It is often said that Maxwell's equations in differential form hold in special relativity while Maxwell's equations in integral form don't hold. Consider one of equations:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}[/tex]

[tex] \oint_{\partial S} \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \frac {1} {c} \frac {d} {dt} \int \mathbf {B} \cdot \mathrm{d} \mathbf {S}[/tex]

Consider the integral form. It means that if one has an alternating magnetic field, then in any contour around this field circulation of electrical field immediately appears . If one takes a very long tube and at one end of the tube somehow generates an alternating magnetic field the in contour (radius R) around the tube circulation of electric field immediately appears. But in relativistic case it can't appear immediately because it will take time [itex]t=\frac {R} {c}[/itex] for news about alternating magnetic field to come to this contour. So here we have the violation of this equation in relativistic case.

Still this 'paradox' can be solved in terms of classical electrodynamics. But how?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Maxwell's equations in relativistic case

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**