A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium , if q is equal to

Options

A. `-(Q)/(2) `
B. ` -(Q)/(4) `
C. ` +(Q)/(4) `
D. ` +(Q)/(2) `

Answer

B

Explanation

For equlibrium of system the net force on any charges must be zero. Considering net force on A, we have `oversetto(F_(AC))+oversetto(F_(AB)) =0 `
` therefore " "(1)/(4 pi in _0) .(Qq)/((®/(2))^(2)) +(1)/(4 pi in _0 ) .(Q^(2))/(r^(2)) =0 rArr (1)/(4 pi in _0) .(Q)/(2) [4q +Q] =0 `
or `" " 4q +Q=0 or q=-(Q)/(4) `