. E LECTROSTATIC P OTENTIAL Consider any general static charge configuration. We define potential energy of a test charge q in terms of the work done on the charge q . This work is obviously proportional to q , since the force at any point is q E , where E is the electric field at that point due to the given charge configuration.
It is, therefore, convenient to divide the work by the amount of charge q , so that the resulting quantity is independent of q . In other words, work done per unit test charge is characteristic of the electric field associated with the charge configuration. This leads to the idea of electrostatic potential V due to a given charge configuration. From Eq.
( . ), we get: Work done by external force in bringing a unit positive charge from point R to P = V P – V R P U U ( . ) where V P and V R are the electrostatic potentials at P and R, respectively. Note, as before, that it is not the actual value of potential but the potential difference that is physically significant.
If, as before, we choose the potential to be zero at infinity, Eq. ( . ) implies: Work done by an external force in bringing a unit positive charge from infinity to a point = electrostatic potential ( V ) at that point.