The four fundamental fundamental equations of electromagnetism.

learn more… | top users | synonyms

4
votes
4answers
865 views

Do Maxwell's equations independently impose constraints on the speed of light?

My question is about the relations and equations that makes us to impose constraints on the velocity at which electromagnetic waves propagate. Do Maxwell's equations independently impose constraints ...
4
votes
2answers
325 views

When studying electrodynamics do we assume Maxwell's Equations or derive them?

This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then ...
0
votes
1answer
203 views

Gauss's / Divergence theorem in Classical electrodynamics for the Electric field [duplicate]

Can somebody explain the proof of Gauss's theorem / divergence theorem taking the vector as electric field $$\iiint(\nabla\cdot\vec E)\mbox{ d} V=\iint \vec E \cdot\hat{n} \mbox{ d} ...
0
votes
1answer
399 views

Are Lorentz force and maxwell's equations independent? [duplicate]

The Lorentz force and Maxwell's Equations gives answers to many physics problems, and the answers given by both methods are consistent. For example, consider the problem of a conducting rod of ...
1
vote
0answers
67 views

Maximise magnetic force at one point while minimizing at another

Is it possible to have a magnet that attracts one object strongly, but not another object behind that first object? Given an (electro-) magnet M above two thin parallel steel sheets P1 and P2 in the ...
2
votes
1answer
222 views

Why is there no (time derivative of charge density) in the $B$ field in Jefimenko's equations?

I was going through Griffiths chapter on potentials and fields just to brush up on a few old things. He gets to Jefimenko's equations by this general path: Maxwell's equations Introduce scalar and ...
1
vote
1answer
274 views

Solution Maxwell's equations cylinder

I face some trouble solving Maxwell's equations inside a cylinder with perfect conductor boundaries (in 3D) ? We work with cylindrical coordinates $(r, \phi, z)$ and we make the assumption that fields ...
0
votes
0answers
134 views

Solving the source free Maxwell equations for plane waves

I've been trying to solve the maxwell equations: $$\nabla\cdot\vec{D}=0,\quad \nabla\cdot\vec{B}=0$$ $$\nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t},\quad \nabla\times\vec{H}=\frac{\partial ...
0
votes
2answers
3k views

Lorentz and Galilean transformation

I read about Lorentz and Galilean transformation in a book of modern physics some days back, but couldn't clearly understand the difference between the two? Also it was stated there that maxwell's ...
2
votes
2answers
128 views

Does $E$ cause $B$ or does $B$ cause $E$ in Maxwell's equations?

From the Maxwell's equations we get $$\frac{\partial E}{\partial x} = -\frac{\partial B}{\partial t}$$ and $$\frac{\partial B}{\partial x} = -\mu_0\epsilon_0\frac{\partial E}{\partial t}$$ ...
5
votes
2answers
748 views

Why is glass much more transparent than water?

There is a related question (Why glass is transparent?) but I am coming at it only from Maxwell's equations. One can determine the skin depth $δ$ for poor conductors like (pure) water and glass using ...
7
votes
3answers
1k views

Maxwells Equation from Electromagnetic Lagrangian

In Heaviside-Lorentz units the Maxwell's equations are: $$\nabla \cdot \vec{E} = \rho $$ $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + ...
1
vote
1answer
133 views

Electric Potential at nano scale

I’ve a got a question; and I am hopeful that you can provide any information or direct me to a better resource. I'm not a physicist; so please correct me if I'm wrong. Scanning Probe Microscopy (SPM) ...
1
vote
1answer
92 views

Maxwell equations and Fourier decomposition

I'm currently working on maxwell equations and in order to lower the fields dimension, we perform a Fourier decomposition (according to $\theta$) due to the system symmetry. For any vector field ...
0
votes
2answers
325 views

An Electromagnetic Paradox?

The above diagram represents an isolated system with two masses $M$, at position $X$, and $m$, at position $x$, connected together by an extended spring. Each mass is connected by rigid rods to ...
7
votes
1answer
314 views

Maxwell's Equations in curved spacetime

I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary ...
1
vote
0answers
94 views

Can universe be a closed manifold?

I had a question at MSE which gave a rise to another question. Maxwell equations can be written in form $$d\star F = J$$ Then by Stokes theorem we have $$ \int_U J = \int_U d \star F = ...
2
votes
2answers
438 views

Is there any relation between weak and strong fields, similar to electric and magnetic fields?

Is it possible to unify the strong, weak, electric and magnetic field just by Maxwellian type equations? (Maxwell by adding a small change - unified electric and magnetic field, then Einstein's ...
12
votes
4answers
1k 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 ...
12
votes
4answers
1k 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
217 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
354 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. ...
-1
votes
2answers
151 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
5k 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
135 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.
2
votes
1answer
479 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
278 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" ...
6
votes
3answers
3k 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
131 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 ...
1
vote
1answer
126 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
157 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
211 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
3answers
597 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
275 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 ...
3
votes
1answer
348 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
2answers
667 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: ...
3
votes
3answers
6k 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
433 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
77 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 ...
17
votes
4answers
980 views

Why do Maxwell's equations contain each of a scalar, vector, pseudovector and pseudoscalar equation?

Maxwell's equations, in differential form, are $$\left\{\begin{align} \vec\nabla\cdot\vec{E}&=~\rho/\epsilon_0,\\ \vec\nabla\times\vec B~&=~\mu_0\vec J+\epsilon_0\mu_0\frac{\partial\vec ...
1
vote
1answer
1k 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
2k 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
557 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
87 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 ...
10
votes
4answers
2k 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
1k 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 ...
2
votes
2answers
7k 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 ...
2
votes
2answers
691 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
3answers
1k 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
1answer
463 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 ...