Paper 4, Section I, 7C7 \mathrm{C}

Electromagnetism
Part IB, 2018

Show that Maxwell's equations imply the conservation of charge.

A conducting medium has J=σE\mathbf{J}=\sigma \mathbf{E} where σ\sigma is a constant. Show that any charge density decays exponentially in time, at a rate to be determined.