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
0
votes
3
answers
2k
views
How can I actually use Maxwell's equations to solve an electromagnetism problem?
I studied Maxwell's equations, but when it comes to problem solving my teacher never actually used them, so I was wondering if and when do they come useful?
For example, if I have an empty infinite ...
4
votes
1
answer
600
views
In plasma physics, why are the motional electric field and the frozen-in-flux condition represented by the same equation? ($E = -u \times B$)
I'm trying to refine my understanding of space plasmas, and feel like there's an intuitive understanding here that I'm just missing.
We commonly refer to a motional electric field in the solar wind. ...
- 43
3
votes
2
answers
2k
views
Proof that $||\vec{E}|| = c||\vec{B}||$ for electromagnetic waves from maxwells equations in vacuum
Starting from Maxwell-equations in vacuum :
$$
\nabla \cdot \vec{E} = 0
$$
$$
\nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t}
$$
$$
\nabla \cdot \vec{B} = 0
$$
$$
\nabla \times \vec{B} =...
- 297
1
vote
2
answers
444
views
Doubt On Maxwell's Stress Tensor [closed]
I was reading Introduction to Electrodynamics by D.J. Griffiths, Chapter 8 Conservation Laws, Maxwell's Stress Tensor. The starting lines are the following:
Let's calculate the total electromagnetic ...
- 11.9k
0
votes
1
answer
167
views
Amplitude of EM waves
I'm trying to calculate the Amplitude of electric field in the EM waves using the differential forms from maxwells equations.
I've been given frequency ($10^8$ Hz) and displacement current density ($...
2
votes
0
answers
318
views
The $z$-component of the electric field vector [closed]
It is asked to find the wave equation for the z-component of the electric field vector by using Maxwell’s equations in free space.
Here is my work -
In free space we have the following relation ...
- 55
3
votes
1
answer
19k
views
Magnetic field in a capacitor
If in a flat capacitor, formed by two circular armatures of radius $R$, placed at a distance $d$, where $R$ and $d$ are expressed in metres (m), a variable potential difference is applied to the ...
- 2,547
1
vote
0
answers
101
views
Tensor Notation - David Tongs Notes [duplicate]
I'm trying to understand the Maxwell's Equation example from David Tongs QFT notes. He uses the Lagrangian:
$$
L = -\frac{1}{2}(\partial_{\mu}A_{\nu})(\partial^{\mu}A^{\nu})+\frac{1}{2}(\partial_{\mu}...
- 2,035
4
votes
1
answer
232
views
Does a homogeneous oscillating electric field produce a magnetic field?
I am working on a homework problem that says an electron in a continuous laser field can be modeled as experiencing a homogeneous oscillating electric field $\vec{E}(\vec{r},t)=\cos \omega t \ \hat {z}...
- 4,235
3
votes
1
answer
1k
views
Maxwell stress tensor for electromagnetic wave
Sorry if this is a naive question but I've been struggling in trying to proof this for a week. Consider an electromagnetic wave with wave vector $\vec{k}=k\hat{n}$, the Maxwell stress tensor can be ...
- 1,172
1
vote
2
answers
210
views
Induced EMF in single stationary wire
Suppose we have a conducting stationary wire in a uniform magnetic field: $$\mathbf B(t) = kt \mathbf u_z$$ with $k>0$. Assume the wire is a segment that lies on the $xy$ plane and its length is ...
1
vote
2
answers
753
views
How to derive the formula of angular momentum of light in Maxwell equation?
According to wikipedia,the angular momentum of light is expressed by
$$\epsilon_0\int \left(\vec E\times \vec{A} + \sum_{i=x,y,z}\vec E_i(\vec r\times \vec \nabla)A_i \right) d\vec r$$
How to derive ...
- 87
1
vote
0
answers
207
views
How to calculate the magnetic field of two cylinders when one of them is rotating
Given is the voltage U and the Angular velocity $\omega$. The rotating cylinder is inside the other cylinder and U is measured between them.
To calculate the magnetic field, I tried to solve
$\oint ...
- 23
5
votes
2
answers
3k
views
Derivative of the electromagnetic tensor invariant $F_{\mu\nu}F^{\mu\nu}$
The electromagnetic field tensor is $F_{\mu\nu}=\partial_\mu A_\nu - \partial_\nu A_\mu$. I am trying to calculate the quantity
$$ \frac{\partial(F_{\alpha\beta}F^{\alpha\beta})}{\partial(\partial_{\...
- 661
1
vote
1
answer
536
views
Non-radiation charge density
For all $l,m$ but $l=0,m=0$, can we find $r_0,w_0$ such that the following charge distributions can represent a charge field that does not radiate:
$$
\rho(r,\theta,\phi) = \Re(c_{l,m} Y_{l,m}(\theta,...
- 371
0
votes
3
answers
1k
views
Does a conducting rod moving in a magnetic field itself generate another magnetic field?
A standard problem in elementary EM goes something like this:
An infinite straight wire conducts a stationary current $I$. A conducting rod, perpendicular to the wire, moves with constant velocity ...
- 571
1
vote
1
answer
3k
views
Deriving Ampere's law from Biot-Savart equation [closed]
As an exercise, I've been trying to derive Ampere's law from the Biot-Savart equation (in the static case). So basically I'm trying to prove:
\begin{equation}
\nabla \times \vec{B}(\vec{r}) = \mu_0\...
- 71
20
votes
3
answers
2k
views
Electromagnetism problem: where does the magnetic field come from?
Consider the following problem:
Consider a plane with uniform charge density $\sigma$. Above the said plane, there is a system of conducting wires made up of an U-shaped circuit on which a linear ...
- 571
1
vote
1
answer
70
views
What $\oint\vec{B}\cdot d\vec{l}=51.5\mu T\cdot m$ mean?
I've been stuck on this practice exam question. I'm supposed to find current through a loop using Ampere's law. But instead of $\mu_0$ it says $\mu$ and it's made me very confused because I can't get ...
1
vote
1
answer
1k
views
Why are Maxwell's equations not Galilean invariant? [closed]
So i am writing an essay on the conflict between galilean invarience and maxwell's electromagnetism. I am struggling to come up with 3 evidences that they conflict because I have a mediocre ...
