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.

Find the potential energy of a system of four particles placed at the

1.	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.
Answer» Solution : 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)` .