Q.

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=-B0k∧r≤a;a

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a

-2B0πa2rmRk∧

b

-B0πa2r3mRk∧

c

B0πa2λmRk∧

d

-B0πa2λmRk∧

answer is D.

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Detailed Solution

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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