Four equal point charges, each of magnitude `+Q`, are to be placed in equilibrium at the corners of a square. What should be the magnitude and sign of the point charge that should be placed at the center of the square to do this job?

Answer

`3.54xx10^(-6)C`

Explanation

`F_(3)=F_(2)+2F_(1) cos 45^(@)`
.
or `(kqQ)/((1//sqrt(2))^(2))=(kQ Q)/((sqrt(2)l)^(2))+2(kQ Q)/(l^2)(1)/(sqrt(2))`
`q=(Q(2 sqrt(2)+1))/(4)`
Q should be negative as there is attraction between Q and q. So,
`q=(-Q(2 sqrt(2)+1))/(4)` .