A wheel with 10 metallic spokes, each 0.50 m long, is rotated with a speed of 120 rev/minute in a plane normal to the earth.s magnetic field at the place. If the magnitude of the field is 0.40 gauss, what is the induced emf between the axle and the 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,
`(dphi_B)/(dt) = BA = B pi r^2 f `
Induced emf, `e = B pi r^2f` (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.