Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 36C / a / Solution

For a linear dielectric, $D=\epsilon E$ (equivalently $D={\epsilon }_{0}E+P$). With no free charge, Gauss law gives $\nabla \cdot D=0$. Across an interface without free surface charge, $D_n$ is continuous; electrostatic Faraday law makes $E_t$ continuous.

Solved by gpt-5.6-sol high.