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# 3.3: Oscillation of a Dipole in an Electric Field

Consider a dipole oscillating in an electric field (figure III.3). When it is at an angle $$\theta$$ to the field, the magnitude of the restoring torque on it is $$pE \sin \theta$$, and therefore its equation of motion is

$I\ddot \theta = -pE\sin \theta \label{1}$

where $$I$$ is its rotational inertia.

$$\text{FIGURE III.3}$$

For small angles, Equation $$\ref{1}$$ can be approximated as

$I\ddot \theta \approx -pE\theta$

and so the period of small oscillations is

$\label{3.3.1}P=2\pi\sqrt{\frac{I}{pE}}.$

Would you expect the period to be long if the rotational inertia were large? Would you expect the vibrations to be rapid if $$p \text{ and }E$$ were large? Is the above expression dimensionally correct?