A conducting loop of radius 10/[ ]^ 1/2 cm is placed perpendicular to a uniform magnetic field 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is

Step-by-step solution

Given radius of the loop, r = 10 cm = 0.1 m Area of the loop, A = r^2 = ( 0.1 )^2 = 0.01 m ^2 Initial magnetic field, B_i = 0.5 T Final magnetic field, B_f = 0 T Time interval, t = 0.5 s Since the magnetic field decreases at a steady rate, the rate of change of magnetic field is constant. dB dt = B_f - B_i t = 0 - 0.5 0.5 = -1 T/s According to Faraday's law of induction, the induced emf is given by: e = - d dt = -A dB dt e = -0.01 (-1) = 0.01 V = 10 mV Since the rate of change of magnetic field is constant, the ind