Question #90693

A very long cylindrical metallic cathode of radius $r_1$ is illuminated by monochromatic light of frequency $\nu$. The work function of the cathode material is $\Phi$. A coaxial cylindrical metallic anode of radius $r_2$ ($r_2 > r_1$) surrounds the cathode. The region between the cylinders contains a non-uniform radial electric field $\vec{E} = \frac{\lambda_c}{2\pi\epsilon_0 r} \hat{r}$, where $r$ is the radial distance from the central axis, $\hat{r}$ is the unit radial vector, $\epsilon_0$ is the vacuum permittivity, and $\lambda_c$ is a positive constant. If the most energetic photoelectrons emitted from the cathode just fail to reach the anode, what is the required value of $\lambda_c$? (Assume $h\nu > \Phi$ and $e$ is the elementary charge).