A conducting circular loop made of a thin wire, has area \(3.5\times10^{-3}\ \mathrm{m^2}\) and resistance \(10\ \Omega\). It is placed perpendicular to a time dependent magnetic field \(B(t)=(0.4\,\mathrm{T})\sin(50\pi t)\). The field is uniform in space. Then the net charge flowing through the loop during \(t=0\ \mathrm{s}\) and \(t=10\ \mathrm{ms}\) is close to :
Show Hint
- 0.14 mC
- 0.7 mC
- 0.21 mC
- 0.6 mC
The Correct Option is A
Solution and Explanation
\(B(0)=0\); \(B(10\ \mathrm{ms})=0.4\sin(50\pi\times0.01)=0.4\sin\frac\pi2=0.4\ \mathrm T\).
\(q=\frac{3.5\times10^{-3}\times0.4}{10}=1.4\times10^{-4}\ \mathrm C=0.14\ \mathrm{mC}\).
Answer: (1) 0.14 mC
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