All Questions
92
questions
2
votes
1
answer
76
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
248
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 ...
- 1,616
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
140
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
$$
\frac{\partial^{2} E_x}{\...
- 1
1
vote
0
answers
55
views
How is $E×B$ zero? [closed]
I was reading Feynman lectures vol. 2 pg no. 291. There I found the general solution of one dimensional planar waves along $x$ direction. My question is the when I apply dot product on $E$ and $B$ ...
- 157
0
votes
1
answer
313
views
Equations of motion of $\mathcal{L}= - \frac{1}{4}F^{2}_{\mu \nu} - A_{\mu}J_{\mu}$ in momentum space
I'm reading the Matthew D. Schwartz, Quantum field theory and the standard model, p.128 and some question arises.
Consider a lagrangian $\mathcal{L}= - \frac{1}{4}F^{2}_{\mu \nu} - A_{\mu}J_{\mu}$ ($...
- 317
1
vote
1
answer
142
views
Relation between Area under $I$-$H$ hysteresis Loop and $B$-$H$ hysteresis Loop [closed]
If the area under the I-H hysteresis loop and B-H hysteresis loop are denoted by $A_1$and $A_2$ (The symbols have usual meaning as set in electromagnetics), then
$A_2=\mu_oA_1$
$A_2=A_1$
$A_1=\...
- 113
2
votes
1
answer
1k
views
Expressing Maxwell's equations in tensor notation
I've been teaching myself relativity by reading Sean Carroll's intro to General Relativity textbook, and in the first chapter he discusses special relativity and introduces the concept of tensors, ...
- 187
3
votes
1
answer
112
views
Nabla commutation in electromagnetism
I don't know how to work with the 'reversed' dot product operator,
$$v\cdot \nabla$$
I arrived to expressions like this trough doing some calculus, and I don't know how to continue with the calculus ...
- 529
0
votes
2
answers
349
views
Maxwell Equations Solution for single charged particle
Is it possible to find an analytic solution to maxwell equation when I have only one charged particle (and without any neglections):
With $\rho=q\delta(r-r_a)$, $J=q\dot{\vec{r_a}}\delta(r-r_a)$ and $...
- 1,734
3
votes
2
answers
247
views
Using Faraday's law twice
I have trouble understanding Faraday's law when there is an induced current which in turn induces another current in the same circuit. I shall illustrate my confusion with an homework problem and I ...
- 963
1
vote
0
answers
51
views
Equations of Motion for Hidden Photon
I was reading a paper called Parametrically enhanced hidden photon search by Peter Graham et al. In the paper, a Lagrangian that describes the theory of the hidden photon is
$$\mathcal{L}=-\frac{1}{4}(...
- 51
0
votes
1
answer
320
views
Can both magnetic and electric fields induce current from an EM wave?
I was reviewing a homework problem I completed for class, but I saw different explanation that contradict each other.
My teacher says that this position for the waves is optimal for maximum induced ...
1
vote
0
answers
79
views
Proof $\Delta \vec{E} = \frac{1}{c^2} \frac{\partial ^2\vec{E}}{\partial t^2}$ [closed]
Here's what I'm doing, but I'm not sure if this is correct.
Furthermore, I think $c^2$ is the speed of light, however is $c^2 = (\mu_0\epsilon_0)^{-1}$ as follow?
$$\nabla \times (\nabla \times \vec{...
- 29
1
vote
1
answer
807
views
Hamiltonian classical electrodynamics
After coming across the Lagrangian density of the Maxwell equations
$$
\mathcal{L} = -\frac{1}{4\mu_0} F_{\mu\nu}F^{\mu\nu}-J_\mu A^\mu = \frac{\varepsilon_0}{2}||\mathbf{E}||^2-\frac{1}{2\mu_0}||\...
- 181
3
votes
2
answers
505
views
Faraday's law for a 3-dimensional conductor plate moving in a uniform magnetic field
I am struggling to understand this supposedly simple problem I found in a highschool textbook.
A metallic plate is moving with constant velocity v in a region in which
there is a uniform magnetic ...
- 1,104
1
vote
1
answer
670
views
Changing Electric Field in a Capacitor
A capacitor has circular plates with radius $R$ and is being charged by a constant current $I$. The electric field $E$ between the plates is increasing, so the energy density is also increasing. This ...
1
vote
1
answer
471
views
Is it possible to find potential difference between two point in case of induced EMF created by a time-varying magnetic field?
Q: There is a uniform time varying magnetic field in a circular region as shown in the figure. find out the potential difference across 2 point along an elliptical path as shown in figure.
As far as ...
- 1,022
0
votes
1
answer
236
views
How to find potential difference between two points in a loop in case of motional emf? [closed]
Given below is a question in my physics textbook.
A rectangular frame of wire abcd has dimensions 32 cm×8.0 cm and a total resistance of 2.0 Ω. It is pulled out of a magnetic field B=0.02 T by ...
- 1,022
1
vote
2
answers
139
views
Motion of Test Charge in EM Field [closed]
I have a negative infinite sheet of charge moving at a velocity $v$ in the $+x$ direction. A test charge $Q$ with mass $m$ moves at a constant velocity $v$.
My Question is simple: How will the test ...
- 313
0
votes
1
answer
534
views
Understanding why $\frac{\partial (F_{\mu \nu} F^{\mu \nu})}{\partial (\partial_\lambda A_\beta)}=4 F^{\lambda \beta}$ in Maxwell's Equations [duplicate]
In trying to derive Maxwell's equations from
$$S=\int d^4 x\left(-\frac 1 4 F_{\mu \nu}F^{\mu \nu}\right)$$
Where
$$F_{\mu \nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$$
I'm trying to show that
$$\frac{\...
- 394
3
votes
3
answers
2k
views
Simple derivation of the Maxwell's equations from the Electromagnetic Tensor
Lets start by considering the electromagnetic tensor $F^{\mu \nu}$:
$$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
0
votes
2
answers
287
views
Interpreting discontinuity in the Poynting vector
An infinite cylinder of radius R has a uniforme current distribution through its surface $\vec \kappa (t)=\kappa(t)\vec \phi$. Find a) the magnetic field generated by the distribuition, b) the induced ...
- 548
2
votes
1
answer
67
views
$\vec H$ calculation, given $\vec J$, exercise confusion [closed]
I would like to calculate $\vec H $ at every point, given the following pattern (which extends infinitely at $x$ and $y$ directions).
(we are viewing at $xz$ plane)
$$
\vec J(x,y,z)=
\begin{cases}
\...
- 161
1
vote
2
answers
597
views
Lagrangian for the Maxwell equations
In his book 'Classical Electrodynamics' Kurt Lechner wants to find a Lagrangian $\mathcal{L}$ so that the Euler Lagrange equations
$$\partial_\mu\frac{\partial\mathcal{L}}{\partial(\partial_\mu A_\nu)}...
- 57
0
votes
0
answers
186
views
Maxwell's equations in vacuum - EL in tensor notation [duplicate]
Following David Tong's great lecture notes on QFT I've got struggling with the following steps he did. Can someone explain the steps between those three lines?
1.1.3 A final Example: Maxwell's ...
1
vote
3
answers
13k
views
Deriving the wave equation for electromagnetic waves
I'm currently referring to the wave equation derivation given in "Introduction to Electrodynamics" by David J. Griffiths. It follows something like this:
The electromagnetic wave equations are given ...
- 87