First slide

Dipole

Question

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

NA

Solution

Torque $\vec{τ} = \vec{P} \times \vec{E}$
$\Rightarrow 2 (m {(\frac{d}{2})}^{2}) α = - (q . d) E \sin θ (N e g a t i v e s i g n m e a n s r e s t o r i n g t o r q u e) F o r s m a l l o s c i l l a t i o n s \sin θ ≃ θ \Rightarrow (\frac{m d^{2}}{2}) α = - (q . d) E θ \Rightarrow α = - \frac{2 q E}{m d} θ H e n c e, ω = \sqrt{\frac{2 q E}{m d}}$

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