Question

A conducting circular loop made of a thin wire, has area $3.5\times {10}^{-3}{m}^2$ and resistance $10\Omega$. It is placed perpendicular to a time dependent magnetic field $B\left(t\right)=\left(0.4T\right)\sin \left(50\pi t\right)$. The field is uniform in space. Then the net charge flowing through the loop during $t=0s$ and $t=10ms$ is close to:

• A. $0.14mC$
• B. $0.21mC$
• C. $6mC$
• D. $7mC$

Answer 1

The correct option is A $0.14mC$

$Q=\frac{\Delta \varphi }{R}=\frac{1}{10}A(B_f-B_i)=\frac{1}{10}\times 3.5\times {10}^{-3}(0.4\sin \frac{\pi }{2}-0)$
$=\frac{1}{10}(3.5\times {10}^{-3})(0.4-0)$
$=1.4\times {10}^{-4}=0.14mC$