Past exam of the mathematics course of the University of Cambridge / 2004 / ib / Paper 1 / 7B (Electromagnetism)

In vacuum SI notation, Maxwell's equations areTaking the divergence of the last equation, using that the divergence of a curl vanishes and then the first equation, givesThis is local conservation of electric charge. For spatially uniform electrical conductivity, Ohm's law $J=\sigma E$ gives $\nabla \cdot J=\sigma \rho /{ϵ}_0$, soFor a homogeneous dielectric conductor with permittivity $ϵ$, replace ${ϵ}_0$ by $ϵ$. This charge relaxation is a statement about bulk charge; charge transported to a boundary is still accounted for by the conservation law.