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Question

A molecule with dipole moment p is placed in an electric field of strength E. Initially the dipole is aligned parallel to the field . If the dipole is to be rotated to be anti-parallel to the field , the work required to be done by an external agency is

A
2pE
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B
2pE
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C
pE
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D
2pE
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Solution

The correct option is B 2pE
Let the dipole moment be p and the external electric field strength be E.

From the data given in the question,

Initially, the dipole is along the direction of electric field

Initial Potential energy of dipole Ui=pEcosθi

Ui=pEcos0=pE

Now, the dipole is rotated and kept in a direction anti-parallel to the direction of electric field.

In this situation, Potential energy of dipole is given by

Uf=pEcosθf

Uf=pEcos180=+pE

We know that, Workdone in rotating the electric dipole W=UfUi

W=pE(pE)=2pE

Hence, option (d) is the correct answer.

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