  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.
