Dr. Miller has taken ill and lies on a hospital bed. A coil having 400 turns is

Question

Dr. Miller has taken ill and lies on a hospital bed. A coil having 400 turns is wrapped around his chest, and his breathing means the area of the coil changes by 3.45 Times 10^-3 m^2 every 6.0 s. If the component of the Earth's magnetic field at a right angle to the coil is 42.0 mu T (i.e., it has already taken the cosine term into account) and remains the same ns he breathes, what is the average induced emf? Ever make a smoothie with a bicycle? "Bike Blenders" have a rider pedal a stationary bike and convert the energy into spinning a blender.- Instead of directly converting that mechanical energy of peddling the exercise bike into the mechanical energy of spinning the blender, we will make a generator to produce electricity from the exercise bike. We will assume you can get a gearing that produces a generator rotation rate of 300 rpm, and that the coil of the bicycle generator has 400 turns and encompasses an area of 3.00 Times 10^-3 m^2. If the magnetic field in which the coil is spinning has a magnitude of 0.25 T, what is the maximum emf that can be generated by this bicycle generator? Despite being an astronomer, Dr. Miller was off by several orders of magnitude when discussing the strongest magnetic fields. The strongest pulsars (called "magnetors") actually have magnetic fields up to 10^15 T! If you were to take a length of wire and place it in an equatorial orbit around the pulsar in a manner which had the wire always directed toward the pulsar, it would have a velocity vector that was always at a right angle to the magnetic field of the pulsar. If this velocity were 1.5 Times 10^6 m/s and the wire was 10 m long, what would the resulting motional emf be? Assume that at the distance of the orbiting wire the magnetic field of the pulsar is 10^13 T and is constant across the length of the wire.

Explanation / Answer

Question 3:

Using Faraday's law,

e = NB dA/dt; ------->[1]

given, N = 400 turns; B = 42.0*10-6 T; dA = 3.45*10-3 m2; dT = 6.0 s;

plug into [1], we get

e = 400*42*10-6*3.45*10-3 /6.0

e = 9.66*10-6 V

the average induced emf, e =  9.66*10-6 V

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