Question

Answer the following question.
Two-point charges q₁ and q₂ are kept at a distance of r₁₂ in air. Deduce the expression for the electrostatic potential energy of this system.

Answer 1

Electrostatic potential energy of a system is defined as the total amount of the work done in bringing the various charges to their respective position from infinitely large mutual separation.

Let us consider a charge q₁ at a postion vector r₁ and q₂ at infinity which is to be brought at point P₂ having position vector r₂. and dW is the small amount of work done in moving a charge to a distance dx.

`dW = vec"F". vecdx`

`dW = -(kq_1q_2)/(r^2). dx`

`W = -int_∞^(r12) (kq_1q_2)/(r^2).dx`

`W = -Kq_1q_2 int_∞^(r12) 1/r^2. dx`

`W = -Kq_1q_2 [-1/r]_∞^(r12)`

`W = Kq_1q_2[1/(r_12)]`

`W = U = (Kq_1q_2)/(r_12)`.