Dipole in a Uniform External Field

Let us consider a permanent dipole of dipole moment p in a uniform external electric field E. Then, a force qE and -qE act on q and -q respectively. The net force on the dipole is zero due to the uniform electric field E. However, the charges are separated, so the forces act at different points, resulting in a torque on the dipole. So, the magnitude of the torque will be

Firstly, we will draw AM ⊥ XY 
Then, In Δ AMO
Sinθ = Perpendicular / Hypotenuse 
Sinθ = AM / AO
AM  = AO Sinθ
AM  = a sinθ ( AM is the perpendicular distance ⊥r, which is between the Force and the axis of rotation. )
Similarly, In Δ BDO, BD = a sinθ

As, we also know that ( τ = ⊥r F sinθ or τ = ⊥r x F ) and ( F = q E ) so,
Magnitude of torque ( τ ) = τ₁ + τ₂
                                              = q E a sinθ + q E a sinθ
                                              = 2 q E a sinθ
                                              = p E sinθ     
                                              = p x E