A charge q is placed at the centre of the line joining two equal charges Q. 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

C

Explanation

`F_(Q) = (1)/(4pi epsi+(0)) .(Qq)/(r^(2)) + (1)/(4pi epsi_(0)).(Q^(2))/(4r^(2))`
For equilibrium `F_(Q) = 0 rArr (Qq)/(r^(2)) + (Q^(2))/(4r^(2)) = 0 or q + (Q)/(4) = 0 or q = (Q)/(4)`