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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 fieeld is zero everywhere on the $\theta=\frac{\pi}{2}$ plane
• B
  the electric fi,eld everywhere on the $\theta=\frac{\pi}{2}$, plane is normal to the plane
• ✓
  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