Question

In a cylindrical structure, magnetic field $B$ is changing as $B=B_0+\alpha t$. The value of emf induced in the loop shown in the figure is (Given Line $AOB$ is circular and $\alpha ,B_0$ are constant values).

• A. $\frac{\pi a^2\alpha }{2}$
• B. $\pi a^2\alpha$
• C. $a^2\alpha$
• D. None of these

Answer 1

The correct option is A

$\frac{\pi a^2\alpha }{2}$

We know that ,

Induced emf is rate of change of flux $e=-\frac{d\varphi }{dt}$
$=-\frac{d(B.A)}{dt}=-A\frac{dB}{dt}$

$|e|=\frac{\pi a^2\alpha }{2}$