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A line charge ,λ per unit length is pasted uniformly on to the rim of a wheel of mass m and radius R. The wheel has light non-conducting spokes and is free to rotate about a vertical axis as shown in figure. A uniform magnetic field extends over a radial region of radius r given by B=-B0kra;a<R = 0 (otherwise). What is the angular velocity of the wheel when this field is suddenly switched off?

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a
-2B0πa2rmRk∧
b
-B0πa2r3mRk∧
c
B0πa2λmRk∧
d
-B0πa2λmRk∧

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detailed solution

Correct option is D

Induced electric field (in clockwise sense):E=a22RdBdtI ω=∫τ dt⇒mR2ω=∫qERdt=∫qa22RdBdtRdt=λ2πR2Ra2R∫dB⇒ω=B0πa2λmR⇒ω→=-B0πa2λmRk∧(because clockwise sense)

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