Derivation of electric potential energy of a system of two point charges in the absence of external electric field
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= q1/40r12
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 + q2q1/40r12
U = q2q1/40r12
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= q1/40r12
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 + q2q1/40r12
U = q2q1/40r12