Question

A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/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 ${60}^{\circ }$.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 increased?

Answer 1

$\because H=Bcos\theta =0.4\times cos{60}^0=0.2G=0.2\times {10}^{-4}T$ which is parallel to the plane of the wheel.

The emf induced is

$E=\frac{1}{2}B{l}^2\omega$

where $\omega =\frac{2\pi N}{t}$

$E=\frac{1}{2}0.2\times {10}^{-4}\times (0.5{)}^2\times \frac{2\times 3.14\times 120}{60}=3.14\times {10}^{-5}V$

The emf induced is independent of the number of spokes as the emfs across them are in parallel. So it is unaffected by the increase in th number of spokes.