A wheel with metallic spokes each long is rotated with a speed of rev/min in a plane normal to the earth's magnetic field at the place.If the magnitude of magnetic field is , what is the induced emf between the axle and the rim of the wheel ?
Step 1. Given data:
Number of metallic spokes =
Spoke's length or radius of the wheel, or =
Wheel's rotation = rev/min = rev/sec
Magnitude of the field = Gauss =
Step 2. Formula used:
Induced emf between axle & rim is given by,
, where all the symbols are described above.
Step 3: Calculation
We know, that one revolution =
For two revolutions, angular velocity
Velocity of spoke at rim =
Velocity of spoke at axle =
Average velocity =
Step 3. Calculations:
Putting all the given values in the above equation, we get
Hence, the induced emf between the axle and the rim of the wheel is .