# Interpenetrating charged ball and wire.

**Electricity and Magnetism**Level 5

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**

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

\( Q = 5 mC\)

\( \lambda = 3mC / m\)

\(M = 2Kg\)

\(m = 1 Kg\)

\(R = 1m\)