Maximum EMF in a rotating coil, in an AC generator?

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SUMMARY

The discussion centers on the relationship between electromagnetic force (EMF) and magnetic flux in AC generators, specifically when a coil rotates within a magnetic field. It is established that maximum EMF occurs when the coil is parallel to the magnetic field due to the highest rate of change of magnetic flux, despite the magnetic flux being zero at that position. The relevant equation for EMF is given as EMF = Δ(φ2 - φ1) / Δt, emphasizing the importance of the rate of change of flux rather than the flux itself.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with AC generator operation
  • Basic knowledge of calculus for rate of change calculations
  • Knowledge of magnetic flux concepts
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  • Learn about the operation and design of AC generators
  • Explore the mathematical derivation of EMF in rotating systems
  • Investigate the role of calculus in analyzing changing magnetic fields
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This discussion is beneficial for high school physics students, educators teaching electromagnetism, and anyone interested in the principles of AC generators and electromagnetic induction.

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Homework Statement


Im currently in my last year of high school, and I'm writing a report on AC generators. I've heard a number of different things from different sources. When the coil is perpendicular to the magnetic field, maximum magnetic flux is flowing through the coil. This is then at a minimum when the coil is parallel to the field.

EMF is induced when there is a rate of change of magentic flux through the loop. Why then is EMF at a maximum when the coil is parallel? i.e it was turned from being perpendicular to now being parallel.

Any help would be greatly appreciated!

Homework Equations


EMF = \Delta ( \phi2 - \phi1) / \Delta t


The Attempt at a Solution


My attempt is my failed understanding of the concept.


 
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The EMF depends not on the flux through the coil, but instead on the rate of change of the flux through the coil, as you said.

When the coil is parallel the flux may be 0, but the rate of change of the flux is not zero. At that point, the flux is increasing at it's fastest rate. This is why the EMF is at its highest positive value at this point.

Does this make sense?

(In order to actually compute the rate of change of the flux in this problem, you'll need calculus, and more information about how the coil is rotating.)
 

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