A conducting ring of radius r is placed in a varying magnetic field perpendicular to the plane of the ring. If the rate at which the magnetic field varies is x, the electric field intensity at any point of the ring is ________.

Fill in the blank with the correct answer from the options given below.

$r x / 2$

The correct answer is Option (2) → $r x / 2$

The magnetic flux $(\phi)$ through the ring is,

$\phi=B×Area=B.(πr^3)$

Induced emf, $ε=\left|\frac{d\phi}{dt}\right|=πr^2\left|\frac{dB}{dt}\right|=πr^2x$

and,

$ε=\int E.dI=E×(2πr)$   $[E → Constant]$

$⇒E×(2πr)=πr^2x$

$⇒E=\frac{πr^2x}{2πr}=\frac{rx}{2}$