A ring of radius r, made of insulating material, ischarged with linear charge density. uniform and full charge q. Thering is initially at rest, but is free to rotate around its axis ofsymmetry, and is located in a region of constant magnetic field (Bext ) produced by an infinite solenoid of radius b>>r., withits axis of symmetry aligned with the direction of the fieldmagnetic (see figure). Suppose the field is generated by ne loadcarriers per unit of length (electron density) of the solenoid thatmoves at speed ve (velocity azimuthal). The entire system is in asteady state and is isolated. Suppose now that for some accident -or by prior arrangement - the current in the solenoid isinterrupted. Evaluate the following two hypotheses:

I) When the current is stopped, this flow should go tozero. There will therefore be a field induced electrical circuitthat will circle in circles centered on the axis ofsymmetry the ring will experience a tangential electric field.This electrical force will result in a net torque on thering. From these arguments, we would expect that as thecurrent in the solenoid disappeared, the ring began to spin. If weknew the moment of inertia of the ring (I) and the current in thesolenoid, we could calculate the resulting angular velocity andtherefore its angular momentum (L).

II) But we can also make a different argument. Using theconservation principle of angular momentum, we could say that theangular momentum of the system, including the ring and all otherequipment is initially zero, so the angular momentum of theassembly must remain zero. There must be no rotation when the chainis interrupted.

i.Which argument is correct? Will the ring rotate ornot?

ii. If you consider the ring to rotate, obtain anexpression for the final angular velocity of the ring and itsangular momentum as a function of problem data.

iii. Would it be possible to know where the initialangular momentum comes from? Try to get it. Is it comparable tofinal angular momentum?