TTwo small identical dipoles AB and CD,each of dipole moent p are kept at an anglre of 120 degree ai in figure.What is the resultant dipole of this combination?If this system is subjected to electric field(E) directed along +x axis what will be the magnitude and direction of torque acting on this?

Asked by Rajeev | 12th May, 2015, 03:17: PM

Expert Answer:

The two dipoles are placed at an angle 120°.
 
The dipole moment of AB is directed towards B and that of CD is directed towards C.
 
 
 
Hence, the resultant dipole moment is given as
 
begin mathsize 14px style straight R equals square root of straight p squared plus straight p squared plus 2 ppcos 120 end root equals square root of 2 straight p squared minus fraction numerator 2 straight p squared over denominator 2 end fraction end root equals straight p end style
 
When the system is subject to an electric field, there is a torque acting on the dipoles.
 
The field is directed towards X-axis. The angle COR in the above diagram will be 60°.
 
Hence, the angle between the resultant dipole moment and electric field is 90 - 60 = 30°.
 

 
Therefore, the torque on the system is
 
begin mathsize 14px style straight tau equals pEsinθ equals pEsin 30 equals pE over 2 end style
 
The direction of torque is perpendicular to both p and E.

Answered by Romal Bhansali | 12th May, 2015, 06:00: PM