Question

A rectangular coil of $100$ turns and size $0.1m\times 0.05m$ is placed perpendicular to a magnetic field of $0.1T$. If the field drops to $0.05T$ in $0.05$ second, the magnitude of the e.m.f. induced in the coil is

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $\sqrt{0.5}$
• D. $\sqrt{6}$

Answer 1

Answer: (C)

Given, $n=100$ turns, $A=0.1\times 0.05m^2$
$B_1=0.1T,B_2=0.05T,dt=0.05s$
We know that,
$e=\left|\frac{-d\varphi }{dt}\right|=\frac{d}{dt}(nBA\cos \theta )=\frac{nAdB\cos \theta }{dt}$
Here,$\theta =0^{\circ }$
$\therefore e=\frac{nAdB}{dt}=\frac{100\times 0.1\times 0.05\times (0.1-0.05)}{0.05}$
$\Rightarrow e=0.5V$