Question #43436

A rigid, non-conducting circular ring of radius $R$ is placed coaxially inside a long solenoid. The solenoid produces a uniform magnetic field $B_0 \hat{k}$ along its axis (the $z$-axis). Additionally, a long straight wire carrying a constant current $I$ is placed exactly along the $z$-axis. An electron of mass $m_e$ and charge $-e$ is constrained to move without friction on the ring. Initially, the ring is deep inside the solenoid, and the electron revolves with an angular velocity $\vec{\omega}_0 = \omega_0 \hat{k}$. The ring is then slowly translated along the $z$-axis to a region far outside the solenoid where the solenoid's magnetic field is negligible. The long straight wire extends infinitely and its field remains present throughout. What is the final angular velocity $\vec{\omega}_f$ of the electron?