• Support PF! Buy your school textbooks, materials and every day products Here!

Maxwell's equations in relativistic physics

  • Thread starter elivil
  • Start date
  • #1
15
0

Homework Statement


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:
[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 then 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?


Homework Equations


[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]


The Attempt at a Solution


Maybe it takes time for propagation of alternating magnetic field from one end of the tube to the point A where cross-section of the tube by the plane of the contour is. So in fact it takes equal time to propagate inside the tube and outside the tube so it appears as simultaneously arising magnetic field at point A in the tube and electric field in the contour around the tube. But I'm not quite sure.
 

Answers and Replies

  • #2
Chi Meson
Science Advisor
Homework Helper
1,789
10
This should be moved to the advanced physics forum. I'd take a stab at it, but my Maxwell is rusty, and I might hurt myself with it.
 

Related Threads for: Maxwell's equations in relativistic physics

Replies
4
Views
432
  • Last Post
Replies
11
Views
3K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
9
Views
3K
  • Last Post
Replies
3
Views
834
Replies
2
Views
4K
Top