A non-conducting ring of mass m = 4 kg and radius R = 10 cm has a charge Q = 2 C uniformly distributed over its circumference. The ring is placed on a rough horizontal surface such that the plane of the ring is parallel to the surface. A vertical magnetic field B = 4 t 3 T is switched on at t = 0 . At t = 5 s ring starts to rotate about the vertical axis through the centre. The coefficient of friction between the ring and the surface is found to be k 24 . Then the value of k is

Question

A non-conducting ring of mass m = 4 kg and radius R = 10 cm has a charge Q = 2 C uniformly distributed over its circumference. The ring is placed on a rough horizontal surface such that the plane of the ring is parallel to the surface. A vertical magnetic field B = 4 t 3 T is switched on at t = 0 . At t = 5 s ring starts to rotate about the vertical axis through the centre. The coefficient of friction between the ring and the surface is found to be k 24 . Then the value of k is,

MARKS App · Accepted Answer

The induced electric field at the periphery of the ring is E = R 2 d B d t ⇒ E = R 2 12 t 2 = 6 R t 2 When the ring is about to slip, q E R = μ m g R ⇒ 6 q R t 2 = μ m g ⇒ μ = 6 q R t 2 m g = 3 4 = 18 24 k = 18

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