Question

A wheel with $8$ metallic spokes each $50cm$ long is rotated with a speed of $120rev/min$ in a plane normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the place is $0.4G$ and the angle of dip is ${60}^o$. Calculate the emf induced between the axle and the rim of the wheel. How will the value of emf be affected if the number of spokes were to be increased ?

Answer 1

$H=Bcos\theta =0.4cos{60}^o=0.2G=0.2\times {10}^{-4}T$.
This component is parallel to the plane of the wheel. Thus, the emf induced is given as,
$E=\frac{1}{2}B{l}^2\omega$
Where, $\omega =\frac{2\pi N}{t}$
$E=\frac{1}{2}\times 0.2\times {10}^{-4}\times (0.5{)}^2\times \frac{2\times 3.14\times 120}{60}$
$=3.14\times {10}^{-5}V$
The value of emf induced is independent of the number of spokes as the emf across the spokes are in parallel. So, the emf will be unaffected with the increase in spokes.