Angular Momentum with a Twist! (E&M)

[PoopinForPeace]

So, after thinking myself in circles on this conceptual problem my professor posed in class I thought I would post this and see if anyone else has any input. The problem is as follows:

Basically, there is a solenoid with a given radius and n turns per unit length. Coaxial with this are two cylindrical shells with length l, one inside the solenoid with a charge Q with a given radius, and the other outside with -Q and again, a given radius. The current through the solenoid is then gradually reduced.

So, the questions start rather simply with determining the angular momentum stored in the fields, which is not the interesting part. It asks to write the induced electric field ( namely, the angular component) in terms of the the rate of change of omega with respect to time for each shell. This is where I thought it became interesting. The important thing here is that as these shells start spinning, they create a magnetic field which also changes the flux through the original solenoid.

So, then accounting for this change in flux I began to re-solve for my non-conservative electric field. Eventually, I took the basic Ampère-Maxwell law (curl of B) and converted it to integral form and began to solve for the magnetic field in hopes to use it to calculate flux and then continue on.

That's basically the problem. If you'd like me to post the complete problem I can, but I thought a summary would suffice. I guess my questions are: Do you think this is a valid approach? How would you approach it? Any thoughts you have on the matter would be greatly appreciated!