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An electric dipole of dipole moment $p$ is aligned parallel to a uniform electric field $E$. The energy required to rotate the dipole by $90^{\circ}$ is
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Verified Answer
The correct answer is:
$p E$
Given $\theta_{1}=0^{\circ}, \theta_{2}=90^{\circ}$
The energy required to rotate the dipole from angle $\theta_{1}$ to $\theta_{2}$ is equal to work done.
$$
\text { i.e., } \begin{aligned}
E=W &=-p E\left(\cos \theta_{2}-\cos \theta_{1}\right) \\
&=-p E\left(\cos 90^{\circ}-\cos 0^{\circ}\right) \\
&=-p E(0-1)=p E
\end{aligned}
$$
The energy required to rotate the dipole from angle $\theta_{1}$ to $\theta_{2}$ is equal to work done.
$$
\text { i.e., } \begin{aligned}
E=W &=-p E\left(\cos \theta_{2}-\cos \theta_{1}\right) \\
&=-p E\left(\cos 90^{\circ}-\cos 0^{\circ}\right) \\
&=-p E(0-1)=p E
\end{aligned}
$$
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