Question

A and B are two points on the axis and the perpendicular bisector respectively of an electric dipole. A and B are far away from the dipole and at equal distances from it. The fields at A and B are Vector E_A and Vector E_B.

(a) Vector E_A = Vector E_B

(b) Vector E_A = 2 Vector E_B

(c) Vector E_A = -2 Vector E_B

(d) |E_B| = 1/2 |E_A|, and Vector E_B is perpendicular to Vector E_A

Answer 1

Correct Answer is: (c) Vector E_A = -2 Vector E_B

E_P = k 2p/r³ √(3cos² θ + 1).

V_P =  k 2p/r² cos θ.

For A, θ  = 0, for B, θ  = 90°, r = OA = OB, tan ϕ = 1/2 tan θ.

θ + ϕ = 90°

or tan(90 - θ) = 1/2 tan θ

or 2cot θ = tan θ

or tan θ = √2.