Question

An electric dipole of moment pvector is placed at the origin along xaxis .the angle made by electric field with x axis at a point p,whose position vector makes an angle ditha with x axis is

Answer 1

Answer:        (A) (π/3) + tan–1(√3/2)

                    from given data, diagram can be drawn as shown,

                    in Δ POS, 60° + α + (180° – θ) = 180°

                                        ∴ θ = 60 + α                                                              (1)

                    Potential at P due to dipole is

                                        v = [1 / (4π∈0)] [(P cos θ) / r2] (P : dipole moment)

                    if the field along & perpendicular to radius vector r be respectively Er & Eθ

                              Er = – (∂v / ∂r) & Eθ = (–1/r) (∂v / ∂θ)

                          ∴ Er = [(– ∂) / ∂r] [{1 / (4π∈0)} {(P cos θ / r2)] = [(2P cos θ) / (4π∈0r3)]

                              Eθ = [(– 1) / r] (∂ / ∂θ) [{1 / (4π∈0)} / (P cos θ) / r2}] [(– 1) / r3]

                                                                                          ∙ [P / (4π∈0)](– sin θ)

                    from figure tan α = (Eθ / Er) = [{(P sin θ) / (4π∈0r3)} / {2P cos θ / (4π∈0r3)}]

                                              = (1/2) tan θ

                              ∴ tan α = (1/2) × tan(π/3) = (√3 / 2)

                    from (1),

                              θ = 60 + tan–1(√3 / 2)

                                 = (π/3) + tan–1(√3 / 2)