A square conducting loop of side 50 cm and resistance 0.5 is moved at a constant speed of 2 m/s through a uniform magnetic field region of width 2 m . The magnetic field is perpendicular to the plane of the loop and has a magnitude of 1 T . The total heat energy dissipated in the loop during its complete passage through the magnetic field region is:

Step-by-step solution

The induced emf in the loop is non-zero only when the magnetic flux through it is changing, which occurs during its entry into and exit from the magnetic field. Magnitude of induced emf during entry and exit: = BvL = 1 2 0.5 = 1 V . Electrical power dissipated during these intervals: P = ^2 R = 1^2 0.5 = 2 W . Time taken to enter the field: t_ entry = L v = 0.5 2 = 0.25 s . Time taken to exit the field: t_ exit = L v = 0.5 2 = 0.25 s . Total time during which heat is dissipated: t_ total = t_ entry + t_ exit = 0.25