Like a Rolling Stone!

The figure shows a non-conducting, non-uniformly charged ring with linear charge densities \(\lambda\) and \(- \lambda\), mass \(m\) and radius \(R\). This ring is placed on a rough horizontal surface and a horizontal electric field \(\vec{E}\) is switched on.

If at some instant, the ring is in the position shown above and is rolling without slipping, find the minimum coefficient of friction \(\mu_{min}\) required.

Details & Assumptions

  1. A uniform gravitational field \(|\vec{g}| = 10 ms^{-2}\) acts downward.
  2. \(\lambda = \dfrac{\pi}{100} Cm^{-1}\)
  3. \(m = 1.5 kg\)
  4. \(R = 0.15 m\)
  5. \(|\vec{E}| = 1000 NC^{-1}\)

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