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An electric dipole of dipole moment vec(...

An electric dipole of dipole moment `vec(p)` is placed in a uniform electric field `vec(E )`. Write the expression for the torque `vec tau` experienced by the dipole. Identify two pairs of perpendicular vectors in the expression. Show diagrammatically the orientation of the dipole in the field for which the torque is (i) maximum and (ii) half the maximum value, and (iii) zero.

Text Solution

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Let a dipole AB is situated in the uniform electric field `vecE`.

The torque on dipole is,
`vectau=vecp xx vecE`, where `vecp` is dipole moment.
Two pairs of perpendicular vectors are `vectau and vecp and vectau and vecE` in the expression.
(i) The torque is the maximum, when = 90° which is shown in following diagram:

The maximum value of torque = pE
(ii) The half of maximum value `= (pE)/(2)`
So, we have pE `sin theta=(pE)/(2)`
or `sin theta =(1)/(2) or theta =30^(@)`
The arrangement is shown as below:

(iii) For zero value of torque, sin `theta=0 or theta=0^(@)`, which is shown below:
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