All Questions
5
questions
5
votes
2
answers
11k
views
Equivalent form of Bianchi identity in electromagnetism
In electromagnetism, we can write the Bianchi identity in terms of the field strength tensor $F_{\mu \nu}$ as,
$$ \partial_{\lambda} F_{\mu \nu} + \partial_{\mu} F_{\nu \lambda}+ \partial_{\nu} F_{\...
- 1,751
2
votes
1
answer
319
views
Proof that 4-potential exists from Gauss-Faraday field equation
This is a problem concerning covariant formulation of electromagnetism.
Given
$$\partial_{[\alpha} F_{\beta\gamma]}~=~ 0 $$
how does one prove that $F$ can be obtained from a 4-potential $A$ such ...
- 626
3
votes
1
answer
2k
views
Electromagnetic Tensor in Cylindrical Coordinates
I understand that the Electromagnetic Tensor is given by
$$F^{\mu\nu}\mapsto\begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\
E_{x} & 0 & -B_{z} & B_{y}\\
E_{y} & B_{z} & ...
- 1,373
2
votes
2
answers
2k
views
Expressing Maxwell's equations in tensor form using Electromagnetic field strength tensor [closed]
I have yet another derivation question from Carroll's General Relativity textbook. Given the electromagnetic field strength tensor is of the form: $$ F_{\mu\upsilon} =
\left(
\begin{matrix}
0 & -...
- 187
1
vote
1
answer
250
views
Question about tensor form of Maxwell equation [closed]
By variating the Maxwell Lagrangian we get the equation of motion. The remaining two Maxwell equations can be written as
$$\epsilon_{\mu\nu\rho\sigma}\partial^{\rho} F^{\mu\nu} = 0.$$
I have also seen ...
- 233