Derive an expression for the electrostatic potential energy of a system of two point charges and find its relation with electric potential of a charge.

Explanation

1. Let two point charges `q_1 and q_2` are separated by distance 'r'in space.
2. An electric field will develop around the charge `q_1`.
3. To bring a charge `q_2` from infinity to the point B some work must be done.
workdone `=q_2v_B`
But `v_(B)=(1)/(4piepsi_0)(q_1)/(r)`
`W=(1)/(4piepsi_0)(q_1q_2)/(r)`
This amount of workdone is stored as electrostatic potential energy (U) of a system of two charged particles. Its unit is joule. `therefore U=(1)/(4piepsi_0)(q_1q_2)/(r)`
5. If the two charges are similar then 'U' is positive . This is in accordance with the fact that two similar charges repel one another and positive work has to be done on the system to bring the charges nearer.
6. Conversely if the two charges are of opposite sign , they attract one another and potential energy is negative.