The line $AA^{\prime}$ lies on a charged infinite conducting plane which is perpendicular to the plane of the paper. The plane has a surface charge density $\sigma$. $B$ is a ball of mass $m$ with a like charge of magnitude $q$. $B$ is connected by a string to a point on the line $AA^{\prime}$. The tangent of the angle $\theta$ formed between the line $AA^{\prime}$ and the string is:

• A
  $\frac{q \sigma}{2 \varepsilon_{0} m g}$
• B
  $\frac{q \sigma}{4 \pi \varepsilon_{0} m g}$
• C
  $\frac{q \sigma}{2 \pi \varepsilon_{0} m g}$
• D
  $\frac{q \sigma}{\varepsilon_{0} m g}$