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,
Asince the potential vanishes at $\theta=\frac{\pi}{2}$, the electric fieeld is zero everywhere on the $\theta=\frac{\pi}{2}$ plane
Bthe electric fi,eld everywhere on the $\theta=\frac{\pi}{2}$, plane is normal to the plane
Cthe electric field everywhere on the $\theta=\frac{\pi}{2}$, plane is along the plane
Dthe electric field vanishes on the $\theta=0$ line
KVPY 2009, Medium
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Cthe electric field everywhere on the $\theta=\frac{\pi}{2}$, plane is along the plane
c (c)
A dipole and its field an axis and equatorial line are shown in above figure. Clearly at $\theta=\frac{\pi}{2}$ plane, electric field is along the plane. So, option $(c)$ is correct.
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