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An electric dipole of moment $p$ is placed in an electric field of intensity $E$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta=90^{\circ}$, the torque and the potential energy of the dipole will respectively be
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Verified Answer
The correct answer is:
$p E \sin \theta,-p E \cos \theta$
Here, Torque $\tau=p E \sin \theta$
Potential energy of the dipole
$\begin{aligned}
U & =-\int \tau d \theta \\
& =-\int_{\pi / 2}^0 p E \sin \theta d \theta=p E[\cos \theta-0] \\
& =-p E \cos \theta
\end{aligned}$
Potential energy of the dipole
$\begin{aligned}
U & =-\int \tau d \theta \\
& =-\int_{\pi / 2}^0 p E \sin \theta d \theta=p E[\cos \theta-0] \\
& =-p E \cos \theta
\end{aligned}$
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