Electrodynamics - relativistic generalization of a formula

In summary, the conversation discusses the use of a Taylor series in U to solve for lambda in the context of Electrodynamics and Special Relativity. The question is raised as to why this specific extension is used and it is suggested that it may be a "naughty question" that expects the reader to be psychic. However, it is pointed out that the first equation given in the rest frame of the ohmic medium can also be used to solve for lambda.
  • #1
Jerbearrrrrr
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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,
[tex]\sigma F^{ab}U_b = J^a + \lambda U^a[/tex]
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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  • #2
Why not just use the first equation you are given (supposed to show)? In the rest frame of the ohmic medium, you have:

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

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

Related to Electrodynamics - relativistic generalization of a formula

1. What is the formula for the relativistic generalization of electrodynamics?

The formula for the relativistic generalization of electrodynamics is known as the Lorentz force equation. It is given by F = q(E + v x B), where F is the force on a charged particle, q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.

2. How does the Lorentz force equation differ from the classical formula for electrodynamics?

The Lorentz force equation takes into account the effects of relativity, such as time dilation and length contraction, which are not accounted for in the classical formula. It also includes the cross product term v x B, which represents the magnetic force on a moving charged particle.

3. What is the significance of the speed of light in the relativistic generalization of electrodynamics?

The speed of light, c, plays a crucial role in the relativistic generalization of electrodynamics. It is the maximum speed at which any object or information can travel in the universe. This is why it appears in the Lorentz force equation and other equations in relativity, as it sets a fundamental limit on the behavior of particles and electromagnetic waves.

4. Can the Lorentz force equation be applied to both electric and magnetic fields?

Yes, the Lorentz force equation can be applied to both electric and magnetic fields. This is because the electric and magnetic fields are intimately connected and can be described by the same set of equations, known as Maxwell's equations. The Lorentz force equation is a direct consequence of these equations and can be used to describe the behavior of charged particles in both electric and magnetic fields.

5. How does the Lorentz force equation support the theory of relativity?

The Lorentz force equation is a fundamental equation in the theory of relativity, as it takes into account the effects of relativity on charged particles. It shows that the forces experienced by a charged particle depend not only on its charge and the electric and magnetic fields, but also on its velocity. This is a key concept in relativity, which states that the laws of physics should be the same for all observers, regardless of their relative motion.

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