The Charge Induced on a Conducting Cylinder by a Point Charge and Its Application to the Measurement of Charge on Precipitation

The solution of the electrostatic boundary value problem for a point charge inside an infinite cylinder is applied to sensors employed in the measurement of charge on precipitation. With these devices the charge induced on a cylindrical segment is measured and must then be related to the actual charge on the particle. This induced charge depends upon the axis ratio of the cylindrical segment and upon the location of the point charge. Here the fractional induced charge is computed for a number of cases: 1) point charge at the centers of cylindrical segments of various axis ratios; 2) point charges moving along the axes of cylinders with axis ratios of 0.25, 0.5, 1.0, and 2.0; and 3) charges moving parallel to but off of the axis of a cylinder with an axis ratio of 1.0. In addition, the effect of the measuring electronics is computed for certain cases. Numerical results such as these will find application in the design of charge sensors, and in some cases may even suffice for their calibration.