Question

Two point charges q₁ and q₂ are located at `vec r_1 and vec r_2` respectively in an external electric field `vec E`. Obtain an expression for the potential energy of the system.

Answer 1

Work done is bringing the charge q₁ from infinity to the position r₁,

W₁ = q₁V(r₁)

Work done in bringing the charge q₂ to the position r₂

`W_2 = q_2V(r_2) + (q_1q_2)/(4piepsilon_0r_2)`

Hence, total potential energy of system,

u = W₁ + W₂

`u = q_2V(r_1) + q_2V(r_2) + (q_1q_2)/(4piepsilon_0r_2)`