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 0.4 G and the angle of dip is 60°. 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 ?
$H=B\cos \theta =0.4\cos {{60}^{0}}$
$=0.2G=0.2\times {{10}^{-4}}T$
This component is parallel to the plane of the wheel. Thus, the emf induced is
$\varepsilon =\frac{1}{2}B{{l}^{2}}\omega $
where $\varepsilon =\frac{2\pi f}{t}$
$\therefore \varepsilon =\frac{1}{2}\times 0.2\times {{10}^{-4}}\times {{(0.5)}^{2}}\times \frac{2\times 3.14\times 120}{60}$
$\varepsilon =3.14\times {{10}^{-5}}V$