The exact relation between the displacement current and the conduction current: Comment on a paper by Griffiths and Heald

Abstract

I introduce the exact relation between the displacement current $\epsilon_0 \partial \v{E}/\partial t$ and the ordinary current $\v{J}$. I show that $\epsilon_0 \partial \v{E}/\partial t$ contains a local term determined by the present values of $\v{J}$ plus a non-local term determined by the retarded values of $\v{J}$. The non-local term implements quantitatively the suggestion made by Griffiths and Heald that the displacement current at a point is a surrogate for ordinary currents at other locations.