On the singularity of the static Green´s function and the derivations of equations associated with potentials

The singularity of the static Green´s function incurs mathematical difficulty. It is pointed out that this singularity is unnecessarily complicated and can be removed by a physically meaningful assumption which regularizes the static Green´s function without substantially affecting the electromagnetic theory. Further, this regularization smooths the electric field in the close proximity of the source and leads to that the electrostatic force due to a charged particle exerted on itself is zero. Thereby, the Poisson equation of the regularized static Green´s function can be obtained in a simple manner. Then, the wave equations of the electric scalar potential and the magnetic vector potential are derived in a new approach. Furthermore, we derive the Lorentz gauge, rather than assume it.