Torque acting on a electric dipole in uniform electric field

*“Torque acting on a electric dipole in uniform electric field”:

Consider an electric dipole AB made up of two point charges  -q and +q of length 2a.  The dipole is placed in a uniform electric field such that it makes an angel θ with the direction of electric field . As a result of couple of force (+q.E) and (-q.E) . The torque acting on the dipole.

“Measurement”— Torque is the product of magnitude of either force acting on a dipole and perpendicular distance between two forces.  it is denoted by τ. and it is vector quantity the direction of it is perpendicular to the plane containing vector p and vector B such that along the direction of rotational axis.

In right ΔABC, sinθ  = BC/AB
                            sinθ  = BC/2a
                             BC    =  2a×sinθ


According to the definition :
Torque, τ = Force× per. distance
                τ = F × BC
                τ = q. E ×  2a×sinθ
                 τ = 2a.q.Esinθ
[since, electric dipole moment,P = 2a.q]

                  τ = P. Esinθ  Nm
     

 ×

pE sin ,

τ= × E→