$A$ point electric dipole placed at the origin has a potential given by $V(r, \theta) = \frac{p \cos \theta}{4 \pi \varepsilon_0 r^2}$,where $\theta$ is the angle made by the position vector with the direction of the dipole. Then,

• A
  since the potential vanishes at $\theta = \frac{\pi}{2}$,the electric field is zero everywhere on the $\theta = \frac{\pi}{2}$ plane.
• B
  the electric field everywhere on the $\theta = \frac{\pi}{2}$ plane is normal to the plane.
• C
  the electric field everywhere on the $\theta = \frac{\pi}{2}$ plane is along the plane.
• D
  the electric field vanishes on the $\theta = 0$ line.