A conducting loop of area 500 cm ^2 is placed perpendicular to a magnetic field. The magnetic field B varies with time t : it increases linearly from 0 to 0.4 T in the first 2 s , remains constant at 0.4 T from t = 2 s to t = 4 s , and then decreases linearly to 0 at t = 6 s . The magnitude of the induced emf in the loop at t = 4.5 s is:

Step-by-step solution

The area of the loop is A = 500 cm ^2 = 500 10⁻⁴ m ^2 = 0.05 m ^2 . At t = 4.5 s , the magnetic field is in the interval from t = 4 s to t = 6 s . The rate of change of the magnetic field in this interval is constant and is given by: dB dt = 0 - 0.4 6 - 4 = -0.2 T/s According to Faraday's law, the magnitude of the induced emf is: = | -A dB dt | = 0.05 0.2 = 0.01 V Converting to millivolts: = 0.01 1000 mV = 10 mV Answer: 10 mV