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?

Options

A. `-(q)/(2)(1+2sqrt(2))`
B. `(q)/(2)(1+2sqrt(2))`
C. `-(q)/(4)(1+2sqrt(2))`
D. `-(q)/(4)(1+2sqrt(2))`

Answer

D

Explanation

`AC=sqrt(21)=BD`
or,`BO=(1)/(sqrt(2))`

`F_(BO)=F_(BD)+(F_(BA)+F_(BC)) cos 45^(@)`
Solving we get
`Q=(q)/(4)(1+2sqrt(2))` Q should be negative of q.