# Delta Functions Reshape Electric Potential > The sources collectively demonstrate the utility of the delta function as a flexible tool for mathematically modeling concentrated charge distributions and reveal how the physical dimensionality of that concentration affects the resulting electric potential. Specifically, modeling a line source (charge along the $$z$$-axis) requires using a two-dimensional delta function $$\delta^{(2)}(x, y)$$—defined as $$\delta(x) \delta(y)$$—within the volume charge density formula $$\rho(x, y, z)=\lambda \delta^{(2)}(x, y)$$, where $$\lambda$$ is the linear charge density. Conversely, modeling a surface source (charge on the $$x-y$$ plane) utilizes a one-dimensional delta function $$\delta(z)$$, leading to the density $$\rho(x, y, z)=\sigma \delta(z)$$, where $$\sigma$$ is the surface charge density. Physically, concentrating charge into lower dimensions progressively smooths the singularity: the most extreme singularity is the $\mathbf{1/r}$ potential characteristic reserved exclusively for the 3D point charge, while a line charge produces a milder logarithmic singularity, and a surface charge completely eliminates the singularity, resulting in a non-singular linear potential near the sheet. ### :paperclips:IllustraDemo {% embed url="" %} ### :paperclips:IllustraDemo hub {% embed url="" %}