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Question

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 earth's magnetic field Bh at a place. If Bh=0.4 G at the place, what is the induced emf between the axle and the rim of the wheel? Note that 1 G=104T?

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Solution

Given,
A wheel with 10 metallic spokes.
Length of metallic spoke =0.5 m
Angular speed of the wheel =120 rev/min
Earth's magnetic field, B=0.4G
The area covered by an angle 4θ.
A=πr2θ2π=r22θ

The induces emf,
E=ϕdt=d(BA)dt

=Br22dϕdt=Br22ω

v=120rev/min=2rev/s

ω=2πr=4πrad/s

r=0.5 m

B=0.4G=0.4×104T

Therefore,
Induced emf is given by,
E=12Br2ω

E=2π×2×0.4×104×(0.52)2

E=6.28×105V
Each spoke will act as a parallel source of emf.
Hence, the emf will be 0.628 mV.

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