Physics - Electrostatics Question with Solution | TestHub

For equilibrium of system of charges,
force produced between q and Q + force produced between Q and Q = 0



$\frac{1}{4\pi {\epsilon }_0}\frac{qQ}{{\left(r/2\right)}^2}+\frac{1}{4\pi {\epsilon }_0}\frac{QQ}{r^2}=0$

$\Rightarrow \frac{4qQ}{r^2}+\frac{QQ}{{\left(r/2\right)}^2}=0\Rightarrow q=-\frac{Q}{4}$