Electrostatic Potential - Principle and Calculation

Let us consider a system of charges consisting of static charges, that is, charges fixed at a position that does not undergo any type of motion. In this system, we define the potential energy of a charge in terms of the work done on the charge. As we know, when a charge, say q, is placed in an electric field E (the electric field at any point due to the charge configuration of the system), it experiences a force proportional to the magnitude of its charge equal to q×E.

If we divide the resultant work done by the magnitude of charge, it becomes independent of the charge. This is how we calculate the electrostatic potential of a charge. In this section, we will learn about the concept of the electrostatic potential of a charge.

Taking an example of a charged particle being brought from a point A to a point B in the electric field, the work done by an external force in bringing this unit positive charge from point A to B is given by,

Where, VA and VB are the electrostatic potential of the particle at points A and B respectively, UA and UB are the potential energy of the particle at points A and B and q is the magnitude of the charge.

As we know that the actual value of the potential at any point holds no significance and we rather calculate the potential difference between two points for any given system of charges.

Now, as we know, the potential energy of a charged particle at infinity is assumed to be zero, so the electrostatic potential of an object is calculated for a particle with reference to infinity.

Electrostatic potential in the region of the electric field, at any point, is defined as the work done in bringing a unit charge from infinity to that point such that the particle undergoes no acceleration.