Electrodynamics - relativistic generalization of a formula

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SUMMARY

The discussion centers on the relativistic generalization of a formula in Electrodynamics, specifically addressing the application of a Taylor series in the context of four-vectors. The participants analyze the substitution of variables in the equation \(\sigma F^{ab}U_b = J^a + \lambda U^a\) and its implications in the rest frame of an ohmic medium. The conversation highlights the necessity of understanding Lorentz boosts and their effects on four-vectors to fully grasp the derivation and application of the formula.

PREREQUISITES
  • Understanding of Electrodynamics principles
  • Familiarity with Special Relativity (SR) concepts
  • Knowledge of four-vector notation and transformations
  • Basic grasp of Taylor series expansions
NEXT STEPS
  • Study Lorentz transformations and their applications in Electrodynamics
  • Explore the derivation of the relativistic form of Ohm's law
  • Learn about the implications of four-vector calculus in physics
  • Investigate the role of Taylor series in theoretical physics
USEFUL FOR

Students and researchers in physics, particularly those focusing on Electrodynamics and Special Relativity, as well as anyone interested in advanced theoretical concepts in electromagnetism.

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[PLAIN]http://img46.imageshack.us/img46/1699/dsfadsfas.png

The formula holds in the rest frame.
Why is this particular extension 'the' extension?
(Context is Electrodynamics/SR. It's just a piddly 16 lecture course that outlines Electrodynamics and SR and a bit of Quantum phenomena at the end. Ohm's law hasn't been mentioned and I don't think you're expected to know a lot about Ohm's law itself)

[edit]
Oh.
If you use a "taylor series in U" as in,
\sigma F^{ab}U_b = J^a + \lambda U^a
and solve for lambda, it does turn out as what it's meant to be.

But why is this the correct thing to substitute in? Or is it a naughty question that demands us to be psychic?
 
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Why not just use the first equation you are given (supposed to show)? In the rest frame of the ohmic medium, you have:

\sigma F^{ab}U_{b}=(0,\sigma\textbf{E})=(0,\textbf{j})

What do you get when you apply a Lorentz boost to this 4-vector?
 

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