A charge q is placed at the centre of the line joining two equal charges Q to establish equilibrium. The system of 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 an system to be in equilibrium ,force on any charge out of the three charges must be zero
`F_(Qq) + F_(qQ) = 0`
`kQq/(r//2)^(2) + kQq/r^(2) = 0`
`rArr 4q/r^(2) + Q/r^(2) = 0`
`rArr 4q = -Q`
`:. Q = -Q/4`