Question

A uniform but time-varying magnetic field $B\left(t\right)$ exists in a circular region of radius $a$ and is directed into the plane of the paper, as shown in the figure. The magnitude of the induced electric field at a point $P$ at a distance $r$ from the center of the circular region -

• A. is zero
• B. decreases as $1/r$
• C. increases as $r$
• D. decreases as $1/r^2$

Answer 1

The correct option is B decreases as $1/r$


From Faraday's Law of Electromagnetic Induction,

$\oint \overrightarrow{E}.d\overrightarrow{l}=-\frac{d{\varphi }_B}{dt}$

For $r\ge a$

$E\left(2\pi r\right)=\pi a^2\left|\frac{dB}{dt}\right|$

$\Rightarrow E=\frac{a^2}{2r}\left|\frac{dB}{dt}\right|$

$\Rightarrow E\propto \frac{1}{r}$

Hence, option $\left(B\right)$ is the correct answer.