Question

A conducting circular loop of resistance $20\Omega$ and cross-sectional area $20\times {10}^{-2}{m}^2$ is placed perpendicular to a spatially uniform magnetic field B, which varies with time t as $B=2\sin \left(50\pi t\right)T$. Find the net charge flowing through the loop in $20ms$ starting from $t=0$.

• A. 0.5 $C$
• B. 0.2 $C$
• C. $0$ $C$
• D. 0.14 $C$

Answer 1

The correct option is C $0$ $C$

$\varphi =B.A$
$\epsilon =\frac{d\varphi }{dt}=A\frac{dB}{dt}=A\times 100\pi \cos \left(50\pi t\right)\Rightarrow I=\frac{dq}{dt}=\frac{\epsilon }{R}\Rightarrow dq=\frac{\epsilon }{R}dt=\frac{A}{R}\left[100\pi cos50\pi t\right]dt\Rightarrow q={\int }_0^{20\times {10}^{-3}}\frac{A}{R}\times 100\pi cos\left(50\pi t\right)dt\Rightarrow q=0C$