A wheel of 20 metallic spokes, each 40 text{ | vedclass

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Question

(A) The induced emf $(e)$ across a single spoke of length $L$ rotating with angular velocity $\omega$ in a magnetic field $B$ is given by the formula:

Vedclass · Accepted Answer

$192 \pi 	imes 10^{-7} 	ext{ V}$

Vedclass · Answer

(A) The induced emf $(e)$ across a single spoke of length $L$ rotating with angular velocity $\omega$ in a magnetic field $B$ is given by the formula: $e = \frac{1}{2} B \omega L^2$. Given: $B = H_{e} = 0.4 	ext{ G} = 0.4 	imes 10^{-4} 	ext{ T}$. $L = 40 	ext{ cm} = 0.4 	ext{ m}$. Frequency $f = 180 	ext{ rev/min} = \frac{180}{60} 	ext{ rev/s} = 3 	ext{ Hz}$. Angular velocity $\omega = 2 \pi f = 2 \pi 	imes 3 = 6 \pi 	ext{ rad/s}$. Substituting these values: $e = \frac{1}{2} 	imes (0.4 	imes 10^{-4}) 	imes (6 \pi) 	imes (0.4)^2$. $e = 0.2 	imes 10^{-4} 	imes 6 \pi 	imes 0.16$. $e = 1.2 \pi 	imes 10^{-4} 	imes 0.16 = 0.192 \pi 	imes 10^{-4} 	ext{ V}$. $e = 192 \pi 	imes 10^{-7} 	ext{ V}$. Since all spokes are connected in parallel between the axle and the rim, the total induced emf remains the same as that of a single spoke.

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