Find the work done to bring `4` particle each of mass `100` gram from distances to the vertices of a square of side `20 cm`.

Explanation

Refer to Fig.

`AC = BD = sqrt((0.2)^(2) + (0.2)^(2)) = 0.2 sqrt(2)m`
Total workdone, is the total potential energy of the system and is given by
`W = U_(BA) + (U_(CB) + U_(CA)) + (U_(DA) + U_(DC) + U_(DB))`
`= 4 U_(BA) + 2 U_(BD)`
`= 4 xx [-(Gm_(1)m_(2))/(AB)] + 2 xx [-(Gm_(1)m_(2))/(BD)]`
`= 4 xx [-(6.67 xx 10^(11) xx 0.1 xx 0.1)/(0.2)]`
`+ 2 xx [-(6.67 xx 10^(-11) xx 0.1 xx 0.1)/(0.2 sqrt(2))]`
`= - 1.33 xx 10^(-11) - 0.47 xx 10^(11)`
`= - 1.80 xx 10^(-11)J`