🎬Electrostatic Potentials-Numerical Validation of Point vs Distributed Charge

The Dirac delta function is the sole mathematical source of the potential's singularity. When Poisson's equation uses the delta function to model a Point Charge, the system's fundamental response is a potential field characterized by a singularity at $r=0$ and the iconic $V(r) \propto 1 / r$ decay that extends to the center. Conversely, when the charge is modeled as a Distributed Source (like the hollow sphere), the potential remains finite and constant inside the charge layer, proving that distributing the charge eliminates the singularity and results in a physically smooth field at the origin.

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