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  • A dipole consists of two particles, one with charge Q and mass m and the other with charge -Q and mass 2 m, separated by a distance L. For small oscillations about its equilibrium position, find th

A dipole consists of two particles, one with charge Q and mass m and the other with charge -Q and mass 2 m, separated by a distance L. For small oscillations about its equilibrium position, find the angular frequency when placed in a uniform electric field E.

Option: 1

\mathrm{\sqrt{\frac{Q E}{3 m L}}}


Option: 2

\mathrm{\sqrt{\frac{3 Q E}{m L}}}


Option: 3

\mathrm{\sqrt{\frac{3 P E}{2 m L}}}


Option: 4

\mathrm{\sqrt{\frac{2 G E}{3 m L}}}


Answers (1)

best_answer

Restoring forque \mathrm{ \tau =-P E \sin \theta }
                 \mathrm{ I_{\mathrm{cm}} \cdot \alpha =-P E(\theta) }
                           \mathrm{\alpha =\frac{P E(\theta)}{I_{\mathrm{cm}}}}

On comparing with \mathrm{\alpha=-\omega^2 \theta}, we have.
                               \mathrm{\omega=\sqrt{\frac{P E}{I_{c m}}}

Here, \mathrm{P=Q L \text { and } I_{C m}=m\left(\frac{2 L}{3}\right)^2+2 m\left(\frac{L}{3}\right)^2}

                                      \mathrm{=\frac{2}{3} m c^2}

                               \mathrm{\omega=\sqrt{\frac{P E}{\frac{2}{3} m L^2}}}

                               \mathrm{\omega=\sqrt{\frac{3 P E}{2 m L^2}}}

Posted by

Pankaj Sanodiya

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