Potential energy of a charge

 in an external field

 

1) Suppose there is already an electric field E.

2) Suppose a charge q is bringing to a position r.

3) if the potential at that position is V(r).

4) then potential energy of the charge at that position is

= q V(r)

 

Potential energy of two charges

 in an external field

 

1) Suppose two charges q1 & q2 are bringing to the positions r1 & r2 in an external electric field E.


2) Suppose V(r1) & V(r2)  are the potentials at the positions r1 & r2


3) then potential energy of the system is


Where r12  is the distance between q1 & q2