Measurement of quasistatic Maxwell's displacement current.

Abstract

We have used a superconducting quantum interference device to measure all components of the small magnetic field inside a coaxial capacitor that is being charged at a low frequency (695 Hz). The expected result is that ${B}_{z}$ and ${B}_{\ensuremath{\rho}}$ should be 0 and that ${B}_{\ensuremath{\varphi}}$ should increase linearly from the end of the capacitor. This prediction depends upon Maxwell's displacement current ${\mathrm{J}}_{D}$ being strictly equal to (1/4\ensuremath{\pi})\ensuremath{\partial}D/\ensuremath{\partial}t in the annular region between the electrodes. Anomalous fields would arise if ${J}_{D}$ twisted a little in going from one electrode to the other. We find no evidence for such a twist. ${B}_{\ensuremath{\varphi}}$ is as predicted; ${B}_{\ensuremath{\rho}}$ and ${B}_{z}$=0 everywhere to within a few percent of ${B}_{\ensuremath{\varphi}}$. Our results show that the displacement current flows within \ensuremath{\Delta}\ensuremath{\varphi}=22\ifmmode^\circ\else\textdegree\fi{} of the radial direction. We have also searched for a B field that is in phase with the charge (rather than the current) and for fields which vary as the second harmonic of the charging frequency. The former search is interpreted to show that in a traveling TEM wave B is perpendicular to E to within 0.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ rad. The latter search is loosely connected to nonlinear electromagnetic effects such as those provided by axions.