A circular coil of 200 turns and radius 0.1 m is rotated at a constant angular velocity of 10 rad s ⁻¹ in a uniform magnetic field of 0.5 T . If the electrical resistance of the coil is 10 , what is the maximum external torque required to maintain this constant rotation?

Step-by-step solution

The area of the circular coil is A = r^2 = (0.1)^2 = 0.01 m ^2 . The maximum induced EMF is _ max = NAB . _ max = 200 0.01 0.5 10 = 10 V . The maximum induced current in the coil is I_ max = _ max R = 10 10 = A . To maintain constant rotation, the external torque must balance the opposing magnetic torque. The magnetic torque on the coil is = MB = (NIA)B . The maximum magnetic torque occurs when the current is maximum and = 1 : _ max = N I_ max A B _ max = 200 0.01 0.5 = ^2 N m . Answer: ^2 N m