Find the potential energy of a system of four particles placed at the vertices of a square of side l. Also obtain the potential at the centre of the square.

Explanation

Consider four masses each of mass m at the corners of a square of side l, We have four mass pairs at distance l and two diagonal pairs at distance `sqrt(2)`l
hence,
W(r) = - 4 `(Gm^(2))/(l) - 2 (Gm^(2))/(sqrt(2)l)`
= - `(2.Gm^(2))/(l ) (2 + (1)/(sqrt(2))) = - 5.41 (Gm^(2))/(l)`
The gravtational potential at the centre of the square `(r = sqrt(2)l//2)` is
U(r) = - `4 sqrt(2) (Gm)/(l)` .