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A wheel with 10 metallic spokes each 0.5...

A wheel with 10 metallic spokes each 0.5 m long, is rotated with a speed of 120 rpm. Please of the wheel is normal to earth's magnetic field at that place. If the magnitude of the field is 0.40 G, what is the induced emf between the axle and rim of the wheel?

Text Solution

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Here, no of spokes, `N = 10`
length of the spoke, `l = radius, r = 0.5 m`,
Frequency, `n = 120` rpm `= 2 rps`.
`B = 0.4` gauss `= 0.4 xx 10^(-4)` tesla, e = ?
As the wheel rotates, linear velocity of spoke end at the `rim = r omega` and linear velocity of spoke end at the axle `= 0`
`:.` Average linear velocity, `upsilon = (0 + r omega)/(2) = (1)/(2) r omega`
As e.m.f. induced acorss the ends of each spoke
`e = B upsilon l = B. ((1)/(2) r omega) . l`
` = B (1)/(2) r 2 pi n l = B r pi n l`
`e = 0.4 xx 10^(-4) xx 0.5 xx (22)/(7) xx 2 xx 0.5`
`= 6.28 xx 10^(-5)` volt
As all spokes are connected in parallel between the axle and the rim, therefore net e.m.f. induced is the same as that induced acorss the ends of each spoke.
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