\(\Rightarrow \mathrm{k} \frac{\mathrm{Qq}}{\left(\frac{\ell}{2}\right)^{2}}+\mathrm{k} \frac{4 \mathrm{q}^{2}}{\ell^{2}}=0\)

where \(\mathrm{k}=\frac{1}{4 \pi \varepsilon_{0}}\)

\(\Rightarrow 4 \mathrm{Q} \mathrm{q}+4 \mathrm{q}^{2}=0\)

\(\Rightarrow \mathrm{Q}=-\mathrm{q}\)