Continuous Charge Distributions

The electric potential (voltage) at any point in space produced by a continuous charge distribution can be calculated from the point charge expression by integration since voltage is a scalar quantity.

The continuous charge distribution requires an infinite number of charge elements to characterize it, and the required infinite sum is exactly what an integraldoes. To actually carry out the integration, the charge element is expressed in terms of the geometry of the distribution with the use of some charge density.