The Electron - Size of Magnetic field vs Size of Electric field

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Discussion Overview

The discussion revolves around the effective scattering cross-sections of the magnetic and electric fields of a free electron, exploring how these two aspects of the electromagnetic field can be experimentally separated and compared. Participants delve into theoretical considerations and potential experimental setups.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the effective scattering cross-section of both the magnetic and electric fields of a free electron, noting their different aspects within the electromagnetic field.
  • Another participant questions how to experimentally separate these two cross-sections, suggesting that a scattering event is necessary for defining a cross-section and expressing uncertainty about the original question's clarity.
  • A third participant references Bohm's work, stating that the magnetic field is approximately 100 times smaller than the electric field but is unsure if this is based on experimental measurement or theoretical estimation.
  • One participant emphasizes that the concept of cross-sections is meaningless without a defined scattering event, suggesting that the ratio of energy densities would be more informative regarding their relative strengths.
  • Another participant challenges the assertion about the magnetic field being smaller, arguing that the magnetic field arises from the electron's spin, a quantum mechanical effect, and should be comparatively small, while the electric field is larger due to electrostatics.
  • This participant proposes using established texts to compute the magnetic energy density from the magnetic moment due to spin and the electric energy density from electrostatics, indicating they will attempt this calculation soon.

Areas of Agreement / Disagreement

Participants express differing views on the relative sizes of the magnetic and electric fields, with some supporting Bohm's assertion and others contesting it based on quantum mechanical principles. The discussion remains unresolved regarding the effective scattering cross-sections and their experimental separation.

Contextual Notes

Participants note the necessity of a scattering event to define cross-sections, highlighting the dependence on experimental conditions and the potential for varying interpretations of the fields' strengths.

Buckeye
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What is the radius or effective scattering cross-section of the magnetic field of a free electron and what is the radius or effective scattering cross-section of the electric field of a free electron? Admittedly the two fields are different aspects of the EM field of the electron.
 
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How do you separate these two cross sections in an experiment? A scattering cross section needs a reaction, so what would your reacton be or in other words, what is being scattered and by what? I am not sure I understand what you are asking and if I do, then your question may be ill-posed.

Are you trying to get a feel for the relative strength between them?
 
Norman said:
How do you separate these two cross sections in an experiment?
Good question. I'd love to know as well. Bohm (QT book) wrote that the magnetic field is roughly 100X smaller than the electric field, but I did not read if that was experimentally measured or estimated from a calculation.
Norman said:
A scattering cross section needs a reaction, so what would your reacton be or in other words, what is being scattered and by what? I am not sure I understand what you are asking and if I do, then your question may be ill-posed.
Sorry, but that's the best way I know how to put it.
Norman said:
Are you trying to get a feel for the relative strength between them?
Actually, I'm interested in the effective volume and the radial density of both. Does that help?
 
Ok, now we are getting somewhere. I think you are asking basically an classical electro/magnetostatics problem.

I will work it out and post what I get later tonight ok.
Cheers,
Ryan
 
By the way, the statement about the cross sections in completely meaningless since you must have some sort of scattering event to define the cross section. You are just looking for the ratio of the energy densities. Which will tell you something about their relative strengths.
 
Buckeye said:
Bohm (QT book) wrote that the magnetic field is roughly 100X smaller than the electric field, but I did not read if that was experimentally measured or estimated from a calculation.

at first glance this seems like it is very wrong. The magnetic field of the electron is due to the magnetic moment from the spin. Spin is a QM effect and therefore should be on the order of hbar which is very, very small. While the electric field is due to electrostatics and should be large when compared to hbar.

I would suggest openning your copy of Jackson and using the magnetic moment from spin to compute the magnetic energy density and then use standard electrostatics to compute the electric energy density. It should be very straight forward.

I will do it tonight or tomorrow morning.
Maybe someone else can weight in on this and see if my intuition is correct.
Cheers,
Ryan
 

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