EM Waves in Conductors: Why Does B Field Lag E Field?

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Discussion Overview

The discussion revolves around the behavior of electromagnetic (EM) waves in conductors, specifically addressing why the magnetic field (B field) lags behind the electric field (E field) when an EM wave enters a conductive material. Participants explore various theoretical and conceptual aspects related to this phenomenon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that the lag of the B field behind the E field may be related to the movement of free electrons in the conductor when an EM wave enters.
  • Another participant suggests that the magnetic field rearranges or polarizes the free electrons, aligning them in a way that accommodates the new distribution, and that this lag increases with the volume of the conductor.
  • A participant proposes using the Lorentz force to determine the direction in which electrons will move within the material.
  • It is acknowledged that while the Lorentz force can indicate the direction of electron movement, it may not fully describe the overall behavior of electrons in a volume conductor under an applied magnetic field.
  • One participant mentions that applying the relationship j=σE in Maxwell's curl B equation results in a positive imaginary part for the effective wave number, leading to the conclusion that B will lag E due to conductivity mechanisms.
  • A question is raised about the possibility of making E lag B instead.
  • In response, it is suggested that exposing a non-linear optical crystal can cause E to lag B, with the refractive index change of the crystal being a contributing factor, as well as the effects of anisotropic materials on the permittivity tensor.

Areas of Agreement / Disagreement

Participants express various viewpoints regarding the lag of the B field behind the E field, with some proposing mechanisms and others questioning the sufficiency of certain models. There is no consensus on the overall explanation or the possibility of E lagging B.

Contextual Notes

Some discussions involve assumptions about the behavior of electrons in conductors and the applicability of the Lorentz force in this context. The relationship between conductivity and the wave number is also noted, but the implications remain unresolved.

Who May Find This Useful

This discussion may be of interest to those studying electromagnetism, materials science, or anyone exploring the behavior of electromagnetic waves in conductive materials.

cragar
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When an EM wave goes in a conductor it says that the B field component lags the E field component, What causes this? I looked in Griffiths and I couldn't find the answer. Does it have something to do with the fact that when the EM wave enters the conductor it is moving the free electrons in the material?
Any input will be appreciated.
 
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cragar said:
When an EM wave goes in a conductor it says that the B field component lags the E field component, What causes this? I looked in Griffiths and I couldn't find the answer. Does it have something to do with the fact that when the EM wave enters the conductor it is moving the free electrons in the material?
Any input will be appreciated.

Exactly. Magnetic field will tend to rearrange/polarize the free electrons in the conductor so that they will align to such a position where B will be seamlessly fitting to new free electron distribution. As the conductor gets bigger in volume, this lag will go bigger as well.
 
can we use the Lorentz force to figure out which way it will move the electrons in the material.
 
Yes Lorentz force can provide the 'directions' electrons will move to, but in a volume conductor it is not sufficient to determine the overall behavior of electrons due to applied magnetic field. It is a law which essentially applies to individual charges but in this case it will be sufficient to determine the flow direction.
 
Letting [tex]j=\sigma E[/tex] in Maxwell's curl B equation gives the effective wave number a positive imaginary part, so B will lag E. This will be true for any mechanism causing the conductivity.
 
Could we ever make E lag B?
 
cragar said:
Could we ever make E lag B?

Yes you can. Exposing to a non-linear optical crystal will hold E and make E lag B. Refractive index change of the crystal originates from this. This originates from polarization as well. Also there will be a delay when exposed to anisotropic material where E will try to change the permittivity tensor (shift it with the clock of oscillation).
 

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