# Distributing charge removes voltage singularities > In electrostatics, the fundamental relationship between the electric potential ($$V(x)$$) and the volume charge density ($$\rho(x)$$) is established by Poisson's Equation ($$\nabla^2 V(x)=-\frac{\rho(x)}{\epsilon\_0}$$), which is derived directly from Maxwell's Equations, specifically the differential form of Gauss's Law. This equation utilizes the Laplacian operator ($$\nabla^2$$) and the permittivity of free space ($$\epsilon\_0$$). The resultant physical field is critically dependent on how the charge is mathematically modeled: when a point charge is modeled using the Dirac delta function, which is the sole mathematical source of the singularity, the system's response is a potential field characterized by a singularity and the iconic decay. Conversely, when the charge is modeled as a distributed source (like a hollow sphere), the singularity is eliminated, proving that the potential remains finite and constant inside the charge layer, resulting in a physically smooth field at the origin. ### :paperclips:IllustraDemo {% embed url="" %} ### :paperclips:IllustraDemo hub {% embed url="" %}