Two small identical electric dipoles AB and CD, each of diople moment p are kept at an angle of `120^(@)` as shown in Figure. What is the resultant dipole moment of this combination ?
If this system is subjected to electric field `vec((E))` directed along `+ X` direction, what will be the magnitude and direction of the torque acting on this ?

Explanation

In fig. two dipole moments `p_(1)` along BA and `p_(2)` along DC act at an angle of `120^(@)`. The resultant dipole moment is along OR
`P_(R) = sqrt(p_(1)^(2) +p_(2)^(2) + 2p_(1) p_(2) cos 120^(@))`
`= sqrt(p^(2) + p^(2) + 2pp (- (1)/(2))) = p`
As `/_AQR = 60^(@)`, therefore,
`/_XQR = theta = 90^(@) - 60^(@) = 30^(@)`
`tau = pE sin theta = pE sin 30^(@) = pE//2`
The direction of torque is perpendicular to `vec(p) and vec(E) , i..e.,` perpendicular to plane of paper and outwards, Fig.