The four fundamental fundamental equations of electromagnetism.

learn more… | top users | synonyms

2
votes
1answer
283 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 ...
2
votes
2answers
515 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 ...
2
votes
1answer
403 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
526 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
1answer
33 views

Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
2
votes
1answer
63 views

What does it physically mean to take the curl of the curl of a field (wave equation derivation)?

What does it physically mean to take the curl of the curl of a field in the derivation of the electromagnetic wave equation from Maxwell's equations, as presented here, on Wikipedia? Why was it a ...
2
votes
2answers
196 views

How are the Lorentz force, Maxwell's third law and Faraday's law of induction clasically related?

Faraday's law of induction can be used in any situation where the magnetic flux is changing through a closed conducting loop. While giving the correct answer, it seems to me that for the following ...
2
votes
0answers
93 views

How to properly construct the electromagnetic tensor in curved space-time? (Part II)

In this question, I am testing what was previously discussed. I can't seem to get my results to match D'Inverno's electromagnetic tensor for a charged point (page 239 of his book - Introducing ...
2
votes
0answers
114 views

One question about derivation of Maxwell equations

I saw the following way of derivation of Maxwell equations: author starts from Lorentz transformations for the 3-vector of force, then he applies them for the Coulomb law, after that gets the Lorentz ...
2
votes
0answers
311 views

Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
2
votes
0answers
336 views

Maxwell equations and symmetry

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry? I believe the homogeneous Maxwell equations obey parity and time ...
2
votes
0answers
419 views

Electromagnetic duality

A key aspect of modern physics is the mapping of theories or different descriptions of a theory into a one-to-one correspondence. As I am trying to further understand the electromagnetic field tensor, ...
2
votes
0answers
102 views

Two spinor tensors and Maxwell's equations

Let's have two symmetric (by the indices) spinor tensors $F_{ab}, F_{\dot {a}\dot {b}}$ and conditions $$ F_{ab}, \partial^{\dot {a} a}F_{ab} = 0, \quad F_{\dot {a}\dot {b}}, \partial^{\dot ...
1
vote
3answers
284 views

How to understand holography and hologram

I've spent some time reading wiki etc. What I get now is that apart from the normal light amplitude information, holograms also record the phase information of light. But this is so difficult for me ...
1
vote
2answers
1k views

What constitutes displacement current? [duplicate]

In the chapter electromagnetic waves I was introduced with the concept of displacement current inside a capacitor. Since the region inside the capacitor is a dielectric there is no charge carriers in ...
1
vote
2answers
787 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
159 views

What would Maxwell's Equations be if we had magnetic charges and magnetic currents?

Mind you, we still have electric charge and electric currents. But, what would Maxwell's equations look like if we had to take magnetic charges and magnetic currents into consideration? Would there be ...
1
vote
2answers
251 views

The fundamental equations of electromagnetism

I'd like to know what are the basic equations of electromagnetism, that can be used to formulate all the other laws and equations. Those basic equations I can think of are Maxwell equations, Lorentz ...
1
vote
1answer
147 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
2answers
64 views

Importance of the $\exp (i \bar{k} \cdot \bar{r})$ part of the plane wave equation

I am having trouble grasping how the equation $\bar{E} \left( \bar{r}, t \right) = \bar{E}_{0} \exp \left[ i \left( \bar{k} \cdot \bar{r} - \omega t \right) \right]$ fully describes a plane wave. ...
1
vote
2answers
80 views

Condition for the magnetic field

Let $B$ be the magnetic field. If $$\nabla \times B = 0$$ and of course $$\nabla \cdot B= 0$$ Can we conclude that $B=0$? For a general field it is wrong because every constant vector will ...
1
vote
4answers
67 views

How seriously should I take the notion of “magnetic current density”

Increasingly I've noticed that people are using a curious quantity $\vec M$ to denote something called magnetic current density in the formulation of the maxwell's equations where instead of $\nabla ...
1
vote
2answers
105 views

Maxwell-Faraday Equation and Electric Fields

I have a question regarding, as the title says, this equation: $\nabla \times \textbf{E}=-\frac{\partial \textbf{B}}{\partial{t}}$ So, the above equation says that the curl of an electric field is ...
1
vote
3answers
239 views

Integration constants in Maxwell's equations (ambiguousness?)

In classical electrodynamics, if the electric field (or magnetic field, either of the two) is fully known (for simplicity: in a vacuum with $\rho = 0, \vec{j} = 0$), is it possible to unambiguously ...
1
vote
1answer
75 views

Is it necessary for EM fields to be dependent & co-exist in static conditions?

I was having a discussion today with one my colleagues in the lab about the independence and co-existence of EM fields.$$$$ My argument: In time-varying fields: EM fields are necessary dependent, ...
1
vote
1answer
58 views

Do the Maxwell equations yield the proper time of electromagnetic waves?

I apologize in advance for possible errors in my premises as I have no precise knowledge of Maxwell equations. Proposals for the correction or even abandon of my question are welcome. As Maxwell ...
1
vote
1answer
311 views

Maxwell's equations of Electromagnetism in 2+1 spacetime dimensions

What would be different in the theory of electromagnetism if instead of considering the equations of Maxwell in 3+1 spacetime dimensions, one would consider 2+1 spacetime dimensions?
1
vote
1answer
211 views

Maxwell's equations as the particular case of massive vector field equation

There was a discussion (please look to the comments on my answer) about getting Maxwell's equations for free spin-1 field by using massive spin-1 representation's equations. I'll start from the ...
1
vote
3answers
404 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
vote
1answer
357 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
2answers
744 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
3answers
322 views

Does light change phase on refraction?

I have seen a lot about when light undergoes a phase change when it is reflected. But does it undergo a phase change when refracted and if so why and if not why not?
1
vote
1answer
61 views

Deriving electric field

Can anyone explain where the following expression for the electric field vector comes from? $$ \mathbf E(\mathbf r,t) = -\nabla \phi(\mathbf r,t) - \frac{\partial}{\partial t}\mathbf A(\mathbf r,t) ...
1
vote
1answer
110 views

Finding the magnetic vector potential by calculus of variations

Given the functional $$F[A]=\int_{\mathbb{R}^3}\{\frac{1}{2\mu(x)}|\nabla\times\vec{A}|^2-\vec{J}\cdot\vec{A}\}d^3x$$ with $\vec{A}$ is a candidate vector potential for the field ...
1
vote
2answers
119 views

How to show with Maxwells Equations that nonaccelerating charges dont radiate? [closed]

How to show with Maxwells Equations that nonaccelerating charges don't radiate?
1
vote
1answer
153 views

How to obtain Maxwell's Lagrangian from complex scalar fields?

I've looked in several books and they all show how to obtain electrical interactions by forcing local gauge invariance of any complex scalar field Lagrangian (like Klein-Gordon or Dirac). I manage to ...
1
vote
2answers
287 views

Where does the 3rd and the 4th Maxwell's equations lead us in the end?

Take the 3rd and the 4th equation from this table. The first tells us that an electric field can be generated by a magnetic field. The second, says that a magnetic field can be generated from an ...
1
vote
1answer
331 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
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?
1
vote
3answers
82 views

Why does the electric field vanish at infinity?

When $r \rightarrow \infty$, $E \rightarrow 0$ for a point charge or set of charges or a finite charge distribution. While this seems obvious, I cannot find a reason why this is true when inspecting ...
1
vote
1answer
29 views

Is electricity constant in standard ECG device? [closed]

I am reading the book Bioelectromagnetism by Malmivuo et al. I am thinking if you need to use Maxwell equations in electromagnetism of ECG device. I am not sure if you need to change the current ...
1
vote
1answer
46 views

Predicting Faraday's law, Changing Fields

Are there other equations that we can predict Faraday's law from? I know that each of Maxwell's equations are 'fundamental', but I feel like Gauss's law and Ampere's Law are very "nice", and for some ...
1
vote
2answers
515 views

Neither Biot-savart nor Ampere Law can solve this problem?

I'm confused about the use of the Ampere's Law and the Biot-Savart Law due the inconvenience of each law. I want to calculate the magnetic field due to current carrying a circular loop over itself, ...
1
vote
1answer
335 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 ...
1
vote
1answer
136 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
94 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 ...
1
vote
1answer
137 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
1answer
91 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
1answer
622 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 ...
1
vote
1answer
170 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 ...