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A ring of mass 4 kg is uniformly charged with a linear charge density λ = 4 C cm - 1 and kept on a rough horizontal surface with a friction coefficient of μ = π 4 . A time-varying magnetic field B = B 0 t 2 is applied in a circular region of radius a a < r perpendicular to the plane of the ring as shown in the figure. Find out the time when the ring just starts to rotate on the surface. (take a = 5 cm , g = 10 m s -

Correct answer

4

Step-by-step solution

Induced electric field, E ( 2 &#960;r ) = d&#966; dt E = &#960;a 2 2 B 0 t 2 &#960;r Torque due to field about centre of ring, &#964; 1 = ( qE ) r = ( &#955; ( 2 &#960;r ) ) 2 &#960;a 2 B 0 t 2 &#960;r r The ring starts rotating when, &#964; due to electric field = &#964; due to friction. &#964; 1 = &#956;mg r Solving, t = &#956;mg 2 &#960;a 2 B 0 &#955; = 4 &#160; s .

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