Question

A point electric dipole placed at the origin has a= potential given by$V\left(r ,\theta\right)=\frac{p \cos \theta}{4\pi\varepsilon_{o}R^{2}}$ , 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 Jt 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

Answer 1

Answer: (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.