Induced EMF graph of a very small wire moving through a coil

AI Thread Summary
The discussion focuses on the behavior of induced electromotive force (emf) in a small wire moving through a magnetic coil. Initially, the induced emf increases as the wire cuts through more magnetic flux lines, but once fully within the magnetic field, the emf begins to decrease as it cuts flux lines in the opposite direction. The key point raised is whether the magnetic flux changes while the wire is stationary within the field, leading to confusion about the induced emf. It is concluded that if the wire moves at a constant velocity, the magnetic flux through the loop remains constant, resulting in no induced emf during that time. Understanding the relationship between magnetic flux and induced emf is critical for solving such problems.
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Homework Statement


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Homework Equations



induced emf = - d(magnetic flux)/dt

The Attempt at a Solution


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I believe the graph will start initially curving upwards, because it begins to cut more and more flux lines which lead to an increased induced emf. Once it is "fully" within the magnetic field, it will slope downwards to a negative induced emf as it begins to cut flux lines in the other direction. The peaks will have the same induced emf as the velocity is constant so the rate of change of flux should be equal for entering and leaving the coil. My solution was like this:

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It's wrong, but I can't quite understand.
 
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The loop is small which means it spends some time entirely between the poles of the magnet. While doing this, is the magnetic flux through it changing? If so, how?
 
I guess the magnetic flux isn't changing, because it's moving at a constant velocity. So that would mean no increase/decrease in the rate of change of magnetic flux, so no induced emf?
 
Yup.
 
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