Question

A conducting circular loop made of a thin wire, has area $3.5\times {10}^{-1}{\text{m}}^2$ and resistance $10\Omega$. It is placed perpendicular to a time dependent magnetic field $B\left(t\right)=\left(0.4\text{T}\right)\sin \left(50\pi t\right)$. The net charge flowing through the loop during $t=0\text{s}$ and $t=10\text{ms}$ is close to:

• A. $7\text{mC}$
• B. $21\text{mC}$
• C. $14\text{mC}$
• D. $6\text{mC}$

Answer 1

The correct option is C $14\text{mC}$

$\text{Net charge flowing,}Q=\frac{\Delta \varphi }{R}$

$\Rightarrow Q=\frac{1}{10}A(B_f-B_i)$

$\Rightarrow Q=\frac{1}{10}\times 3.5\times {10}^{-1}(0.4\sin \frac{\pi }{2}-0)$

$\Rightarrow Q=\frac{1}{10}(3.5\times {10}^{-1})(0.4-0)$

$\Rightarrow Q=1.4\times {10}^{-2}=14\text{mC}$

Hence, option $\left(A\right)$ is correct.