Saturday, July 30, 2016

Electrostatic Potential Energy Expression

We shall do some work in bringing the two charges to a certain separation against the electric force of repulsion between them. Once after this work is done, energy used for this purpose cannot disappear. It will convert into electrostatic potential energy between that charged particles and hence conservation of energy concept is satisfied.

Let us consider two charges separated by a certain distance. Between them there is certain potential energy. We can define work done as the product of potential difference between the charges and charge that is brought towards the other charge. Once the job is done this work done is actually stored in the form of electrostatic potential energy.

We can derive an expression for electrostatic potential energy of a charged particle placed on the surface of a sphere as shown in the diagram below. 

It can be noticed that we shall do work in bringing each charge to that particular location and we shall do the work for that. All that work done is stored in the form of potential energy. The same is the case with four charges placed at the four corners of a square as shown below.

If three charges are to be placed at the three corners of a triangle, we need to do some work and that work is stored in the form of potential energy. We can write the expression for it as shown in the diagram below.

We can even a small problem about the case of triangle with the solution as shown below.

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