A point charge q is located at the center of a toroidal coil of rectangular cross section, inner radius a, outer radius a + w, and height h, which carries a total of N tightly-wound turns and current I.

(a) Find the electromagnetic momentum p of this configuration, assuming that w and h are both much less than a (so you can ignore the variation of the fields over the cross section).

(b) Now the current in the toroid is turned off, quickly enough that the point charge does not move appreciably as the magnetic field drops to zero. Show that the impulse imparted to q is equal to the momentum originally stored in the electromagnetic fields.