Electric Potential

Shown here is the calculation for the potential difference at a distance x away from a uniformly charged ring on its axis, and at a distance x away located at the top of the ring, and centered in the middle of the ring. 

We can also break up the ring into infinitesimally small units of charge dq and integrate as you move around the ring at a distance x away on the rings axis. 

Here is the potential difference at a distance x away from a uniformly charged ring centered on its axis with respect to a point at infinity.

Here is the calculation of a potential difference 15 cm above a 16 cm long rod, 10 cm from the left end of the rod.

Here are the calculations using excel.

Equipotential Surfaces around a single charge, in between to charged plates, and around a uniformly charged ring.