Calculation of capacitances.


When the printing level for segments and charges is set to 'all' the charges on all the segments are given, individually and cumulatively. The cumulative values can be used for example to deduce the total charge on a particular electrode when unit voltage is applied to it. This type of information can therefore be used to deduce capacitances. For examples of the procedure see test2d06, 2D sphere, test2d07, 2D coaxial cylinders, test3d06, cube, test3d07, 3D sphere, test3d15, 3D disc, test3d17, tetrahedron, test3d18, square and test3d19, unit triangle and summary of capacitance tests.


Further details:

When there are 2 electrodes, such as 2 discs, then to find the capacitance we need the charges when one electrode has V1 = 0.5 and the other has V2 = -0.5. These charges can be deduced from the ‘unit charges’ in the ray output file or can be obtained directly by setting the applied voltages to these 2 values. Note that the total charge is not zero for the ‘unit charges’. For example when V1 = 1 and V2 = 0 the charges are those for V1 = 0.5, V2 = -0.5 (call these Q) but with extra charges added (call them q), giving Q + q. Similarly when V1 = 0 and V2 = 1 the charges are those for V1 = -0.5, V2 = 0.5, with extra charges, giving charge -Q + q, which is not the negative of (Q + q). This might give the impression of a lack of symmetry.