Calculating electromagnetic force and energy using singularity functions

The purpose of this article is to provide physical insight into a new analytical approach to calculate electromagnetic force and energy using singularity functions, specifically the unit impulse function and its integral, the unit step function. The electromagnetic force acting on a charged conductor is expressed in terms of a special singularity integral which is the sifting integral of the unit step function. The well-known parallel-plate capacitor problem in electrostatics is considered as an example to demonstrate the validity and use of this special integral. The authors believe that this technique can easily be extended to problems involving high-frequency microwave systems such as waveguides and resonant cavities.