Question

A square loop of side $22cm$ is converted into circular loop in 0.4 sec. A uniform magnetic field of $0.2T$ is directed normal to the loop then the emf induced in the loop is:

• A. $-6.6\times 10^{-3}V$
• B. $-6.6\times 10^{-5}V$
• C. $6.6\times 10^{-3}V$
• D. $6.6\times 10^{-5}V$

Answer 1

Answer: (A)

$e=-\frac{d\varphi }{dt}=-\frac{BdA}{dt}=-0.2\frac{(dA)}{0.4}$
$e=-\frac{dA}{2}$
$dA=\left[\pi r_1^2-r_2^2\right]$
For circle $r_1=\frac{44}{\pi }\times 10^{-2}m,$
For square $r_2=22\times 10^{-2}m$
$dA=\left[\pi {\left(\frac{44}{\pi }\right)}^2\times 10^{-4}-{\left(22\times 10^{-2}\right)}^2\right]$
$=484\times 10^{-4}\left[\frac{4}{\pi }-1\right]$
$=484\times 10^{-4}[1.27-1]$
$=130.68\times 10^{-4}$
$\therefore e=-\frac{dA}{2}=-\frac{130.68\times 10^{-4}}{2}$
$=-65.34\times 10^{-4}V.$