A conducting circular loop of radius 20 cm and resistance 4 m is placed perpendicular to a uniform magnetic field of 0.5 T . The magnetic field is reduced to zero at a constant rate in 0.2 s . The total heat dissipated in the loop during this time interval is:

Step-by-step solution

The area of the circular loop is: A = r^2 = ( 20 10⁻² )^2 = ( 400 10⁻⁴ ) = 0.04 m ^2 The magnetic field decreases to zero at a constant rate. The rate of change of the magnetic field is: | dB dt | = 0.5 0.2 = 2.5 T/s The magnitude of the induced emf is: = A | dB dt | = 0.04 2.5 = 0.1 V The electrical power dissipated as heat in the loop is: P = ^2 R = (0.1)^2 4 10⁻³ = 0.01 0.004 = 2.5 W The total heat dissipated during the time interval t = 0.2 s is: H = P t = 2.5 0.2 = 0.5 J Answer: 0.5 J