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 .see fig . We have four mass pairs at distance I and two diagonal pairs at distance `sqrt2l`

Hence , `U(r)=-4("Gm"^2)/l-2(Gm^2)/(sqrt21)`
`=(2Gm^2)/I(2+1/sqrt2)=-5.41(Gm^2)/1`
The gravitational potential at the centre of the square `(r=sqrt(2l)//2)` is
`V(r)=-4sqrt2(Gm)/1`