Rotating Charged Cylinder with Hanging Mass · CAP 2001 #B3
Physics · electromagnetism
Problem
Consider a long horizontal cylindrical shell, of length l, radius R which can rotate freely about its longitudinal axis with a moment of inertia I. The material that composes it is electrically insulating and non-magnetic. A massless string attached to a vertically hanging mass m is then wound around the cylinder drum. The mass is released from rest at time t = 0.
(a) Determine the angular acceleration and kinetic energy of the system after the hanging mass has fallen a distance h.
(b) A net amount of positive charge Q, of negligible mass, is deposited uniformly on the outside drum of the shell before the mass is released. Redo part (a) under these conditions. Calculate the difference in kinetic energy between the two cases Q = 0 and Q ≠ 0. Do you have any idea as to where the "missing" kinetic energy went?
HINT: The magnetic field due to a very long solenoid of length l and N turns carrying a current I produces no net magnetic field outside the solenoid, but a net uniform magnetic field of strength μ0NI/l inside the solenoid. The field is directed along the solenoid axis.