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Q.
A dipole moment ‘$P$’ and moment of inertia $I$ is placed in a uniform electric field $\vec{E}$. If it is displaced slightly from its stable equilibrium position, the period of oscillation of dipole is
KCETKCET 2020Electrostatic Potential and Capacitance
Solution:
Dipole moment $= p$
electric field $= E$
centroid axis $= I$
Explanation
When displaced at an angle $\theta$ from its mean position the magnitude of restoring torque is $T =$ $- p \sin \theta$
For small angular displacement $\sin \theta \approx \theta$
$
\begin{array}{l}
T =- pE \theta \\
\alpha=\frac{ T }{ I }=-\left(\frac{ PE }{ I }\right) \theta \\
=- w ^2 \theta \\
w^2=\frac{P E}{I} \\
T =2 \pi \sqrt{\frac{ I }{ PE }} \\
\end{array}
$
(P.E $=$ moment in electric field)