Like a Rolling Stone!

The figure shows a non-conducting, non-uniformly charged ring with linear charge densities λ\lambda and λ- \lambda, mass mm and radius RR. This ring is placed on a rough horizontal surface and a horizontal electric field E\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 μmin\mu_{min} required.

Details & Assumptions

  1. A uniform gravitational field g=10ms2|\vec{g}| = 10 ms^{-2} acts downward.
  2. λ=π100Cm1\lambda = \dfrac{\pi}{100} Cm^{-1}
  3. m=1.5kgm = 1.5 kg
  4. R=0.15mR = 0.15 m
  5. E=1000NC1|\vec{E}| = 1000 NC^{-1}

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