A cycle wheel 12 metalli spokes each 0.2 m long. It make 60 revolutions in 1 minute in a phane normal to earth's magnetic field of `0.4 xx 10^(-4)` T. Calculate the induced e.m.f. between the axle and rim of the wheel.

Explanation

Here, `n = 12, l = 0.2 m`.
`v = 60` rpm `= (60)/(60) = 1` rps
`B = 0.4 xx 10^(-4) T, e = ?`
`upsilon = r omega = r (2 pi b) = 2 pi v l`
`= 2 xx 3.14 xx 1 xx 0.2 = 1.256 ms^(-1)`
As the spoke rotates about the axle, therefore linear velocity of each spoke at the axle `upsilon_(1) = 0`.
And linear velocity of each spoke at the rim,
`upsilon_(2) = 1.256 m//s`.
Average velocity of spoke `= (upsilon_(1) + upsilon_(2))/(2)`
`= (0 + 1.256)/(2) = 0.628 m//s`
As all spokes are in parallel, therefore, e.m.f. induced two ends of every spoke `= e = B upsilon l`
`= 0.4 xx 10^(-4) xx 0.628 xx 0.2 = 5 xx 10^(-6) V`