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ID: 2295456 • Letter: W
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When you answer these questions, please show how you arrived to the answers. I need to understand how you got your answer. Thank you.
State Faraday's law of induction. What is Lenz s law? A circular coil of wire with 10 turns and a 4.0 cm radius is located between the poles of a large electromagnet that produces a uniform magnetic field of 0.5 T The surface of the loop, which is originally parallel to the field, is rotated in 0.1 s so that its surface is perpendicular to the field. Calculate the average induced emf across the ends of the loop as the coil rotates. An airplane with a wing span of 50 m flies horizontal to the earth at a location where the downward component of the earth's magnetic field is 0.6 times 10" T. Find the difference in potential between the tips of the wing when the velocity of the plane is 250 m/s.Explanation / Answer
Faraday's Law states that any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc.
Lenz's Law states that when an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant.
Problem No. 1 )
N = 10 turns
Area : A = pie x r^2 = 3.14 x (4/100)^2 = 0.005m^2
changes in the magnetic field : delta(B) = (0 - 0.5) T = -0.5 Tesla
delta(t) = 0.1 seconds
average emf induced in the coil :
=> E = -N A (delta(B)/delta(t))
=> E = -(10) (0.005) (-0.5 / 0.1)
=> E = 0.25 volt
Problem No. 2)
By definition,
EMF is the rate of change of magnetic flux.
Remember the plane is cutting perpendicularly to the magnetic field, hence
in 1s,
the plane travels 250m,
the wing span is 50m,
hence the wing sweeps over an area of 250x50m = 12500 square metres,
change in magnetic flux = 12500 x 0.6 x 10^-4 = 0.75V/s
since change in magnetic flux in 1s is 0.75,
rate of change of magntic flux is 0.75, and hence EMF is 0.75V.
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