Question

A rectangular loop of sides $a$ and $b$ is placed in $x-y$ plane. A uniform but time varying magnetic field of strength $\overrightarrow{B}=20t\hat{i}+10t^2\hat{j}+50\hat{k}$ is present in the region. The magnitude of induced emf in the loop at time $t$ is :

• A. $20+20t$
• B. $20$
• C. $20t$
• D. zero

Answer 1

Answer: (D)

zero

$\overrightarrow{S}=\left(ab\right)\hat{k}$ $\to$ perpendicular to x-y plane
$\varphi =\overrightarrow{B}\cdot \overrightarrow{S}=\left(50\right)\left(ab\right)=$ constant
$\frac{d\varphi }{dt}=0$
$\therefore e=0$