When a charged particle is made to move in an electrostatic field in a direction opposite to the direction of the field, work is done by an external agency. This work is stored as potential energy of charge in accordance with the law of conservation of energy. So, an electric charge placed at a point in an electric field has potential energy, which is a function of its position.
The electric potential at any point in an electric field is equal to the work done against the electric force in moving a unit positive charge from outside the electric field to that point. Electric potential is a scalar quantity, as it is related to work done.
The potential at a point is taken positive when work is done against the field by a positive charge but negative when work is done by the electric field in moving the unit positive charge from infinity to the point in the field.
Consider two points A and B in an electric field. If a test charge q0 is moved from point A to point B along any path by an external force, the amount of work done by the external force is given by
WAB = q0 (VB – VA)
Thus, potential difference between points A and B is
VAB = VB – VA = WAB/q0
A potential difference is said to exist between two points in an electric field, if work is done against the electric force in moving a positive test charge from one point to the other. The SI unit of potential and potential difference is volt.
If one joule of work is done in taking a test charge of one coulomb from one point to the other in an electric field, the potential difference between these points is said to be one volt.