An infinite cylindrical solenoid of radius R is wound tightly with n turns per unit length of a wire that carries a current I. A bead of mass m and charge q slides freely on a non-conducting circular wire of radius r > R that is concentric with the solenoid. Let the bead be at rest (ignore gravity) and then reduce the current in the solenoid winding to zero. The bead begins to slide around the wire.

(a) Use Faraday’s law to find the speed ν of the bead after the magnetic field in the solenoid has disappeared.

(b) Show that an application of conservation of linear momentum leads to the same answer.

(c) Explain why the electric and magnetic fields produced by the moving charge do not contribute to the momentum balance in part (b).