2. Bicycle Speed Sensor http://surlybikes.com/bikes/steamroller fork Suppose a s

Question

2. Bicycle Speed Sensor http://surlybikes.com/bikes/steamroller fork Suppose a speed sensor for a bicycle is made by mounting a small coil on the inside of the fork, facing the spokes. A small magnet is mounted on one of the spokes. As the wheel spins the magnet flies past the coil, producing an EMF according to Faraday's law. (a) We considered three types of Faraday's Law problem in class. Which type of problem is this one? Which equation should we use in thinking about the problem? Why? (Don't worry about the values of the variables at this point.) (b) Suppose the magnet flies past the coil in the indicated direction. The magnet will pass under the coil and its field points out of the page. What are the directions of the coil current as the magnet enters the coil region and leaves the coil region? (Explain.) (c) It can be shown that the speed of the magnet relative to the coil is Vm 0.8 Vb , where Vm is the speed of the magnet and vb Is the speed of the bike along the street. Using the following parameters, estimate the magnitude of the EMF produced by the coil: vb2 m/s, the coil size is 1 cm and it has 100 turns, the field produced by the magnet has magnitude 0.1 T. (Explain your calculation carefully.) magnet coil

Explanation / Answer

a. for the three types of faradays laws problems involving relatove motion between the coils and the magnet, this one has stationary coils and moving magnet.

hence we will ise the following equation for calculation of the speed

emf generated in the coil = V

V = -d(phi)/dt

where d(phi) is rate of change of magnetic flux through the coil

now, the emf reaches its peak once every rottion

hence frequency of the peak voltage be f

then

T = 1/f

and

angular speed of the cycle tyre = 2*pi*f

hence

speed of cycle = 2*pi*f*r ( where r is radis of the bicycle tyre)

b. for the given case

magnet flies below the coil and its magentic field is out of th epage

when the magnet enters its motion near the loop, the flux thourgh the coil, out of the page increases

hence

from lenz's law, the current in coil is clockwise

and when the magnet leaves the coils vicinity, the current is reverse, i.e. counter clockwise

c. vm = 0.8 vb

vm is speed of magnet

vb is speed of cycle

vb= 2m/s

A = 1cm^2

n = 100 turns

B = 0.1 T

hence

phi = B*A

d(phi)/dt = B*1cm*vm*N

hence

V = 0.1*0.01*0.8*2*100 = 0.16 V

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