c
In equilibrium, \(\mathrm{F}_{\mathrm{e}}=\mathrm{T} \sin \theta\)

\(\mathrm{mg}=\mathrm{T} \cos \theta\)

\(\tan \theta=\frac{F_{e}}{m g}=\frac{q^{2}}{4 \pi \epsilon_{0} x^{2} \times m g}\)

\(\therefore x = \sqrt {\frac{{{q^2}}}{{4\pi {\varepsilon _0}\,\tan \,\theta \,mg}}} \)

Electric potential at the centre of the line

\(V=\frac{k q}{x / 2}+\frac{k q}{x / 2}=4 \sqrt{k m g / \tan \theta}\)