# Interpenetrating charged ball and wire.

Consider a very long non-conducting wire carrying uniform charge per unit length $$\lambda$$, and mass $$M$$ , and a non-conducting ball of radius $$R$$ and mass $$m$$ carrying uniformly distributed charge $$- Q$$ . The ball can be treated as a charged cloud, i.e. the wire is free to penetrate through the ball without friction. Clearly, $$x=0$$ is the equilibrium position. Find the frequency(in $$sec^{-1}$$) of small oscillations to the nearest integer .

Details

• $$\frac{1}{4 \pi \epsilon_{0}} = 9 \times 10^9 Nm^2/C^2$$

• $$Q = 5 mC$$

• $$\lambda = 3mC / m$$

• $$M = 2Kg$$

• $$m = 1 Kg$$

• $$R = 1m$$

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