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Question
A bicycle wheel with metal spokes of 1 m long rotates in Earth’s magnetic field. The plane of the wheel is perpendicular to the horizontal component of Earth’s field of 4 x 10-5 T. If the emf induced across the spokes is 31.4 mV, calculate the rate of revolution of the wheel.
Solution
Length of the metal spokes, l = 1 m
Rotational area of the spokes, A = π² = 3.14 x (1)² = 3.14 m²
Horizontal component of Earth’s field, B = 4 x 10-5 T
Induced emf, e = 31.4 mV
The rate of revolution of wheel,
`"l", omega = "e"/("NBA" sin theta)` ..[N = 1, θ = 90°, sin 90° = 1]
`= (31.4 xx 10^-3)/(1 xx 4 xx 10^-5 xx 3.14 xx sin 90^circ)`
`= (3.14 xx 10^-3)/(12.56 xx 10^-5)`
`= 2.5 xx 10^2`
ω = 250 revolutions/second
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