The four fundamental fundamental equations of electromagnetism.
11
votes
4answers
249 views
Are the Maxwell equations a correct description of the wave character of photons?
In basic quantum mechanics courses, one describes the evolution of quantum mechanics chronologically. Interference experiments with particles showed that particles should have a wave character; on the ...
7
votes
2answers
146 views
What could magnetic monopoles do that electrically charged particles can't?
I understand the significance to physics, but what can a magnetic monopole be used for assuming we could free them from spin ice and put them to work? What would be a magnetic version of electricity?
...
3
votes
1answer
58 views
Electromagnetic black hole?
So I was thinking about something for the past while
Consider a large spherical foam-ball with homogeneous density. Where a foam ball is defined as an object that can absorb matter with 0 friction ...
1
vote
3answers
62 views
Magnetic B Field of Point Charge Not at Constant Velocity
I'm working on an N-body simulator for charged particles. I know that moving charged particles generate a magnetic field, and another moving charged particle could be effected by this magnetic field.
...
0
votes
0answers
23 views
Counting the modes of the vector potential in a coulomb gauge
With a view to quantising the EM field, consider a classical free field in the absence of charge and currents, we can take a coulomb gauge, $\phi=0, \partial_kA_k=0$. The physical fields in terms of ...
-1
votes
2answers
64 views
Is there any correlation between mass-energy equivalence and Maxwell's 4th equation?
I wonder, how came in both equations proportionality constant is exactly $c^2$?
$$c^2(\nabla \times B) = \partial E/\partial t$$
where $E$ - electric field
$$c^2m = E$$
where $E$ - energy
I am ...
2
votes
4answers
101 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 ...
1
vote
1answer
83 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
99 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:
$$S = \int dt \int ...
1
vote
1answer
90 views
Uncertainty-principle and the Maxwell formalism of electromagnetic waves
An electromagnetic wave (like a propagating photon) is known to carry it's electric and magnetic field-vectors perpendicular and each depending on the differential change of the other thus "creating" ...
5
votes
3answers
230 views
Faraday's law - does the induced current's magnetic field affect the change in flux?
I've had this conceptual problem with Faraday's law and inductance for a while now.
Take the example of a simple current loop with increasing area in a constant field (as in this answer). So ...
4
votes
2answers
114 views
Twistor Function for Coulomb Field
In an article by Penrose in Hughston and Ward "Advances in Twistor Theory", it is claimed that the twistor function
$$ f(Z^\alpha) = \log{\frac{Z^1Z^2 - Z^0Z^3}{Z^2Z^3}}$$
produces an anti-self-dual ...
0
votes
0answers
49 views
Solution of Maxwell's equation for simple, time-harmonic wire
I would like to compute the electric field $\boldsymbol{E}$ in the time-harmonic case for a (thick) wire parallel to the $z$-axis, but I can't quite get to it.
What I've got so far:
The current ...
1
vote
0answers
29 views
Show that the plane of incidence is perpendicular to the surface of reflection
Is it possible to derive from the boundary conditions of the Maxwell equations for E and H, that the plane of incidence for an EM wave is perpendicular to the reflection surface? How? If not, what ...
2
votes
0answers
50 views
Electromagnetic inertia due to advanced radiation?
The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by
$$\phi = \frac{q}{r}$$
$$\mathbf{A} = \frac{q\mathbf v}{r}$$
where the constants ...
3
votes
2answers
104 views
Magnetostatics of Current-Carrying wire
A question has been nagging at me about Faraday's Law as related to a wire with a constant current:
If you have a circular loop of wire with some small resistivity, connected to a battery so that it ...
0
votes
2answers
154 views
Advanced Heaviside-Feynman formula implies electromagnetic inertia?
The Heaviside-Feynman formula (see Feynman Lectures vol I Ch.28, vol II Ch. 21) gives the electric and magnetic fields measured at an observation point $P$ due to an arbitrarily moving charge $q$
$$ ...
1
vote
1answer
100 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
92 views
Faraday's Law and Galilean Invariance
In Jackson's text he says that Faraday law is actually:
$$
\oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = -k\iint_{\Sigma} \frac{\partial \mathbf B}{\partial t} \cdot ...
1
vote
1answer
311 views
Special Relativity: Transforming Maxwell's equations
I'm working through Einstein's original 1905 paper*, and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame.
The paper proceeds as follows:
...
2
votes
3answers
978 views
What does this quote about the four dimensional divergence of an antisymmetric tensor mean?
In the beginning, God said that the four dimensional divergence of an antisymmetric second rank tensor equals zero and there was light.
Can someone explain what is the meaning of this quote by ...
2
votes
1answer
215 views
Electrodynamics and the Lagrangian density
Could anyone tell me what equations can I obtain from the Lagrangian density
$${\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 ...
1
vote
2answers
70 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 ...
8
votes
3answers
353 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 ...
1
vote
1answer
324 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
1answer
428 views
Maxwell's Correction to Ampere's Law
I have not yet officially studied Electromagnetism but am trying to teach myself at the moment. I understand Maxwell's equations in the context of Magneto- and Electrostatics: they are equivalent, ...
0
votes
0answers
233 views
Faraday law, third Maxwell's equation in Mathematica
Three question about this equation:
$
\displaystyle\nabla\times\mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t}
$
1 If I solve this equation with Mathematica, I find the magnetic field ...
1
vote
1answer
67 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 ...
5
votes
1answer
319 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 ...
0
votes
3answers
274 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 ...
1
vote
2answers
1k 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
342 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 ...
0
votes
2answers
392 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
0answers
188 views
Magnetic field in case of 4 parallel wires… [closed]
I'm looking at four parallel wires of finite length L that are assumed infinitely thin. They are arranged in a square configuration and their currents flow in directions as shown in the figure...
...
0
votes
0answers
201 views
Proof of equality of the integral and differential form of Maxwell's equation
Just curious, can anyone show how the integral and differential form of Maxwell's equation is equivalent? (While it is conceptually obvious, I am thinking rigorous mathematical proof may be useful in ...
5
votes
4answers
186 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 ...
2
votes
2answers
206 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 ...
3
votes
1answer
196 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 ...
3
votes
3answers
500 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
1answer
122 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 ...
1
vote
2answers
376 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.
0
votes
2answers
356 views
Positive emf? What does positive emf mean?
Could someone please explain to me why we want to take the "magnitude" of the emf?
2
votes
1answer
237 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 ...
13
votes
3answers
516 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 ...
1
vote
1answer
116 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 ...
0
votes
1answer
229 views
Solution to the Maxwell's equation
Question goes as
Show that the solutions to the Maxwell's equations
$$ \nabla \times \vec H = \frac 1 c \frac{\partial \vec E}{\partial t}+\frac {4\pi} c \vec J, \hspace{ 2 mm} \nabla \times ...
2
votes
2answers
349 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 ...
4
votes
1answer
294 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 ...
2
votes
2answers
148 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
174 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 $D$:
...
