A charge Q is placed at the centre of the line joining two charges q and q. For the system of three charges to be in equilibrium, what should be the value of Q?

Explanation

Here Q is in equilibrium as it is at the centre and net force on it is zero. For equilibrium of q, net force on it is zero
`(1)/(4pi in_(0))(Qq)/((r//2)^(2)) + (1)/(4pi in_(0)) (q^(2))/(r^(2)) = 0`
where r is separation between q and q `rArr Q = (-q)/(4)`