An electron dipole of moment `vecp` is placed in a uniform electric field `vecE` . Write the 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.

Explanation

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^(@)` , which is shown as below :