Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 36D / a / Solution

A dielectric is a medium whose constituent charges become polarized by an applied electric field; it may also acquire a magnetization. Spatial variation of $P$ leaves uncompensated dipole charge, giving ${\rho }_{\mathrm{bd}}=-\nabla \cdot P$. Time-dependent polarization transports charge and aligned microscopic current loops contribute magnetization current, giving the bound charge and bound current