A cycle wheel with 10 spoken, each of the length 0.5m, is moved at a speed of `18 km//hour`, in a plane normal to the earth's magnetic induction of `3.6 xx 10^(-5)T`. What is the emf induced between the axle and the rim of the cycle wheel?

Options

A. `30 mu v`
B. `35 mu v`
C. `40 mu v`
D. `45 mu v`

Answer

D

Explanation

`v=18 km//h = 18000/3600 = 5 m//s`
and `v = r omega = r cdot (2 pi f)` where f =frequency of rotation
`:. f = v/(2 pi r) = 5/2 pi xx 0.5) = 5/(pi) Hz`
The induced emf across each spoke
`e=(d phi)/(dt) = (d(AB))/(dt) = B(dA)/(dt) = B cdot pir^(2)f`
`:. e = 3.6 xx 10^(-5) xx pi xx (0.5)^(2) xx 5/(pi)`
`=4.5 xx 10^(-5) v = 45 xx 10^(-6) v`
`:. e = 45 mu v`.