Potential Difference

Consider an isolated point charge + q lying at O. A and B are two points in its electric field. Let W_AB be the work done by an external agent in moving a unit positive charge from A to B. We may define the potential difference between two points in an electric field as the amount of work done in moving a unit positive charge from one point to the other against electrical forces, or W_AB = V_B - V_A.

Here, V_A  and V_B stand for the potentials at A and B.
The SI unit of potential difference is Volt.
The potential difference between two points is 1volt if 1 joule of work is done in moving 1 coulomb of charge from one point to the other against electric forces.

Electric Potential. If A is at infinity, then V_A = O

. :    W = V_B

Here, W is the work done in moving a unit positive charge from infinity to the point B. V_B is the potential at B.

Hence the electrical potential at a point positive charge from infinity to that point, without acceleration, against electrical forces.

The potential at a point near an isolated positive charge is positive. The potential at a point near an isolated negative charge is negative.

Equipotential Surface. If all the points of a surface are at the same electric potential, then the surface is called an “equipotential surface”.

In the case of an isolated point charge, all point equidistant from the charge is at the same potential. Thus equipotential surface in this case will be a series of concentric sphere with the point charge as their centre. The potential will, however, be different for different spheres.

If a test charge q is moved between any two points on an equipotential surface through any path, the work done is zero. This is because the potential difference between two points A and B is defined by

    V_B - V_A = W_AB / q.

If V_A = V_B, then W_AB = 0. Hence the electric field vector E must be everywhere normal to an equipotential surface.
Two equipotential surfaces cannot intersect each other.