Question

A wheel with 8 metallic spokes each 50cm long is rotated with a speed of 120rev./min . The earth's magnetic field at the place is 0.4G 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 ?

Answer 1

$$\begin{gathered} Verticalcomponentofearthmagneticfieldisgivenby: \\ {B}_v=B\sin \delta \\ B=0.4G \\ \delta =60 \\ {B}_v=B\sin 60 \\ {B}_v=0.4\times \frac{\sqrt{3}}{2} \\ {B}_v=0.692G=0.692\times {10}^{-4}tesla \\ lengthofthestrokewillactasthediameter. \\ radiusr=\frac{50}{2} \\ r=25cm=0.25m \\ Areaa=\pi r^2 \\ a=3.14\times 0.25\times 0.25 \\ a=0.19m^2 \end{gathered}$$
$$\begin{gathered} \omega =2\pi \nu \\ \nu =120revolutionpermin=2revpersecond \\ \omega =2\times 3.14\times 2 \\ \omega =12.56radpersecond \\ inducedemfisonestoke \\ e=B_{v}a\omega \cos \omega t \\ e=0.692\times {10}^{-4}\times 0.19\times 12.56\cos \omega t \\ e=0.1\times {10}^{-3}volt=0.1millivolt \\ forthe8stokes \\ e=8\times 0.1millivolt \\ e=0.8millivolt \\ asnoofstokesincreases. \\ inducedemgincreases. \end{gathered}$$