Two small identical electrical dipoles AB and CD each of dipole moment 'p' are kept at an angle of ` 120 ^(@) ` as shown in What is the resultant dipole moment of this combination ? If this system is subjected to electric field.
` oversetto E` directed along +X direction ,what will be the magnitude and direction of the torque acting on this?
` (##U_LIK_SP_PHY_XII_C01_E09_029_Q01.png" width="80%">

Explanation

As shown in let two identical electric dipoles AB and CD are kept at an angle ` theta= 120 ^(@) ` ,where their dipole moment have magnitude
` " "| oversetto (p_A) |=|(oversetto p_C)| =p`
The resultant dipole moment subtend an angle ` (theta)/(2) = 60 ^(@) ` from either of two dipoles ` oversetto (p_A) or oversetto (p_B) ` Therefore `oversetto (p_R) ` subtend an angle `30^(@) ` from +X direction
If the system is subjected to electric field `oversetto E ` directed along +X direction, the torque acting on the system is
` oversetto tau = oversetto (p_R) xx oversetto E `
Thus ,the magnitude of torque is ` | oversetto (tau)| =pE sin 30^(@) =(1)/(2) pE ` and the torque is directed into the plane of paper i.e., the torque tends to align the system along the direction of electric field `oversetto E `
` (##U_LIK_SP_PHY_XII_C01_E09_029_S01.png" width="80%">