A wheel with 10 metallic spokes each 0.5 m long is rotated with a speed of 120 rpm, in a plane normal to earth's magnetic field at the place. If the megnitude of the field is 0.40 gauss, what is the induced e.m.f. between the axle and rim of the wheel.

Explanation

Here each spoke of wheel act as a source of an induced emf (cell) and emf's of all spokes are parallel.
`f = 120 "rev"//"min" = 2 "rev"//"second"`
`B = 0.40 "gauss" = 0.4 xx 10^(-4)T`,
Area swept, by each spoke per second, `A = pi r^(2) f`
Magnetic flux cut by each spoke per second,
`(d phi_(B))/(dt) = BA = B pi r^(2) f`
Induced emf, `e = B pi r^(2) f` (numerically)
`e = 0.4 xx 10^(-4) xx (22)/(7) xx 0.5 xx 0.5 xx 2`

`e = 6.29 xx 10^(-5) "volt"`
Induced emf in a wheel is independent of no. of spokes.