A particle of mass \( \mathrm{m} \), charge \( -\mathrm{Q} \) is constrained to move along the axis of a ring of radius \( \mathrm{a} \). The ring carries a uniform charge density \( +\lambda \) along its circumference. Initially, the particle lies in the plane of
P the ring at a point where no net force acts on it. The period of oscillation of the particle when it is
W. displaced slightly from its equilibrium position is
- (A) \( \mathrm{T}=4 \pi \sqrt{\frac{\varepsilon_{0} \mathrm{ma}^{2}}{\lambda \mathrm{Q}}} \)
(B) \( \mathrm{T}=2 \pi \sqrt{\frac{2 \varepsilon_{0} \mathrm{ma}^{2}}{\lambda \mathrm{Q}}} \) (C) \( \mathrm{T}=2 \pi \sqrt{\frac{4 \varepsilon_{0} \mathrm{ma}^{2}}{\lambda \mathrm{Q}}} \)
(D) \( \mathrm{T}=2 \pi \sqrt{\frac{\varepsilon_{0} \mathrm{ma}^{2}}{2 \lambda \mathrm{Q}}} \)
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