A solid conducting disc of radius R is free to rotate about its central axis, which is fixed. The disc is placed in a uniform magnetic field B that is directed normally into the plane of the disc. Electrical contact is made at the centre by a sharp brush and at the rim by a sliding ring, so that the disc forms part of an external circuit of resistance R0. The disc is set into steady rotation with constant angular speed ω by an external motor.
(a) Show that the emf developed between the centre and the rim of the disc is 21BR2ω.
(b) Calculate the steady current flowing through the external resistance R0.
(c) Determine the magnetic torque that opposes the rotation of the disc.
(d) Prove that the mechanical power which the motor must supply to keep the disc spinning at the constant angular speed ω is equal to the rate of Joule heating in the resistance R0.