Question #43770

An evacuated, non-conducting thin tube forms a semi-circle of radius $R$ in the $xy$-plane, extending from $\theta = 0$ to $\theta = \pi$. A photoelectric emitter is located at $\theta = 0$ and a collector is at $\theta = \pi$. A uniform time-varying magnetic field $\vec{B} = \alpha t \hat{k}$ (where $\alpha > 0$ is a constant and $\hat{k}$ is the unit vector out of the page) exists everywhere in the cylindrical region $r \le R$. Monochromatic light of frequency $\nu$ is incident on the emitter, which has a work function $\phi$. Electrons are emitted and constrained to travel through the tube to the collector. What is the minimum stopping potential $V_0$ (applied such that the collector is at a lower potential than the emitter) required to prevent the fastest electrons from reaching the collector? (Assume $e$ is the magnitude of the electron charge)