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?

Explanation

Data: `r=l=0.5m, v=18 km//h = 18000/3600 = 5m//s, B= 3.6 xx 10^(-5) T, v=omegar=(2pif)r`
`therefore f=v/(2pir) = 5/(2pi xx 0.5) = 5/pi` Hz
Induced emf across each spoke,
`|E| = (dPhi_(m))/(dt) = d/(dt)(AB) = B(dA)/(dt) = B(pir^(2)f)`
`therefore |E| = 3.6 xx 10^(-5) xx pi xx (0.5)^(2) xx 5/pi = 4.5 xx 10^(-5)` V
Since the spokes have common ends (the axle and wheel rim), they are connected in parallel. Hence, the emf induced between the end of a single spoke and the other common end of ten spokes is also `4.5 xx 10^(-5)` V