Is Faraday's law applicable on a lesser scale?

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Discussion Overview

The discussion explores the applicability of Faraday's law of electromagnetic induction at smaller scales, particularly regarding the interaction of moving electrons within a solenoid. Participants examine theoretical implications and limitations of the law in contexts beyond traditional macroscopic scenarios.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that an electron moving through a solenoid could induce an EMF, drawing parallels to how a magnet induces current when moving through a solenoid.
  • Others argue that while an electron generates a magnetic field due to its motion, the relationship between electric and magnetic fields is complex and requires understanding Maxwell's equations.
  • A participant mentions the classical radius of the electron as a scale limit for the applicability of Faraday's law, suggesting that it is fundamentally relevant even if not practically feasible.
  • One participant challenges the practicality of creating a solenoid at such a small scale, indicating limitations in experimental realization.
  • Another participant emphasizes that while Faraday's law is traditionally demonstrated with solenoids, its essence lies in the generation of spatially-varying electric fields from time-varying magnetic fields, which varies based on specific situations.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Faraday's law at smaller scales, with no consensus reached on whether it can be effectively applied to scenarios involving individual electrons and small solenoids.

Contextual Notes

Limitations include the practical challenges of constructing small solenoids and the dependence on the definitions of electric and magnetic fields as they relate to moving charges. The discussion also highlights unresolved aspects of how Faraday's law translates to microscopic scales.

radaballer
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Farraday's law tells us a magnet traveling through a solenoid will induce a current. It is understood electromagnetic properties and magnetic properties are somewhat interchangeable, and this allows magnets to move electrons in the wire. Can it then be inferred that an electron moving through a solenoid (a much smaller one) would cause an induced EMF.
 
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Electric and magnetic fields aren't quite interchangeable, although they are both parts of the electromagnetic field. You have to understand Maxwell's equations to see their connection.

An electron moving through a solenoid will cause an induced EMF, because a moving charge generates a magnetic field. There are a couple equivalent ways of thinking about this. The moving charge is a current, and the current creates a magnetic field which is changing as the current shifts. Or, in the frame of reference of the electron, it creates an electric field. In the frame of reference of the solenoid, the electric field is transformed into an electromagnetic field via a Lorentz transform, and the magnetic portion interacts with the solenoid.
 
Thank you Khashishi
 
radaballer said:
Farraday's law tells us a magnet traveling through a solenoid will induce a current. It is understood electromagnetic properties and magnetic properties are somewhat interchangeable, and this allows magnets to move electrons in the wire. Can it then be inferred that an electron moving through a solenoid (a much smaller one) would cause an induced EMF.
The Faraday's law should be working at least within the scale where electrodynamics is applicable - up to classical radius of electron (re)

re = e2/mc2
where e - electric charge of an electron, m - its mass, and c is the speed of light. The magnitude of the scale is approximately one fermi. This is a rather fundamental aspect of the question than practical.

Grigori Saiyan
 
You can't make a solenoid that small anyways.
 
Yes, of course. That's why I am saying this is just a formal aspect, but not practical one. Faraday's law has been discovered with the use of solenoidm, but its vey meaning is in generating spatially-varying electric field induced by a time-varying nagnetic field and vice versa (reflected in one of Maxwell equations). Sources and scales of electric and magnetic fields depend on situations
 

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