Question

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