Find the electrostatic potential energy of the following charge configuration.
Three point charges each of magnitude q, are kept at the vertices of an equilateral triangle of side a.

Explanation

Three positive charges of magnitude = q
Side of equilateral triangle = a

To find out electrostatic potential energy,
consider that the charges are infinitely apart initially
`(ABimpliesoo, BCimpliesoo, ACimpliesoo)`
That the potential energy of the system in the given configuration is zero (initially)
Create the given configuration of the charges from the initial configuration under electrostatic conditions. This can be done in the following two steps.
(i) Hold a charge `+q` at rest at A and transport another `+q` from infinity to point B and do not let `+q` ever accelerate.
Work done in holding `+q` at rest at A = work done in transporting the other `+q` from infinity to `B=(1)/(4piin_(0))(q^(2))/(a)`
(ii) Hold the `(+q)` at A & B at rest transport `+q` from infinity to C (without any acceleration). The work done in this process can be calculated by principle of superposition.
Work done in transporting `+q` from infinity to C if only a `+q` at A is present `=(1)/(4piin_(0))(q^(2))/(a)`
Work done in transporting `+q` from infinity to C if it only a `+q` at B is present `=(1)/(4piin_(0))(q^(2))/(a)`
Therefore, total work done in making this configuration of charges from the initial configuration of zero potential energy = work done in step (i) + work done in step (ii).
`(1)/(4piin_(0))(q^(2))/(a)+(2q^(2))/(4piin_(0)a)=(3q^(2))/(4piin_(0)a)`
This work done is equal to the electrostatic potential energy of given configuration.