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

Explanation

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) )`

`= (2Gm^2)/ (l) (2 + (1)/( sqrt2) ) = -5.41 (Gm^2)/ (l)`
The gravitational potential `U( r)` at the centre of the square `(r =sqrt(2) l // 2)` is `U( r) = - 4 sqrt(2) (GM)/( l)`