Question

Derive expression for potential energy between two charges in absence of electric field

Answer 1

We have to consider two charges q1 , q2, located at r1 and r2 respectively. The work done in bringing charge q1 from infinity to r1 is zero because there is no potential in absence of electrical field.

Work done in bring the charge q2from infinty to r2 against the field due to charge q1 is = q1V

where V is potential at point r2 due to the charge q1.

As, V= q1/4πε0r12

where 'r12' is the distance between charge 'q1 ' and 'q2 '.

Therefore potential energy of the system is given by the total work done in bring the two charges from infinity to their respective points.

U = 0 + q2q1/4πε0r12

U = q2q1/4πε0r12