We will now construct a method to calculate the electric potential resulting from a continuous charge distribution in a similar fashion to how we developed expressions for the electric field due similar distributions.

- Construct a diagram with a coordinate set of axes
- Locate the point at which we want to calculate the absolute potential and label appropriate distances
- Divide the total charge distribution into small charge segments (deltaq)
- Develop an expression for one piece and then sum up the contributions for all of the charge segments
- Replace the sum of the charge segments with an integral incorporating expressions for the charge density and an appropriate infinitesimal (ds, dA, dV).
- Integrate and simplify

We will use this technique to calculate the electric potential along the axes of a thin ring of charge, a uniformly charged disk, and a concentric set of cylinders.

Uniformly Charged Ring

Suppose we have a ring of charge with a uniform charge distribution, λ, and radius a. We will now develop an expression for the electric potential at a position on the positive x-axis, at point P in the following diagram.

Since the ring has a uniform distribution of charge, we know that the total charge equals

allowing us to write an expression for the electric potential at point as

If we let x = 0, then we find that the potential at the center of the ring equals