All Questions
92
questions
2
votes
1
answer
74
views
How to derive $\partial^{\nu}F^{\mu\alpha} + \partial^{\alpha}F^{\nu\mu} + \partial^{\mu}F^{\alpha\nu}=0$ for the Electromagnetic field tensor? [closed]
The problem says to show that
$$\partial_{[\mu}F_{\alpha\nu]}=F^{\mu\alpha, \nu} + F^{\nu\mu,\alpha} + F^{\alpha\nu,\mu}=0$$ stems from Maxwell equations.
I haven't been able to find this anywhere on ...
- 21
0
votes
3
answers
225
views
Derivation of Maxwell's equations using Lagrangian formalism [duplicate]
Some time ago, I read in Landau's Theoretical Physics Course you could derive Maxwell's equations using the Lagrangian formalism, and I find this to be exciting. Unfortunately, I don't have access to ...
- 1,629
0
votes
0
answers
54
views
Where does the $\eta^{\mu\nu}$ come from? (Maxwell Lagrangian, QFT) [duplicate]
From the Lagrangian in Maxwell theory
$$L = -\frac{1}{2}(\partial_{\mu} A_{\nu})(\partial^{\mu} A^{\nu}) + \frac{1}{2}(\partial_{\mu}A^{\mu})^2 - A_{\mu}J^{\mu}$$
I have to calculate $\frac{\partial L}...
- 361
0
votes
1
answer
139
views
Dummy index question
The Maxwell's Lagrangian density is given by the equation, $$\mathcal L = -\frac{1}{4} \space F_{\mu\nu} \space F^{\mu\nu},$$ where $F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu A^\mu$.
Hence, one ...
- 171
1
vote
0
answers
55
views
Finding the equation of motion for vector potential $A_{\mu}$ in topologically massive electrodynamics
Essentially I want to vary the action
$$
S_M = \int d^3x \sqrt{-g} \left[- \frac{1}{4} F^{\mu \nu} F_{\mu \nu} - \frac{\alpha}{2} \epsilon^{\mu \nu \rho} A_\mu F_{\nu \rho} \right]
$$
with respect to $...
- 21
2
votes
0
answers
60
views
Uniqueness of solutions of Maxwell equations [closed]
I have this exercise on my electromagnetism course :
Consider that there exist two pairs of fields E and B that satisfy Maxwell's equations, with the same boundary conditions and have the same ...
- 21
0
votes
0
answers
43
views
How to connect $x$, $y$ component of 2D electromagnetic wave equation?
I want to solve following Maxwell's equation.
$$
\triangledown ^{2}E+\frac{\omega^{2}}{c^{2}}E=0
$$
But, Electric field has x, y component in 2D geometry.
So, it will be
$$
\frac{\partial^{2} E_x}{\...
- 1
1
vote
0
answers
54
views
How is $E×B$ zero? [closed]
I was reading Feynman lectures vol. 2 pg no. 291. There I found the general solution of one dimensional planar waves along $x$ direction. My question is the when I apply dot product on $E$ and $B$ ...
- 157
0
votes
1
answer
309
views
Equations of motion of $\mathcal{L}= - \frac{1}{4}F^{2}_{\mu \nu} - A_{\mu}J_{\mu}$ in momentum space
I'm reading the Matthew D. Schwartz, Quantum field theory and the standard model, p.128 and some question arises.
Consider a lagrangian $\mathcal{L}= - \frac{1}{4}F^{2}_{\mu \nu} - A_{\mu}J_{\mu}$ ($...
- 327
1
vote
1
answer
142
views
Relation between Area under $I$-$H$ hysteresis Loop and $B$-$H$ hysteresis Loop [closed]
If the area under the I-H hysteresis loop and B-H hysteresis loop are denoted by $A_1$and $A_2$ (The symbols have usual meaning as set in electromagnetics), then
$A_2=\mu_oA_1$
$A_2=A_1$
$A_1=\...
- 113
2
votes
1
answer
1k
views
Expressing Maxwell's equations in tensor notation
I've been teaching myself relativity by reading Sean Carroll's intro to General Relativity textbook, and in the first chapter he discusses special relativity and introduces the concept of tensors, ...
- 187
3
votes
1
answer
110
views
Nabla commutation in electromagnetism
I don't know how to work with the 'reversed' dot product operator,
$$v\cdot \nabla$$
I arrived to expressions like this trough doing some calculus, and I don't know how to continue with the calculus ...
- 529
0
votes
2
answers
342
views
Maxwell Equations Solution for single charged particle
Is it possible to find an analytic solution to maxwell equation when I have only one charged particle (and without any neglections):
With $\rho=q\delta(r-r_a)$, $J=q\dot{\vec{r_a}}\delta(r-r_a)$ and $...
- 1,734
3
votes
2
answers
246
views
Using Faraday's law twice
I have trouble understanding Faraday's law when there is an induced current which in turn induces another current in the same circuit. I shall illustrate my confusion with an homework problem and I ...
- 963
1
vote
0
answers
51
views
Equations of Motion for Hidden Photon
I was reading a paper called Parametrically enhanced hidden photon search by Peter Graham et al. In the paper, a Lagrangian that describes the theory of the hidden photon is
$$\mathcal{L}=-\frac{1}{4}(...
- 51