Charges 4Q, q and Q are placed along x-axis positions x=0, x=`(l)/(2)` and x=l respectively. The value of q so that the force on charge Q is zero is

Options

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

Explanation

Net force on charge Q due to 4Q and q is given by
`F = (1)/(4 pi in_(0)).(4Q^(2))/(l^(2))+(1)/(4pi in_(0)). (qQ)/(((l)/(2))^(2))`

F = 0
`therefore (4Q^(2))/(l^(2)) = -(4Qq)/(l^(2))` or q=-Q