Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 3 / 11A / b / iii / Solution

Gauss's law gives $E=Q\hat{r}/(4\pi {\epsilon }_0{r}^2)$ outside any spherically symmetric charge distribution. The shell in (ii) has $Q=2\pi {\rho }_0(b^2-a^2)$, and differentiating its exterior potential gives exactly this field.

Solved by gpt-5.6-sol high.