What happens if a current flows through a wire wrapped around a magnetised material?

A cylinder of radius $a$ has a uniform magnetisation along its axis, which results in zero bound volume current density and a bound surface current density $M\hat{\phi}$. A coil with $N$ turns and wire resistance $R$ and a given wire radius is wrapped around the magnetisation in the form of a solenoid with radius $b>a$. When the magnetised cylinder is flipped a charge $q$ flows through the wire in the coil. What happens in this situation, ignoring the self-inductance of the wire? (It was a question in my exam today asking to compute the new magnetisation of the cylinder that I couldn't do and am intrigued - before this was asked I had calculated the $\vec{H}$ and $\vec{B}$ fields everywhere.)

My initial thoughts were that if there is a charge flowing into the wire then there is then a current flowing through it since the flow of charge is what current is. This can then be modelled as a solenoid with a magnetic field inside of $\vec{B}=\mu_0nI\hat{z}$.

While the charge is flowing into the wire, would there then be a time-dependent current increasing with time? I was thinking of computing change in flux and thus induced emf inside the solenoid, and then go on to somehow combine this with what I had already discovered about the magnetised cylinder.

Could someone please take me through the physics of what is going on in this situation?

• Your thoughts are correct, looking at the induced emf by considering the change in magnetic flux is one way to handle such a problem. You can think of it as a non-driven RL circuit. Technically, there would be some self-inductance and a little bit of capacitive reactance during the initial switch, but the non-driven (i.e., no external power supply) RL circuit should work... – honeste_vivere Jan 14 '16 at 13:57
• The coil is fixed in space, the magnetized cylinder is rotated along with the coil, the total resistance I would assume is R, although the question did not specify. – ODP Jan 20 '16 at 14:44