Calculation of the Capacitance of a Circular Annulus by the Method of Subareas

Abstract

1. The basic theory of approximate calculation by the use of subareas of the capacitance of a plane area and of the distribution of charge density over it is outlined. 2. The method of subareas is employed to obtain an accurate value for the capacitance of an annulus of ratio of outer to inner radius of ro/ri=1.5. 3. The fourth approximation to the capacitance of a specified circular disk, as calculated by the method of subareas, is found to be in good agreement with the known exact value. As a circular disk is an annulus of ratio of radii ro/ri=∞, it is to be concluded that the fourth approximation for the much narrower annulus of ratio 1.5 is very nearly the exact value. This conjecture is substantiated by the curve of Figure 3. 4. Comparison in Figure 6 of the charge distribution on a circular disk as determined both from the known equation and by the method of subareas indicates that calculation of charge distribution by use of subareas affords a good approximation to the actual distribution. Accordingly, the charge distribution of Figure 7 for the much narrower annulus is to be considered as a close approximation to the actual distribution. 5. The universal curve of Figure 8 yields the capacitance of an annulus of any stated ratio of external to internal radii.