A short electric dipole is situated at the origin of coordinate axis with its axis along x-axis and equator along y-axis. It is found that the magnitudes of the electric intensity and electric potential due to the dipole are equal at a point distance `r=sqrt(5) m` from origin. Find the position vector of the point in first quadrant.

Explanation

`:' |E_(P)|=|V_(P)| :. (kp)/r^(3) sqrt(1+3 cos^(2) theta)=(kp cos theta)/r^(2) rArr 1+3 cos^(2) theta=5 cos^(2) theta rArr cos theta=1/sqrt(2)rArr theta=45^(@)`
Position vector `vec(r)` of point P is `vec(r)=sqrt(5/2) (hat(i)+hat(j))`