A wheel with 10 metallic spokes each `0.5`m long is rotated with a speed of `120` rev/min in a plane normal to the horizontal component of the earth's magnetic field `H_(E )` at a place. If `H_(E )=0.4G` at the place, what is the induced emf between the axle and the rim of the wheel ? (Take , 1gauss `=10^(-4)T`.)

Explanation

`:.` Induced emf `=(d)/(dt)B.A=B((dA)/(dt))`
`=B.(pir^(2))/(T)=(1//2)omegaBr^(2)`
As, `(dA)/(dt)=(pir^(2))/(T)` and `T=2pi//omega` `( :. omega=2pif=2pi.(120)/(60)=4pi)`
`=(1//2)xx4pixx0.4xx10^(-4)xx(0.5)^(2)`
`=6.28xx10^(-5)V`
The number of spokes is immaterial because each spoke acts like a cell connected in parallel with other cells of equal emf.