A circular coil of 100 turns and radius 10 cm is placed with its plane perpendicular to a uniform magnetic field of 2 T . The coil is part of a closed circuit such that the total resistance of the system is 4 . If the coil is completely flipped (rotated by 180^ ) in 0.5 s , the total charge that flows through the circuit is:

Step-by-step solution

Initial magnetic flux through the coil, _i = N B A = N B ( r^2) When the coil is flipped by 180^ , the area vector points in the opposite direction to the magnetic field. The final magnetic flux is _f = -N B A Magnitude of the change in flux is: | | = | _f - _i| = |-N B A - N B A| = 2 N B ( r^2) Given N = 100 , B = 2 T , and r = 0.1 m : | | = 2 100 2 (0.1)^2 = 4 Wb The total induced charge Q flowing through the circuit depends only on the net change in flux and the total resistance R , and is independent of the tim