All Questions
12
questions
2
votes
1
answer
1k
views
Expressing Maxwell's equations in tensor notation
I've been teaching myself relativity by reading Sean Carroll's intro to General Relativity textbook, and in the first chapter he discusses special relativity and introduces the concept of tensors, ...
- 187
4
votes
1
answer
235
views
Understanding tensor and covariance
I'm really struggling to understand the use of tensors when we want to have a covariant equation.
From what I understand, if we write an equation using tensors only, then the physics behind it will be ...
- 41
2
votes
1
answer
139
views
Electromagnetic Potential in Relativity
Studying Special Relativity we discover that Maxwell's Equations can be also written in the following way:
$$\partial _\mu F^{\mu\nu}=\mu_0J^\nu$$
$$dF=0$$
Where: $F$ is the Electromagnetic Tensor, $J$...
- 4,577
2
votes
1
answer
430
views
How to be sure that a law is invariant under Lorentz's Transformation?
For starters let's talk about Maxwell's Equations; we know that Maxwell's Equations are invariant under Lorentz's Transformation, after all this is why all the relativity business got started. To ...
- 4,577
3
votes
3
answers
2k
views
Simple derivation of the Maxwell's equations from the Electromagnetic Tensor
Lets start by considering the electromagnetic tensor $F^{\mu \nu}$:
$$F^{\mu \nu}=\begin{bmatrix}0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & ...
- 4,577
3
votes
2
answers
617
views
Extending Maxwell's Equations from Flat Spacetime To Curved Spacetime
Assume we are working on a Minkowski (i.e. flat) spacetime.
Let $A^{\mu} = ( \phi/c, \textbf{A})$ be the contravariant potential four-vector. Then, assuming a covariant Minkowski metric of $\eta_{\...
- 55
5
votes
3
answers
2k
views
Write electromagnetic field tensor in terms of four-vector potential
How can we know that the electromagnetic tensor $F_{\mu\nu}$ can be written in terms of a four-vector potential $A_{\mu}$ as $F_{\mu \nu} = \partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu}$? In the ...
- 257
1
vote
1
answer
660
views
Derivation of Covariant Maxwell's Equations
I am trying to derive the covariant formulation of Maxwell's equations.
I understand that all four of Maxwell's equations can be written compactly as
$$\partial_{\mu}F^{\mu\nu} - j^{\mu} = 0 \;, \...
- 13
0
votes
1
answer
171
views
Generalization of the Coulomb Force to the Lorentz-Force - Is it "guessing"?
it's me again, and I'm still stuck with the paper Generalization of Coulomb’s law to Maxwell’s equations using special relativity by Kobe, like in my previous question.
My problem now lies in ...
- 6,763
2
votes
1
answer
857
views
Tensor Formulation of Maxwell's Equations
I've been reading up about the tensor formulation of Maxwell's Equations of Electromagnetism, and the derivations I have seen (found here: http://www.lecture-notes.co.uk/susskind/special-relativity/...
- 231
1
vote
1
answer
2k
views
Tensor notation of Maxwell's equations
Tensor notation of Maxwell's equation read
$$\partial_\mu F^{\mu\nu} = j^\nu.$$
So when we explicitly try to find the Maxwell's equation from the above tensor equation we only get gauss law and curl ...
- 340
24
votes
4
answers
4k
views
Why do Maxwell's equations contain each of a scalar, vector, pseudovector and pseudoscalar equation?
Maxwell's equations, in differential form, are
$$\left\{\begin{align}
\vec\nabla\cdot\vec{E}&=~\rho/\epsilon_0,\\
\vec\nabla\times\vec B~&=~\mu_0\vec J+\epsilon_0\mu_0\frac{\partial\vec E}{\...
- 9,675