Scaling relations for parallel disc Capacitance with Dielectric media

TL;DR

This paper introduces a scaling relation for the capacitance of dielectric-filled circular discs, enabling simplified calculations across various aspect ratios and permittivities by relating them to free space capacitance.

Contribution

It presents a novel scaling approach that relates dielectric capacitance to free space calculations, applicable over a wide range of permittivities and aspect ratios.

Findings

Capacitance depends only on a scaled separation for given disc radius.

Scaling improves with higher relative permittivities.

Method allows using free space computational tools for dielectric media.

Abstract

Total capacitance of a dielectric filled circular disc configuration (radius r and separation d) has been numerically evaluated over relative permittivities ranging from 1 to 80 and aspect ratios ranging from 0.001 to 10. A new perspective is presented by which, the total capacitance, for a given disc radius r, is found to depend only on a simple scaled disc separation for the whole range of aspect ratios and relative permittivities considered. The scaling notion stems from noting that the path length has to be larger than what it would be in free space to have the same potential difference across the charged discs since the electric field strength is reduced within a homogenous dielectric medium by the relative permittivity. This scaling permits translation of practical measurements across a range of aspect ratios and relative permittivities. Further, the scaling feature allows for any computational approach that determines the total capacitance in free space, to be applicable for dielectric media having relative permittivities in the range 1 to 80. It is believed that the scaling would become better with increasing relative permittivities for practically relevant separations.