A conducting loop of radius R is present in a uniform magnetic field B perpendicular the plane of the ring….

Q: A conducting loop of radius R is present in a uniform magnetic field B perpendicular the plane of the ring. If radius R varies as a function of time t , as R = R₀ + t . The e.m.f induced in the loop is

(A) 2 π (R₀ + t) B clockwise

(B) π(R₀ + t)B clockwise

(C) 2 π (R₀ + t)B anticlockwise

(D) zero

Solution : Magnetic flux $\displaystyle \phi = B A cos0^o $

$\displaystyle \phi = B \pi R^2 $

$\displaystyle \phi = B . \pi (R_0 + t)^2 $

$\displaystyle e = \frac{d\phi}{dt} $

$\displaystyle e = 2 B . \pi (R_0 + t) $