Is the Biot-Savart Law reversible?

[vanhees71]

The quasi-stationary approximation is valid in regions close to the sources, i.e., at distances smaller than the typical wavelength of an electromagnetic field. In this "near-field zone" you can neglect retardation. That's why the quasitationary approximation works for usual household AC.

Again, the charge and current density of a single charge is given by
$$\rho(t,\vec{x})=q \delta^{(3)}[\vec{x}-\vec{y}(t)], \quad \vec{j}(t,\vec{x})=q \dot{\vec{y}}(t) \delta^{(3)}[\vec{x}-\vec{y}(t)],$$
where $\vec{y}(t)$ is the trajectory of the particle in a fixed reference frame. You clearly see that even for a uniformly moving particle these are not stationary, and you have to use the retarded expressions to get the correct field. In that case you can also use the trick with the Lorentz boost, I've demonstrated some postings before.

 

[carrz]

The quasi-stationary approximation is valid in regions close to the sources, i.e., at distances smaller than the typical wavelength of an electromagnetic field. In this "near-field zone" you can neglect retardation. That's why the quasitationary approximation works for usual household AC.

So there are two different scenarios where standard Biot-Savart and Coulomb's law deviate:

a. charges have non-uniform velocity

b. charges are moving at high velocity


Has this been experimentally confirmed, and can you point some reference about it?

 

[vanhees71]

Maxwell electrodynamics and its quantized version, QED, can be considered as the best tested theory ever in the sense that some fundamental properties like the (anomalous) magnetic moment of the electron is confirmed to agree with the value predicted by theory of 13 significan decimal places. For a first orientation on this, see

http://en.wikipedia.org/wiki/Precision_tests_of_QED

Concerning the classical limit, the functioning of high-energy particle accelerators like the LHC at CERN also shows that Maxwell electrodynamics and relativistic (!) particle dynamics works with high precision.

Relativistic effects are not always related with large speeds. E.g., the homopolar generator can only be understood when the relativistic structure of the theory is used, and there no high speeds (compared to the speed of light in vacuo) is involved. Have a look here

http://en.wikipedia.org/wiki/Faraday_paradox

Last but not least, any device using e.m. waves to transmit signals (radios, cell phones, etc.) prove the correctness of Maxwell's prediction of electromagnetic waves.

 

[carrz]

Maxwell electrodynamics and its quantized version, QED, can be considered as the best tested theory ever in the sense that some fundamental properties like the (anomalous) magnetic moment of the electron is confirmed to agree with the value predicted by theory of 13 significan decimal places. For a first orientation on this, see

http://en.wikipedia.org/wiki/Precision_tests_of_QED

Concerning the classical limit, the functioning of high-energy particle accelerators like the LHC at CERN also shows that Maxwell electrodynamics and relativistic (!) particle dynamics works with high precision.

Relativistic effects are not always related with large speeds. E.g., the homopolar generator can only be understood when the relativistic structure of the theory is used, and there no high speeds (compared to the speed of light in vacuo) is involved. Have a look here

http://en.wikipedia.org/wiki/Faraday_paradox

Last but not least, any device using e.m. waves to transmit signals (radios, cell phones, etc.) prove the correctness of Maxwell's prediction of electromagnetic waves.

Biot-Savart and Lorentz force have nothing to do with radiation or em waves, just force. They do not compare with Maxwell equations, not all of them anyway. I'm not convinced experimental verifications of QED actually prove Lorenz or Coulomb force will vary depending on velocity. The only thing I found related to that actually suggests otherwise, that is experimental checks on photon mass are measured relative to Coulomb's law and depend on its constancy.

 

[Matterwave]

Biot-Savart and Lorentz force have nothing to do with radiation or em waves, just force. They do not compare with Maxwell equations, not all of them anyway. I'm not convinced experimental verifications of QED actually prove Lorenz or Coulomb force will vary depending on velocity. The only thing I found related to that actually suggests otherwise, that is experimental checks on photon mass are measured relative to Coulomb's law and depend on its constancy.

The Lorentz force is correct, even relativistically and even for accelerating charges. This is only a force law. The Coulomb's law is valid for only electro-statics because it depends on a static electric field to derive the force.

 

[Dale]

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