A wheel with ten metallic spokes each `0.50 m` long is rotated with a speed of `120 rev//min` in a plane normal to the earth's magnetic field at the place. If the magnitude of the field is `0.4` gauss, the induced e.m.f. between the axle and the rim of the wheel is equal to

Options

A. `1.256xx10^(-3)V`
B. `6.28xx10^(-4)V`
C. `1.256xx10^(-4)V`
D. `6.28xx10^(-5)V`

Answer

D

Explanation

Induced emf between the axle and the rim is given by
`e=(1)/(2)Bl^(2)omega=pil^(2)fB" "["as " omega=2pif]`
`=0.4xx10^(-4)xx(0.5)^(2)xx(3.14)xx(120)/(60)=6.28xx10^(-5)V`