In the given figure,two tiny conducting balls of identical mass $m$ and identical charge $q$ hang from non-conducting threads of equal length $L$. Assume that $\theta$ is so small that $\tan \theta \approx \sin \theta$,then for equilibrium,$x$ is equal to:

• A
  ${\left( {\frac{{{q^2}L}}{{2\pi {\varepsilon _0}mg}}} \right)^{\frac{1}{3}}}$
• B
  ${\left( {\frac{{q{L^2}}}{{2\pi {\varepsilon _0}mg}}} \right)^{\frac{1}{3}}}$
• C
  ${\left( {\frac{{{q^2}{L^2}}}{{4\pi {\varepsilon _0}mg}}} \right)^{\frac{1}{3}}}$
• D
  ${\left( {\frac{{{q^2}L}}{{4\pi {\varepsilon _0}mg}}} \right)^{\frac{1}{3}}}$