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A bicycle wheel with metal spokes of 1 m...

A bicycle wheel with metal spokes of 1 m long rotates in Earth's magnetic field. The plane of the wheel is perpendicular to the horizontal component of Earth's field of `4xx10^(-5)T.` If the emf induced across the spokes is 31.4mV, calculate the rate of revoution of the wheel.

Text Solution

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Given : Length of metal spokes of a bicycle wheel = 1 m
`"Area"=pi^(2)=3.14xx1xx1=3.14m^(2)`
Horizontal component of earth's magnetic field `B=4xx10^(-5)T`
Induce emf across to spokes e = 31.4 mV
To find :
Rate of revolution of wheel `omega=?`
Formula :
`e=NABomegasintheta" "theta=90^(@),N=1`
Solution :
`omega(e)/(AB)=(31.4xx10^(-3))/(3.14xx4xx10^(-5))=(10)/(4)xx10^(2)`
`omega=250" revolutions "//" second. "`
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