A square-shaped copper coil has edges of length 50 cm and comprises 50 turns. It is positioned perpendicular to a 1.0 T magnetic field. The coil is removed from the magnetic field in 0.25 s and restored to its original place over the subsequent 0.25 s . Determine the magnitude of the average emf induced in the loop during its entire motion.

Step-by-step solution

The initial magnetic flux linked with the coil is given by _i = NBA (0^ ) . Given N = 50 , B = 1.0 T , and A = (0.5 m )^2 = 0.25 m ^2 : _i = 50 1.0 0.25 = 12.5 Wb The coil is removed from the magnetic field and then restored to its original position. Therefore, the final magnetic flux linked with the coil is the same as the initial flux: _f = 12.5 Wb The total change in magnetic flux over the entire motion is: = _f - _i = 12.5 - 12.5 = 0 By Faraday's law of induction, the average induced emf is given by: e_ avg = -