A circular loop of radius 20 cm and resistance 2 is placed in a time varying magnetic field B = (2t^2 + 2t + 3) T . At t = 0 , for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at t = 3 s is 50 A . The value of is _______. (Take = 22/7 )

Step-by-step solution

The magnetic flux linked with the circular loop is given by = BA . Since the plane of the loop is perpendicular to the magnetic field, the angle between the area vector and the magnetic field is = 0^ . = B r^2 Given r = 20 cm = 0.2 m , the area of the loop is: A = (0.2)^2 = 0.04 m ^2 The induced emf in the loop is given by Faraday's law of induction: |E| = d dt = A dB dt Given the magnetic field B = 2t^2 + 2t + 3 , we differentiate it with respect to time t : dB dt = d dt (2t^2 + 2t + 3) = 4t + 2 At t = 3 s , the r