Electric potential: The electric potential at a point in an electric field is the amount of work done in moving charge from infinity to that point.

 The S.I. unit of electric potential is volt (V). The electric potential at a point in an electric field is said to be 1 volt if one joule of work done had to be done in moving a positive charge of 1 coulomb from infinity to that point against the electrostatics forces.

Electric potential due to a point charge: Consider a positive point charge q placed at the origin o. We wish to calculate its electric potential at a point p at distance r from it, as shown in fig. By definition the electric potential at point p will be equal to the amount of work done in bringing a unit positive charge from infinity to a point P.

Suppose a test charge q₀ is in placed at point A at distance x from o. by Couloms law the electrostatic force acting on charge q₀ is

The small amount of work done in moving the test charge q₀ from A to B through small displacement dx against the electrostatics force is

dw = F. dx = fdx 180° = -F dx

The total work done in moving the charge q₀ from infinity to the point P will be

 

Hence the work done in moving a unit test charge from infinity to point p or the  dielectric potential at point p is

Clearly, we V α  1/r . Thus the electric potential due to a point charge spherically symmetric as it depends only on the distance of the observation point from the charge and potential at infinity is zero, fig shows the variation of electrostatic potential V α  1/r and the electrostatic field E ∝1/r² with distance r from a charge q.

Potential Difference: It may be defined as the amount of work done in moving a unit positive charge from one point to the other against the electrostatics forces.

Consider a point charge +q located at a point o. let A and B be two points in its electric field. When a test charge q₀ is moved from A to B, a work W_AB has to be done in moving against the repulsive force Exerted by the charge +q. We then calculate the potential difference between points A and B by the equation:

S.I. unit of potential difference is volt(V). It has been named after the Italian scientist Alexandro Volta.

Or 1V = 1 NmC^-1 or 1C^-1

Hence potential difference between two points in an electric field is said to be 1 volt if 1 joule of work has to be done in moving a positive charge of 1 coulomb form one point to the other against the electrostatic forces.