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Question

A wheel with 10 metallic spokes each 0.5m long is rotated with a speed of 120 rev/min in a plane normal to the earth's magnetic field at the place.If the magnitude of magnetic field is 0.4G, what is the induced emf between the axle and the rim of the wheel ?


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Solution

Step 1. Given data:

Number of metallic spokes N = 10

Spoke's length or radius of the wheel, r or L = 0.5m

Wheel's rotation f = 120 rev/min = 2 rev/sec

Magnitude of the field B= 0.4 Gauss = 0.4×10-4T

Step 2. Formula used:

Induced emf between axle & rim is given by,

e=Bvl, where all the symbols are described above.

Step 3: Calculation

We know, that one revolution = 2πrad

For two revolutions, angular velocity ω=22πrad=4πrads

Velocity of spoke at rim = ωr

Velocity of spoke at axle = 0

Average velocity v= ωr+02=ωr2

Step 3. Calculations:

Putting all the given values in the above equation, we get

e=0.4×10-4×12×4π×0.5×0.5=6.28×10-5V

Hence, the induced emf between the axle and the rim of the wheel is 6.28×10-5V.


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