Three point charges are arranged at the corners of a square

Three point charges are arranged at the corners of a square of side l as shown in the figure.

What is the potential at the fourth corner (point A), taking V=0 at a great distance? V_A=?

Give your answer in terms of Q, l, ?₀ and appropriate constants.

Solution

electric potential = kQ/R

here, k- coloumbs constant, R- distance, Q- charge

potential due to +Q charge: V =k Q/ sqrt(2) * L

potential due to +3Q charge: V =3kQ/L

potential due to -2Q charge: V= -2kQ/L

so, the potential:

     V = kQ/L + kQ/ sqrt(2) * L = kQ/L (1+ 1/ sqrt(2)) = (1.7)kQ/L