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 .


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

  • \( Q = 5 mC\)

  • \( \lambda = 3mC / m\)

  • \(M = 2Kg\)

  • \(m = 1 Kg\)

  • \(R = 1m\)


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