A square loop ACDE of area 20 $c{m}^2$ and resistance 5 $\Omega$ is rotated in a magnetic field $B=2T$ through 180$°$ in 0.01 $s$ .

Find the magnitude of average values of $e$, $i$ and $△q.$

Let us take the area vector $S$ perpendicular to plane of loop inwards. So initially, $S\uparrow \uparrow B$ and when it is rotated by $180°$, $S\uparrow \downarrow B$. Hence, initial flux passing through the loop,

${\varphi }_i=BS\cos \left(0°\right)=\left(2\right)(20\times {10}^{-4})\left(1\right)=4.0\times {10}^{-3}Wb$

Flux passing through the loop when it is rotated by $180°$

${\varphi }_f=BS\cos \left(180°\right)=\left(2\right)(20\times {10}^{-4})(-1)=-4.0\times {10}^{-3}$

Therefore, change in flux,

 $∆{\varphi }_B={\varphi }_f-{\varphi }_i=-8.0\times {10}^{-3}Wb$

Given, $∆t=0.01s$, $R=5\Omega$

$\left|e\right|=\left|-\frac{∆{\varphi }_B}{∆t}\right|=\frac{8.0\times {10}^{-3}}{0.01}=0.8V$

$i=\frac{\left|e\right|}{R}=\frac{0.8}{5}=0.16A$

and

$∆q=i∆t=0.16\times 0.01=1.6\times {10}^{-3}C$