Accurate approximations for the shape-dependent electrostatic energy of a uniformly charged rectangular plate

Abstract

We consider a simple approach to calculate approximately the stored electrostatic energy of a uniformly charged rectangular plate. It is expected that the method may work reasonably well when one dimension of the rectangular plate is considerably larger than the other one (for instance, when length of rectangular plate is much larger than its width). However, to our surprise, we find out that the results obtained are not only simple and accurate, but they also apply to any arbitrary shape of the rectangular plate including the square shape.

Keywords

• Uniform charge density
• Rectangular plate
• Electrostatic potential
• Electrostatic energy
• Surface charge density