STUDY OF FRINGING-FIELD EFFECTS ON THE CAPACITANCE OF A DIELECTRIC DISK WITH A CIRCULAR CONDUCTING HOLE

The capacitance of a thin dielectric sheet with a conducting hole is s trongly influenced by the fringe effects around the edges of the hole, particularly when the hole size beomes comparable to the size of the sheet. We present here a numerical study of this situation. By a finit e-difference scheme, the potential, field, and surface-charge densitie s in and around the hole are calculated. The sharp edge of the hole re presents a singularity, and the asymptotic behavior of the field and s urface-charge densities in the vicinity of the singular point are disc ussed both analytically and numerically. It is found that the scaled d ifference between a numerical simulation and the simple parallel-plate -capacitor formula changes with the relative size of the hole in a com posite power-law relation.