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  4. An electric dipole of moment p is Iying along a uniform electric field E. The work done in rotating the dipole by 90° is

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Q. An electric dipole of moment $p$ is Iying along a uniform electric field $E$. The work done in rotating the dipole by $90^{\circ}$ is

Haryana PMTHaryana PMT 2008Electric Charges and Fields

Solution:

When an electric dipole is placed in an electric field $E$,
a torque $\tau=p \times E$ acts on it.
This torque tries to rotated the dipole through an angle $\theta$.
If the dipole is rotated from an angle $\theta_{1}$ to $\theta_{2}$,
then work done by external force is given by
$W=p E\left(\cos \theta_{1}-\cos \theta_{2}\right)$
Putting $\theta_{1}=0^{\circ}, \theta_{2}=90^{\circ}$
in the Eq. (i), we get
$W=p E\left(\cos 90^{\circ}-\cos 90^{\circ}\right)$
$= pE (1-0)$
$= pE$