There are four charges, each with a magnitude Q. Two are positive and two are negative. The charges are fixed to the corners of a square of side 'L', one to each corner, in such a way that the force on any charge is directed toward the center of the sqaure. Find the magnitude of the net electric force experienced by any charge?

Explanation

From Coulombs law, force between +Q and +Q is `F_(1)=(KQ^(2))/L^(2)`
Force between +Q and -Q is `F_(2)=(-KQ^(2))/L^(2)`
Resultant of `F_(1)` and `F_(2)` is
`F_(12)=sqrt(F_(1)^(2)+F_(2)^(2))=sqrt(((KQ^(2))/L^(2))^(2)+((-KQ^(2))/L^(2))^(2))`
`implies F_(12)=(KQ^(2))/L^(2) sqrt(2)`
Force between -Q and +Q is `F_(3)=(-KQ^(2))/(2L^(2))`
The force on any charge is `F =F_(12)+F_(3)`
`=(KQ^(2))/L^(2) sqrt(2)-(KQ^(2))/(2L^(2))`
`implies F=(KQ^(2))/L^(2)(sqrt(2)-1/2)`
`:. F=1/(4pi epsi_(0)) Q^(2)/(2L^(2))(2sqrt(2)-1)[ :' K=1/(4pi epsi_(0))]`