# 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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