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Q.

A non-conducting ring of mass m and radius R is charged as shown. The charge density charge per unit length is λ. It is then placed on a rough non-conducting horizontal surface time t=0, a uniform electric field E=E0i^ is switched on and the ring starts rolling without sliding. Determine the friction force (magnitude and direction) acting on the ring when its start moving.

A non - conducting ring of mass m and radius R is charged as shown. The charged  density i.e. charge - Sarthaks eConnect | Largest Online Education Community

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a

2λRE0

b

5λRE0

c

8λRE0

d

λRE0

answer is C.

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Detailed Solution

dF=λ(Rdθ)E0

Perpendicular distance between two of opposite pairs of dF will be
r=2Rsinθ  dτ=dFr=2λR2E0sindθ  τ=0π\2d2τ=2λR2E0
These pairs of forces will not provide net force,

A nonconducting ring of mass m and radius R, with charge per unit

Let force of friction on ring is f in forward direction.

For pure rolling to take place,
a=Rα   or   fm=Rτ-fRmR2
or f=τR-f   or   f=τ2R=λRE0

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