An electric dipole of moment $\vec{P}$ is lying along a uniform electric field $\overrightarrow{\mathrm{E}}$…

An electric dipole of moment $\vec{P}$ is lying along a uniform electric field $\overrightarrow{\mathrm{E}}$. The work done in rotating the dipole through $\frac{\pi^c}{3}$ is $\left[\sin 30^{\circ}=\cos 60^{\circ}=0 \cdot 5, \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2\right]$
  1. 3 pE
  2. $\sqrt{2} \mathrm{pE}$
  3. pE
  4. $\frac{\mathrm{pE}}{2}$

Solution

The P.E. of a dipole in an electric field is $\mathrm{W}=-\mathrm{pE} \cos \theta$
When $\theta=0^{\circ}$, $\mathrm{W}_1=-\mathrm{pE} \cos (0)=-\mathrm{pE}$
When $\theta=\frac{\pi}{3}=60^{\circ}$, $\mathrm{W}_2=-\mathrm{pE} \cos \left(60^{\circ}\right)=\frac{-\mathrm{pE}}{2}$ $\begin{aligned} \therefore \quad \text { Work done }=\mathrm{W}_2-\mathrm{W}_1 & =-\frac{\mathrm{pE}}{2}-(-\mathrm{pE}) \\ & =\frac{\mathrm{pE}}{2} \end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 1)

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