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An electron dipole of moment vecp is placed in a uniform electric field vecE . Writethe expression for the torque vectau experienced by the dipole.Identify two pairs of perpendicular vectors in the expression . Shown diagrammatically the orientation of the dipole in the field for which the torque is (i)the maximum , (ii)Half the maximum value , (iii)Zero. |
Answer» Solution :Let a DIPOLE AB is situated in the uniform electric field `vecE`, The torque on dipole is , `vectau=vecpxxvecE`,where `vecp`is dipole moment from the line charge . Also E and unit vector n normal to curved suface are in the same direction , So `theta=0^(@)`.Contribution of curved suface of cylinder towards electric flux will be zero (null) Two pairs of PERPENDICULAR vectors are `vectau andvecpandvectauandvecE`in the expression . (i)The torque is the maximum , when `theta=90^(@)`which is shown in following DIAGRAM :  (ii)The maximum value of torque =pE The HALF of maximum value `=(pE)/(2)` So , we have `pEsintheta=(pE)/(2)` or`sintheta=(1)/(2)` or `theta=30^(@)` The arrangement is as given below or shown as below :  (iii) For zero value of torque , `sintheta=0ortheta=0^(@)` , whichis shown as below : 
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