The figure belowshows a cutaway viewof an infinite cylindrical solenoid with radius R that creates a magnetic field B = B inside itself. An infinitely long cylinder of insulating material with radius a < R, permeability μ₀, and permittivity ϵ₀ sits inside (and coaxial with) the solenoid. The cylinder is filled uniformly with charge with density  ρ̃ > 0. A uniform surface charge σ makes the cylinder electrically neutral.

(a) Find the total electromagnetic angular momentum (per unit length) of this system.
(b) Compute the instantaneous torque (per unit length) which acts on the cylinder as the magnetic field is reduced to zero with a time dependence B(t).
(c) Show that the final mechanical angular momentum of the cylinder is equal to the initial angular momentum calculated in part (a).

Transcribed Image Text:

σ B p a B R