A point electric dipole placed at the origin has a potential given by `V(r.theta) = (pcos theta)/(4piepsilon_0 r^2)` where q is the angle made by the position vector with the direction of the dipole. Then

Options

A. Since the potential vanishes at `theta =pi/2` the electric field is zero
B. The electric field everywhere on the `theta =pi/2` plane is parallel to the plane
C. The electric field everywhere on the `theta =pi/2` plane is perpendicular to the plane
D. The electric field vanishes on the `theta = 0` line

Answer

C

Explanation

Potential due to dipole
`V(r, theta)=(Pcos theta)/(4piepsilon_0r^2)`
Electric field due to dipole
`E(r, theta)= (Psqrt(3cos^2theta+1))/(4piepsilon_0r^3)`
`vecE_("axial")= (2vecP)/(2pir^3epsilon_0),vecE_({:("equatorial"),((theta//pi//2)):})=(-vecP)/(4piepsilon_0r^3)`
Hence electric field everywhere as the `theta =pi//2` plane is perpendicular to the plane.