An electric dipole is placed at the origin as shown in figure. A, B, C and D are four points where the electric fields are perpendicular to the dipole axis. Then which of the following figures is correct?

At any arbitrary point P defined by (γ, θ), direction of electric field E→ is defined by tan∝=12tanθ Evidently when E→ is perpendicular to P→, θ+α=900,∴tan90p−θ=12tanθ⇒tanθ=±2∴θ=tan−12,π−tan−12,π+tan−12,2π−tan−12hence points A, B, C and D symmetrically lie in the 1st, 2nd, 3red and 4th quadrants respectively. Electric fields at C and D are mirror images of those at A and B.