# 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.

### Brief audio

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### Condensed Notes

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