A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev. `"min"^(-1)` in a plane normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the place in 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.

Explanation

Length of each spke, L = 50 cm = 0.5 m,
`omega=(2pixx120)/(60)=4pi" rad".s^(-1)`
Horizontal component of earth's magnetic field,
`B=0.4cos60^(@)=0.2G=0.2xx10^(-4)T`
`therefore` The emf induced between the two ends of a spoke,
`e=(1)/(2)BomegaL^(2)`
`=(1)/(2)xx0.2xx10^(-4)xx4pixx(0.5)^(2)`
`=3.14xx10^(-5)V`
Each metal spoke behaves like a cell of emf e. All such indentical cells connected in parallel. So the total emf does not depend on the number of spokes.