Paul De Young, of Hope College, points out that because the cylinders in Ex. 8.4 are left rotating (at angular velocities wa and wb, say), there is actually a residual magnetic field, and hence angular momentum in the fields, even after the current in the solenoid has been extinguished. If the cylinders are heavy, this correction will be negligible, but it is interesting to do the problem without making that assumption.

(a) Calculate (in terms of wa and wb) the final angular momentum in the fields.

(b) As the cylinders begin to rotate, their changing magnetic field induces an extra azimuthal electric field, which, in turn, will make an additional contribution to the torques. Find the resulting extra angular momentum, and compare it to your result in (a).