Gravitationally Induced Electric Fields in Conductors

An estimate for the gravitationally induced electric field is presented that is based on a statistical model for the electrons in a metal in which their long-range electrostatic interaction with a differentially compressed lattice of positive ions is taken into account. The field is in the upward direction and is estimated to be of the order of magnitude $E\approx \frac{\mathrm{Mg}}{e}$, where $M$ is the atomic mass, $e$ is the electronic charge, and $g$ is the acceleration due to gravity. For copper, $E\approx {10}^{-7\mathrm{}}$ V/m. An earlier estimate by Schiff and Barnhill gives a field in the downward direction equal to $\frac{\mathrm{mg}}{e}$, where $m$ is the mass of the electron. The difference between our result and theirs is due to different treatments of the effect of lattice compressibility.