Gravitationally Induced Electric Field near a Conductor, and Its Relation to the Surface-Stress Concept

The contact potential difference between points just outside different parts of the surface of a conducting body is altered when the body is acted on by a gravitational field, because of the effect of gravity on the work function of the surface. A reciprocity relation due to Schiff and Barnhill relates this effect of gravity to the shift in mass moment of the conductor produced by shifting the position of a test charge near it, and shows how the effect can be expressed as the sum of a purely electronic term and a nuclear term due to distortion of the crystal lattice. It is shown here how the nuclear term, which describes the effect on the work function of the distortion of the body by its own weight, can also be described, via the reciprocity relation, in terms of the local alteration of the surface stress of the body by the electric field due to the test charge. The contribution of the nuclear term to the electric field in a vertical metal tube is expected to be of the order of ${10}^{-9\mathrm{}}$ to ${10}^{-8\mathrm{}}$ V/cm, much larger than the Schiff-Barnhill electronic contribution of -5.6×${10}^{-13\mathrm{}}$ V/cm.