An electric dipole is formed by two equal and opposite charges \(q\) with separation \(d\). The charges the same mass \(m\). It is kept in a uniform electric field \(E\). If it slightly rotated from its equilibrium orientation, then its angular frequency \(\omega \) is

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Answer & Solution

Correct Answer

(B) \(\sqrt {\frac{{2qE}}{{md}}} \)

Detailed explanation

Moment of inertia

\((I)=m\left(\frac{d}{2}\right)^{2} \times 2=\frac{m d^{2}}{2}\)

Now by \(\tau=I \alpha\)

\((q E)(d \sin \theta)=\frac{m d^{2}}{2} \cdot \alpha\)

\(\alpha=\left(\frac{2 \mathrm{qE}}{\mathrm{md}}\right) \sin \theta\) for small \(\theta\)

\({\Rightarrow \alpha=\left(\frac{2 \mathrm{qE}}{\mathrm{md}}\right) \theta}\)

\(\Rightarrow \) Angular frequency \(\omega = \sqrt {\frac{{2qE}}{{md}}} \)

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