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

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In conductors, the magnetic field (B) lags behind the electric field (E) due to the rearrangement of free electrons when an electromagnetic (EM) wave enters the material. This lag increases with the conductor's volume, as the magnetic field aligns with the new distribution of electrons. The Lorentz force can indicate the direction of electron movement, but it does not fully describe their collective behavior in a volume conductor. The relationship between E and B can be analyzed using Maxwell's equations, which show that the effective wave number has a positive imaginary part, confirming that B lags E. Additionally, certain materials, like non-linear optical crystals, can be manipulated to make E lag B instead.
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 j=\sigma E 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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