Question 18.QE.8: Bicycle light generator The label on the Schmidt E6 bicycle ......
Bicycle light generator
The label on the Schmidt E6 bicycle dynamo headlight indicates that the light has a power output of 3 W and a peak emf of 6 V. The generator (also called a dynamo) for the lightbulb has a cylindrical hub that rubs against the edge of the bike tire, causing a coil inside the generator to rotate, as shown below. When the bicycle is traveling at a speed of 5.4 m/s, the coil rotates with frequency of 80 Hz (80 revolutions per second). The \vec{B} field in the vicinity of the coil is uniform and has a magnitude of 0.10 T. The coil is a rectangle with dimensions 1.0 cm × 3.0 cm. Without taking the light apart, determine how many turns there are in the generator coil.
Represent mathematically The number of turns in the coil is related to the maximum emf the generator can produce [Eq. (18.6)]:
\varepsilon_{\text {in } \max }=N B_{\text {ex }} A \omega . (18.6)
\varepsilon_{\text {in } \max }=N B A \omega=N B A(2 \pi f)
Solve and evaluate Solving for N and inserting the appropriate values:
N=\frac{\varepsilon_{\text {in } \max }}{2 \pi f B A}=\frac{6.0 \mathrm{~V}}{2 \pi(80 \mathrm{~Hz})(0.10 \mathrm{~T})(0.01 \mathrm{~m} \times 0.03 \mathrm{~m})}
= 400
A generator coil with this number of turns is reasonable. Let’s check limiting cases. If the magnetic field, the coil area, or the frequency is larger, then fewer turns are needed for the peak emf to be 6.0 V, which is reasonable.
Try it yourself: While riding your bike up a hill, you pedal harder; however, your bike speed reduces from 5.4 m/s to 2.7 m/s. How would these conditions affect the emf produced by the bicycle light generator in the last example?
Answer: The peak emf would be 3.0 V, since the loop turning frequency would decrease to half the previous value.