The locus of the points (in the `xy`-plane) where the electric field due to a dipole (dipole axis is along `x`-axis and its equatorial is along `y`-axis) is perpendicular to its axis, is

Options

A. straight line perpendicular to the axis
B. circle
C. Parabola
D. straight line having inclination `theta= tan^(-1)sqrt(2)` with the axis.

Answer

D

Explanation

For the given point
`theta+alpha= pi//2implies alpha= pi//2-theta`

As `tan alpha= (tan theta)/(2)`
`implies tan((pi)/(2)-theta)= (tan theta)/(2)implies tan theta= sqrt(2)`