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A nonconducting ring of mass m and radiu...

A nonconducting ring of mass m and radius R, with charge per unit length `lambda` is shown in fig. It is then placed on a rough nonconducting horizontal plane. At time t=0, a uniform electric field `vecE =E_(0)hati` is switched on and the ring starts rolling without sliding. Determine the friction force (magnitude and direction ) acting on the ring.

Text Solution

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The correct Answer is:
`2 lambdaRE_(0) hat(i)`
`underset(pi/2)overset(0)(int)2(lambdaRd theta)xxE_(0)R cos theta=FxxR`
`2lambdaR^(2)E_(0)underset(0)overset(pi/2)(int)cos theta d theta=2lambdaR^(2)E_(0)=FR`
`rArr F=2lambdaRE_(0)`
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