A thin fixed ring of radius \( 1 \mathrm{~m} \) has a positive char...

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A thin fixed ring of radius \( 1 \mathrm{~m} \) has a positive charge \( 1 \times 10^{-5} \mathrm{C} \) uniformly distributed over it. A particle of mass \( 0.9 \mathrm{~g} \) and having a negative charge of \( 1 \times 10^{-6} \mathrm{C} \) is placed on the axis at a distance of \( 1 \mathrm{~cm} \) from the centre of the ring. Show that the motion of the negatively charged particle is
\( \mathrm{P} \) approximately simple harmonic. Calculate the time period

W of oscillations.
\( (1982,5 \mathrm{M}) \)
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