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For example, the usual derivation of the complex dielectric constant of metals (using the Drude model) makes use of the Ohm's law in the Maxwell's equations, but what is never mentioned is why they are ignoring the full Lorentz force that the moving electrons would perceive when you include a magnetic field (in this case of the incident EM wave).

Keeping the Drude model in mind, I can see that the magnetic "correction" would be of second order in the relaxation time, but is that the reason why it is usually ignored (for example in skin depth calculations)?

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The magnetic force term in Ohm's law is often ignored where it would complicate description and bring nothing essential - often magnetic force is much smaller than the electric force. In cases magnetic force is essential, like the Hall effect, moving conductor in static magnetic field, current - carrying plasma (pinch effect), it is common to take the magnetic force into account.

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  • $\begingroup$ I think that it should be mentioned at least. Every book that I've read assumes that you know that, even introductory books. $\endgroup$ – Ant Apr 8 '15 at 12:17
  • $\begingroup$ Every book is flawed in some ways. Confronting original papers' and several books' approaches and views is necessary. $\endgroup$ – Ján Lalinský Apr 8 '15 at 19:51

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