The force exerted by an electric field on a long cylindrical conductor

Abstract

The calculations and experiments here described were undertaken in the hope of giving a rational description of the fine jets which a strong electric field can drag from the surface of a conducting fluid. The force on a long axisymmetric conductor in contact with a con­ducting plane and subjected to an electric field parallel to its length is found by replacing the conductor by an axial distribution of charge. This distribution can be determined by means of an integral equation. The solutions for some particular cases were found by means of a computer, and Professor van Dyke, in an appendix, gives a more analytical method of solution. The equivalent distribution of charge is found for half a spheroid standing on a plane. The force acting on this distribution is compared with the known force on the curved surface of a hemispheroid and the result used to show that the error involved in taking them as equal is small. Experiments are described in which cylinders and hemispheroids standing on a horizontal earthed plate were lifted by a vertical field. Agreement between these experiments and calculation when the conductors are sufficiently light indicates that the space charge in the intense field at their upper ends is not large enough to invalidate the calculation, but when the conductors are heavy enough they oscillate instead of rising, an effect which must be due to electric breakdown of the air producing space charges which upset the field.