A conducting circular loop of area 3.5×10⁻³ m² and resistance 10 Ω is placed perpendicular to a spatially uniform magnetic field B(t)=0.4 sin(50πt) T. Find the net charge flowing through the loop from t=0 to t=10 ms.
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Question

A conducting circular loop of area 3.5×10⁻³ m² and resistance 10 Ω is placed perpendicular to a spatially uniform magnetic field B(t)=0.4 sin(50πt) T. Find the net charge flowing through the loop from t=0 to t=10 ms.

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G1 Physics · Accepted Answer

Faraday's law gives ε=−dΦ/dt and i=ε/R. Therefore q=∫i dt=−ΔΦ/R. Here A=3.5×10⁻³ m², B(0)=0 and B(10 ms)=0.4 T. Thus |q|=AΔB/R=(3.5×10⁻³×0.4)/10=1.4×10⁻⁴ C=0.14 mC. The printed source key appears inconsistent with the printed numerical data.