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

Options

A. 0V
B. 0.628 mV
C. 0.628 `muV`
D. `62.8 muV`

Answer

D

Explanation

Induced emf produced between the axle and the rim of the wheel is
`epsilon=(B omegaR^2)/2`…(i)
(Here B=0.4 , `G=0.4 xx10^(-4)` T)
`omega=120 "rev"/"min"=(240pi)/60"rad"/s`
`omega=4pi` rad/s, R=0.5 m, N=10
`therefore epsilon=(0.4xx10^(-4)xx4xx3.14xx(0.5)^2)/2` [ `because` From eqn. (i)]
`=(0.4xx4xx3.14xx0.25xx10^(-4))/2`
`=0.628xx10^(-4)`
`=62.8xx10^(-6)`
`=62.8 muV`