A wheel with 10 metallic spokes each 0.5 m long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of earth’s magnetic field `H_(E)` at a place. If `H_(E)` = 0.4 G at the place, what is the induced emf between the axle and the rim of the wheel? Note that 1 G = `10^(–4)` T.

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.