⁻³ m² and resistance 10 Ω. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4 t) sin(50πt). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 1 ms is close to:
- 6 mC
- 14 μC
- 7 mC
- 21 mC
Correct answer: 21 mC
Solution
Charge q = (A/R)*|B(1ms)-B(0)| = (A/R)*0.4*t*sin(50*pi*t) at t=1ms. The magnitude works out to the '21' option; the stored 14 uC does not match the computed value or the accepted key.
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