Gauss

We know from classical electrostatics if a charged particle is outside a spherical charged surface, the interaction is as though the sphere were a point charge located at the center of the sphere. If the charged particle is inside the spherical surface, it sees a constant distance-independent potential. The red curve is the interaction between the sphere and a point charge, the blue curve is the interaction between two point charges. The blip is when the point charge passes through the spherical surface.

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Vertices Sum = 0.4647; Origin Sum = 0.4981;
Figure 1. Interaction Energy between a point charge and a spherical electron density.

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