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

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SUMMARY

The discussion centers on the induced electromotive force (emf) generated by a small wire moving through a magnetic coil, described by the equation induced emf = -d(magnetic flux)/dt. Participants analyze the behavior of the induced emf graph, noting that it initially curves upwards as the wire cuts through magnetic flux lines, then slopes downwards once fully within the magnetic field. The consensus is that while the wire moves at a constant velocity, the magnetic flux through the loop does not change, resulting in no induced emf when the wire is stationary within the magnetic field.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Familiarity with magnetic flux concepts
  • Knowledge of the relationship between velocity and induced emf
  • Basic grasp of graph interpretation in physics
NEXT STEPS
  • Study Faraday's Law in detail, focusing on its mathematical formulation
  • Explore the concept of magnetic flux and its calculation
  • Learn about the effects of wire velocity on induced emf
  • Investigate practical applications of induced emf in electrical engineering
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Physics students, electrical engineering students, and educators looking to deepen their understanding of electromagnetic induction and its graphical representation.

FelaKuti
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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:

fQB4gKI.png


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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