A circular ring of radius r is placed in a homogenous magnetic field perpendicular to the plane of the ring. The field B changes with time according to the equation B = kt, where k is a constant and t is the time. The electric field in the ring is

$\frac{kr}{2}$

$\oint \vec{E}.\vec{dl}=-\frac{d\phi B}{dt}$

$ or \, E× 2 \pi r=\frac{d}{dt} (Kt × \pi r^2) = K \pi r^2 $

$ or \, E = \frac{Kr}{2}$