The four fundamental fundamental equations of electromagnetism.
32
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2answers
2k views
Why did Feynman's thesis almost work?
A bit of background helps frame this question. The question itself is in the last sentence.
For his PhD thesis, Richard Feynman and his thesis adviser John Archibald Wheeler devised an astonishingly ...
19
votes
6answers
1k views
Do Maxwell's Equations overdetermine the electric and magnetic fields?
Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and ...
13
votes
3answers
506 views
Can light exists in $2+1$ or $1+1$ spacetime dimensions?
Spacetime of special relativity is frequently illustrated with its spatial part reduced to one or two spatial dimension (with light sector or cone, respectively). Taken literally, is it possible for ...
8
votes
3answers
327 views
Why do Maxwell's equations contain each of a scalar, vector, pseudovector and pseudoscalar equation?
Maxwell's equations, in differential form, are
$$\vec\nabla\cdot\vec{E}=~\rho/\epsilon_0,$$
$$\vec\nabla\times\vec B~=~\mu_0\vec J+\epsilon_0\mu_0\partial\vec E/\partial t,$$
$$\vec\nabla\times\vec ...
6
votes
3answers
700 views
Maxwell in multiple dimensions: What happens to curl?
I read this answer a while ago, and while thinking about $\nabla$, I realized something. Since the cross product can be written as a determinant, in higher dimensions we require extra vector inputs. ...
5
votes
4answers
180 views
The necessity of the B field
It is fairly easy using basic special relativity to arrive at the conclusion that the magnetic force effect on nearby charges of wires carrying currents on nearby charges is only due to the length ...
5
votes
3answers
165 views
Faraday's law - does the induced current's magnetic field affect the change in flux?
I've had this conceptual problem with Faraday's law and inductance for a while now.
Take the example of a simple current loop with increasing area in a constant field (as in this answer). So ...
5
votes
2answers
285 views
On Electromagnetic Self Energy
In the process of pair annihilation an electron and a positron annihilate each other to produce a pair of photons, conserving momentum and energy. As the oppositely charged particles approach each ...
5
votes
1answer
286 views
Are the Maxwell's equations enough to derive the law of Coulomb?
Are the 8 Maxwell's equations enough to derive the formula for the electromagnetic field created by a stationary point charge, which is the same as the law of Coulomb?
If I am not mistaken, due to ...
4
votes
3answers
436 views
can one introduce magnetic monopoles without Dirac strings?
To introduce magnetic monopoles in Maxwell equations, Dirac uses special strings, that are singularities in space, allowing potentials to be gauge potentials. A consequence of this is the quantization ...
4
votes
4answers
351 views
How to interpret the continuity conditions in the PDEs (for example, Maxwell equations) originated in physics?
I am currently working on PDEs in physics, mostly Maxwell equations. I am a mathematics graduate student, and this question has been haunting me for years.
In PDE theory, or more specifically the ...
4
votes
2answers
110 views
Twistor Function for Coulomb Field
In an article by Penrose in Hughston and Ward "Advances in Twistor Theory", it is claimed that the twistor function
$$ f(Z^\alpha) = \log{\frac{Z^1Z^2 - Z^0Z^3}{Z^2Z^3}}$$
produces an anti-self-dual ...
4
votes
1answer
278 views
How can the Huygens-Fresnel principle be derived from the Maxwell equations?
The Huygens-Fresnel principle states that every point to which a luminous disturbance reaches becomes a source of a spherical wave. I have been trying to understand this considering a infinite screen ...
3
votes
3answers
1k views
Derivation of Maxwell's equations from field tensor lagrangian
I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = ...
3
votes
3answers
479 views
Maxwell equations invariant under Lorentz transformation but not Galilean transformations
Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?
3
votes
3answers
968 views
Can the Lorentz force expression be derived from Maxwell's equations?
The electromagnetic force on a charge $e$ is
$$F=e(E+v\times B),$$
the Lorentz force. But, is this a separate assumption added to the full Maxwell's equations? (the result of some empirical ...
3
votes
1answer
121 views
Do Maxwell equeations change somehow after Higg's boson finding?
When I was in some physics -lesson, probably something to do with Quantum Physics -- the teacher said that certain Maxwell equations would change if the Higg's boson is found. It is also possible that ...
3
votes
2answers
434 views
Does existence of magnetic monopole break covariant form of Maxwell’s equations for potentials?
Absence of magnetic charges is reflected in one of Maxwell's fundamental equations:
$$\operatorname{div} \vec B = 0 \text{ (1).}$$
This equation allows us to introducte concept of vector potential:
...
3
votes
2answers
112 views
Derivatives of delta function and equation of continuity for a single charge…
For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are fiven by:
\begin{equation} \rho(\textbf{r},t)= ...
3
votes
2answers
83 views
Magnetostatics of Current-Carrying wire
A question has been nagging at me about Faraday's Law as related to a wire with a constant current:
If you have a circular loop of wire with some small resistivity, connected to a battery so that it ...
2
votes
3answers
774 views
What does this quote about the four dimensional divergence of an antisymmetric tensor mean?
In the beginning, God said that the four dimensional divergence of an antisymmetric second rank tensor equals zero and there was light.
Can someone explain what is the meaning of this quote by ...
2
votes
1answer
187 views
Why magnetic monopole found in spin ice don't modify the Maxwell's Equations?
Magnetic monopole predicted by Dirac nearly a century ago was found in spin ice as quasi-particle(2). My question is Why magnetic monopole found in spin ice don't modify the Maxwell's Equations? (I ...
2
votes
4answers
83 views
Displacement Current - How to think of it?
What is a good way to think of the displacement current? Maxwell imagined it as being movements in the aether, small changed of electric field producing magnetic field. I don't even understand that ...
2
votes
2answers
189 views
Invariance of Maxwell's Equations under inverting variables - Reference and use
Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I ...
2
votes
1answer
188 views
Electrodynamics and the Lagrangian density
Could anyone tell me what equations can I obtain from the Lagrangian density
$${\cal L}(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i,\,\,A_{i,j})~=~\frac{1}{2}|\dot A+\nabla\phi|^2-\frac{1}{2}|\nabla \times ...
2
votes
2answers
144 views
Applying $\nabla\times\mathbf{B} = \mu_0\mathbf{J}$ in the presence of magnetic shielding
2012-06-13 - Revised question in experimental format
(This is a thought experiment for which RF experts may have an immediate answer.)
I'll assume (I could be wrong) the possibility of creating a ...
2
votes
2answers
168 views
Understanding Dynamic light scattering
I'd like to understand the physics of dynamic light scattering experiment. In particular I want to understand the basic relation between relaxation time $\tau_q$ and the diffusion coefficient $D$:
...
2
votes
2answers
348 views
A Paradox in Special Relativity
Two inertial frames K and k’ are considered. They are in relative uniform motion along the x-x’ direction with relative speed =v.
In the frame K’ we have a cuboidal piece of dielectric [at rest wrt ...
2
votes
1answer
230 views
why is advanced radiation absent?
the Lienard-Wiechert green functions have future and past null cones of radiation. Maxwell equations allow for a continuous range of mixtures between the retarded and advanced components, but we have ...
2
votes
2answers
339 views
Electron model under Maxwell's theory
I was not able to recall my memories, so:
What is the formula that states the frequency of electrons revolving around nucleus is equal to the frequency of light (or photon) emitted (or radiated)?
(I ...
2
votes
4answers
395 views
How is this classical “paradox” resolved in electromagnetism?
A magnet and a coil move relative to each other. In the frame of reference of the magnet, there is a magnetic field and consequently a force acting on the charges in the coil according to the Lorentz ...
2
votes
0answers
45 views
Electromagnetic inertia due to advanced radiation?
The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by
$$\phi = \frac{q}{r}$$
$$\mathbf{A} = \frac{q\mathbf v}{r}$$
where the constants ...
1
vote
1answer
74 views
Maxwell's Equations-Relativity
How did Maxwell develop the magnetic field without relativity? Was it purely experimental? I don't see how else he would have developed any understanding for the magnetic field.
1
vote
1answer
79 views
Retrieving Maxwell's equations from the minimum action principle
I'm currently working at the start of Alexei Tsvelik's book Quantum Field Theory in Condensed Matter Physics. I'm kinda stumped on a few essential steps.
Starting with the action:
$$S = \int dt \int ...
1
vote
1answer
292 views
Special Relativity: Transforming Maxwell's equations
I'm working through Einstein's original 1905 paper*, and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame.
The paper proceeds as follows:
...
1
vote
1answer
74 views
Uncertainty-principle and the Maxwell formalism of electromagnetic waves
An electromagnetic wave (like a propagating photon) is known to carry it's electric and magnetic field-vectors perpendicular and each depending on the differential change of the other thus "creating" ...
1
vote
1answer
90 views
Faraday's Law and magnetic monopoles
The magnetic monopoles does not exist which can be shown by $ \int {\vec{B} \cdot d\vec{A}} = 0 $.
But in Faraday's Law of electromagnetic induction, we clearly show the EMF induced is the time rate ...
1
vote
1answer
90 views
Faraday's Law and Galilean Invariance
In Jackson's text he says that Faraday law is actually:
$$
\oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = -k\iint_{\Sigma} \frac{\partial \mathbf B}{\partial t} \cdot ...
1
vote
1answer
320 views
Divergence of non conservative electric field
I'm looking for the proof that the 1st Maxwell equation is valid also on non conservative electric field.
When we are talking about a electrostatic field, the equation is ok. We can apply the Gauss ...
1
vote
2answers
372 views
Lorentz Invariance of Maxwell Equations
I am curious to see a simple demonstration of how special relativity leads to Lorentz Invariance of the Maxwell Equations. Differential form will suffice.
1
vote
1answer
65 views
Idea of precursors of the electro-magnetic waves
The idea of the material Maxwell equation is almost clear. But I'm curious about the idea that except for material equation the pure Maxwell equation should work, but in harder sense: more currents ...
1
vote
2answers
974 views
How do you find the magnetic field corresponding to an electric field?
If we are given the electric field $\vec E$ how can I find the corresponding magnetic field? I think I can use Maxwell's equations? In particular, $\nabla\times \vec E= -{\partial \vec B\over \partial ...
1
vote
1answer
113 views
Determine the flow and amplitude equation for thermal energy (with Del operator)
It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
1
vote
2answers
633 views
Conservation of Energy and the Poynting Theorem
Conservation of energy in an electrical circuit can be expressed by Ampere's law $$\nabla \times \textbf{B} = \mu_o
\textbf{J} + \epsilon_o \mu_o \frac {\partial \textbf{E}} {\partial t}$$ when ...
1
vote
0answers
23 views
Show that the plane of incidence is perpendicular to the surface of reflection
Is it possible to derive from the boundary conditions of the Maxwell equations for E and H, that the plane of incidence for an EM wave is perpendicular to the reflection surface? How? If not, what ...
1
vote
2answers
67 views
What's so special about wave solutions of EM?
Maxwell's equations allow for wave solutions via oscillations between electric and magnetic field content.
Couldn't we generate electric waves also if that solution didn't exists?
Imagine there was ...
1
vote
1answer
290 views
Is the induced electric field due to time varying magnetic flux always circular?
According to Faraday's law, changing magnetic flux induces an electric field. Is that electric field always circular?
0
votes
3answers
260 views
Divergence equations (Maxwell)
Let $\mathbf{E}(r,t),\mathbf{B}(r,t)$ be two vector fields (in $\mathbb{R}^3$), s.t. they satisfy fot $t=0$ the equations:
$\nabla \cdot \mathbf{B}(r,0)=0.$
$\nabla \cdot ...
0
votes
2answers
367 views
Deriving the Poynting Theorem
I am trying to derive the Poynting theorem. So far, I've only been able to narrow down which equations I think I'll need to do so. These are the equations:
Maxwell's Equations:
$$
\nabla\times{\bf E} ...
0
votes
2answers
131 views
Advanced Heaviside-Feynman formula implies electromagnetic inertia?
The Heaviside-Feynman formula (see Feynman Lectures vol I Ch.28, vol II Ch. 21) gives the electric and magnetic fields measured at an observation point $P$ due to an arbitrarily moving charge $q$
$$ ...
