A line charge I per unit length is pasted uniformly onto the rim of a wheel of mass m and radius R. The wheel has light non-conducting spokes and is free to rotate about avertical axis as shown in figure. A uniform magnetic field B exists as shown in figure. What is the angular velocity of the wheel when the field is suddenly switched off?

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2πλa2BmR

πλa2BmR

3πλa2BmR

πλa2B2mR

answer is B.

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Detailed Solution

τ=ΔLΔt=IωΔt=mR2ωΔt but τ=λ(2πR)ER=λπa2ΔBΔtR=λπa2BRΔt⇒ mR2ωΔt=λπa2BRΔt⇒ω=λπa2BmR

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