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Two smallidentical electric dipoles AB and CD, each of dipole moment vecp are kept at an angle of 120^(@) to each other in an external electric field vecE pointing along the x-axis as shown in the figure. Find the (a) dipole moment of the arrangement, and (b) magnitude and direction of the net torque acting on it. |
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Answer» Solution :As shown let two identical electric dipoles AB and CD are kept at an ANGLE `theta=120^(@)`, where their dipole MOMENTS have magnitude `|vecp_(A)|=|vecp_(C )|=p` The resultant dipole moment of the COMBINATION `|vecp_(R)|=2p "cos"(theta)/(2)=2p" cos"(120^(@))/(2)=2p" cos"60^(@)=2p xx (1)/(2)=p`. and the resultant dipole moment subtends an angle `(theta)/(2)=60^(@)` from either of two dipoles `vecp_(A) or vecp_(B)`. THEREFORE, `vecp_(R )` subtends an angle `30^(@)` from +X direction.  If the system is SUBJECTED to electric field `vecE` directed along +X direction, the torque acting on the system is `vec tau=vecp_(R ) xx vecE` Thus, the magnitude of torque is `|vectau|=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 `vecE`. |
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