A boy is playing with the empty rim of a cycl | vedclass

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(A) The radius of the rim is $R = 40 \, cm = 0.4 \, m$. The angular speed is $\omega = 20 \, rad \, s^{-1}$.When a metal rim rolls on a horizontal sur

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Zero

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(A) The radius of the rim is $R = 40 \, cm = 0.4 \, m$. The angular speed is $\omega = 20 \, rad \, s^{-1}$.When a metal rim rolls on a horizontal surface, the velocity of the center of mass is $v = R\omega = 0.4 	imes 20 = 8 \, m/s$.The induced e.m.f. in a conductor moving in a magnetic field is given by $\varepsilon = \int (\vec{v} 	imes \vec{B}) \cdot d\vec{l}$.For a rolling rim, the net flux through the loop does not change, or alternatively, the motional e.m.f. generated across the diameter moving through the Earth's magnetic field cancels out due to symmetry.Specifically, for a rim rolling along the North-South direction, the vertical component of the Earth's magnetic field $(B_V)$ is perpendicular to the plane of the rim, but since the rim is moving in its own plane, no flux is cut by the rim itself.The horizontal component $(B_H)$ is parallel to the ground. As the rim rolls, the induced e.m.f. across any diameter is zero because the potential difference generated in one half of the rim is exactly balanced by the other half.Therefore, the net induced e.m.f. in the rim is $0$.

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