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 integral does. 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. 连续电荷分布需要无限多个电荷元来描述，而所需的无限级数正是积分所完成的。要实际进行积分，必须将电荷元用分布的几何形状表示出来，并利用某种电荷密度。