Question

Two small identical electrical dipoles $AB$ and $CD$ each of dipole moment $\overrightarrow{p}$ are kept at an angle of ${120}^o$ as shown in the figure. What is the resultant dipole moment of this combination ? If this system is subjected to electric field $\left(\overrightarrow{E}\right)$ directed along $+X$ direction, what will be the magnitude and direction of the torque acting on this?

Answer 1

The two dipoles are placed at an angle of ${120}^0$

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

$\begin{array}{c}R=\sqrt{P^2+P^2+2PP\cos 120}\\ =\sqrt{2p^2-\frac{2p^2}{2}}\\ =p\end{array}$

when the system is subjected to an electric field ,there is a to sque

acting on the dipole.

The field IS directed towards X-axis .The angle COR in the

above diagram will be ${60}^0$.

Hence,the angle between the resultant dipole moment and electric field

is ${90}^0-{60}^0={30}^0$

$\therefore$ torque on the system is

$\tau =PE\sin \theta =PE\sin 30=\frac{PE}{2}$

The direction of torque is perpendicular to both P and E