A charge q is placed at the centre of the line joining two equal charges Q. Show that the system of three charges will be in equilibrium if ` q= -(Q)/(4) .`

Explanation

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