Question

A rectangular coil of $100$ turns and size $0.1 \,m \times 0.05\, m$ is placed perpendicular to a magnetic field of $0.1 \,T$. If the field drops to $0.05 \,T$ 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)

$\sqrt{0.5}$

Answer 2

Given, $n=100$ turns, $A=0.1 \times 0.05\, m ^{2}$
$B_{1}=0.1\, T , B_{2}=0.05\, T \,, dt =0.05\, s$
We know that,
$e=\left|\frac{-d \phi}{d t}\right|=\frac{d}{d t}(n B A \cos \theta)=\frac{n A d B \cos \theta}{d t}$
Here,$\theta=0^{\circ}$
$\therefore e=\frac{n A d B}{d t}=\frac{100 \times 0.1 \times 0.05 \times(0.1-0.05)}{0.05}$
$\Rightarrow e=0.5 V$