Potential Reference at Infinity

The general expression for the electric potential as a result of a point charge Q can be obtained by referencing to a zero of potential at infinity. The expression for thepotential difference is:

Taking the limit as rb→∞ gives simply for any arbitrary value of r. The choice of potential equal to zero at infinity is an arbitrary one, but is logical in this case because the electric field and force approach zero there. The electricpotential energy for a charge q at r is then where k is Coulomb's constant.