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Question
An electric dipole is held in a uniform electric field.
(i) Show that the net force acting on it is zero.
(ii) The dipole is aligned parallel to the field. Find the work done in rotating it through the angle of 180°.
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Solution
(i) Consider an electric dipole consisting of two equal and opposite point charges, −q at A and + q at B, separated by a small distance 2a.
AB = 2a, having dipole moment
`|vecP| = q(2a)`
Let this dipole be held in a uniform external electric field `vecE`at an angle θ with the direction of `vecE`
Force on charge −q at A= − q ,`vecE` in a direction opposite to `vecE`
Force on charge +q at B = +q ,`vecE` along the direction of `vecE`
Net force on the dipole = qE − qE = 0
(ii) Work done on dipole, W = ΔU = pE (cos θ1 − cos θ2)
W = pE (cos0° − cos180°)
W = 2pE
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