Potential of a Charged Isolated Conductor

An excess charge placed on an isolated conductor will distribute itself on the surface of that conductor so that all points of the conductor—whether on the surface or inside—come to the same potential. This is true even if the conductor has an internal cavity and even if that cavity contains a net charge.

1. The free conduction electrons distribute themselves on the surface in such a way that the electric field they produce at interior points cancels the external electric field that would otherwise be there. 

2. The electron distribution causes the net electric field at all points on the surface to be perpendicular to the surface.

Electric Potential Energy of a System of Point Charges

Potential energy can be defined as the capacity for doing work which arises from position or configuration. In the electrical case, a charge will exert a force on any other charge and potential energy arises from any collection of charges. For example, if a positive charge Q is fixed at some point in space, any other positive charge which is brought close to it will experience a repulsive force and will therefore have potential energy. The potential energy of a test charge q in the vicinity of this source charge will be:

Calculating the Field from the Potential

Potential Due to a Continuous Charge Distribution

For continuous charge distribution, we use another formula.

we have two type.

1. Line of charge

2. Charged Disk

Potential Due to an Electric dipole.

The electric dipole moment for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance between them and the defined direction is toward the positive charge. It is a useful concept in atoms and molecules where the effects of charge separation are measurable, but the distances between the charges are too small to be easily measurable. It is also a useful concept in dielectrics and other applications in solid and liquid materials. Applications involve the electric field of a dipole and the energy of a dipole when placed in an electric field. Then :

Potential Due to a Group of Charge

From the previous subtopic, we calculate the potential due to a point charge but for this subtopic we want to find the potential due to a group of point charge. In one word, 'summation'.

:)

Potential Due to a Point Charge

For more understanding, watch this video.