The four fundamental fundamental equations of electromagnetism.

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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 ...
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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 ...
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Physical meaning of Maxwell's equations and origin of EM waves

Is it possible to describe the physical meaning of Maxwell's equations and show how they lead to electromagnetic wave, with little involvement of mathematics ?
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Divergence of a field and its interpretation

The divergence of an electric field due to a point charge (according to Coulomb's law) is zero. In literature the divergence of a field indicates presence/absence of a sink/source for the field. ...
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1answer
49 views

Maxwell calculations that predicted the generation of waves (further use for wireless telegraphs)

At this point in this documentary about the history of electricity: https://www.youtube.com/watch?v=oPnS2WO2_0k&t=4m40s the guy says the Maxwell calculations predicted the generation of certain ...
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4answers
335 views

Why ONLY Maxwell's equations are the basic equations of electromagnetism?

In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other ...
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1answer
59 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 ...
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1answer
225 views

Plane wave complex notation

As far as I know, the function: $$ \vec{E}(\vec{r},t)=\vec{E_0}\cdot e^{i(\vec{k}\cdot \vec{r}-\omega t)} \hspace{2cm}(1) $$ is a mathematical solution of the wave equation: $$ \nabla^2 ...
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2answers
258 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 ...
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1answer
186 views

E&M and geometry - a historical perspective

Recently, I was contemplating the beautiful formulation of electromagnetism (specifically Maxwell's equations) in terms of differential forms: $$F=\mathrm{d} A\implies \mathrm{d}F=0 ...
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1answer
120 views

Application of Displacement Current

I'm reasonably happy with the derivation and results of displacement current, however, I'd like to be aware of a few practical applications of this idea. So far, the only one I'm aware of is when ...
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1answer
46 views

Is the field generated by an electromagnet always proportional to its current?

Imagine that I use a long wire to create an electromagnet. Let's also assume that the current flowing along the wire is constant, and that the wire is winded on the vacuumm. Is the magnetic field ...
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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 ...
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3answers
253 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 ...
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4answers
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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? ...
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3answers
643 views

Curl of an electromagnetic wave?

I can't understand the concept of the curl of an electromagnetic wave. $$ \nabla \times E = -\frac{\partial \textbf{B}}{\partial t} $$ All of the examples I find show a current through a conductor, ...
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1answer
108 views

Maxwell equations [closed]

$$\oint B.dl = \mu_0\left(I+\epsilon_0\frac{\partial\Phi_E}{\partial t}\right)$$ Please explain the applications , and implications of the modified Ampere's circuital law with Maxwell's addition. ...
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81 views

Jacobian of a transformation on Maxwell equations in cylindrical coordinates

In an area called transformation optics, they transform Maxwell equations from one space coordinate system to another, and then using the fact that Maxwell equations retain the same format under ...
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51 views

Poynting Vector between Capacitor - With electrons in between!

Consider a capacitor with voltage $V = V_0 cos(\omega t)$, radius $a$ and separation $d$. Electrons are distributed uniformly with number density $n$. I want to find the poynting vector between the ...
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2answers
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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 ...
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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 ...
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Electromagnetic fields in daily life [closed]

I have been reading up on electromagnetism lately, and to gain some intuition I wanted to know what effects electric and magnetic fields would have in daily life if they were generated "without any ...
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96 views

Obtain the same Maxwell's equation after a change of coordinates

In the usual $(x,y,z)$ system of coordinates, if we expand the Maxwell's curls equations for phasors $$\nabla \times \mathbf{E} = - \mathbf{J}_m - j \omega \mu \mathbf{H}$$ $$\nabla \times \mathbf{H} ...
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1answer
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Is $H_0^1$ something reasonable for the electric field for a perfect conductor?

I'm trying to pull over some concepts that were derived for Navier-Stokes like equations to Maxwell's equations for the perfect conductor. At a certain point, I am about to assume that the electric ...
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445 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, ...
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0answers
57 views

E and B field from Time Varying Current

How would I go about calculating the B field and E field from a time varying current charging a capacitor. Theoretically I feel like a solution should exist, but there seems to be a dependence between ...
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143 views

When to use which representation for an electric field

In class we covered three types of possibilities to evaluate the electric field for static problems. Unfortunately, most physics textbooks cover these ways without addressing the question of ...
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1answer
180 views

Did Maxwell invent the math to describe the ideas of electromagnetism?

Did he invent surface and line integrals, or did they already exist when he formulated his equations. If they did, already exist, how did they come about in pure math?
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Is my simulation result for unpolarized light correct?

This is a follow-up of this question. After that, I picked up some knowledge of FDTD (an algorithm for solving Maxwell's equations) and simulated following scene: Pic 1 As the picture shows, a ...
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2answers
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Why is the divergence of a magnetic field equal to zero?

We know due to Maxwell's equations that: $$\vec{\nabla} \cdot \vec{B}=0$$ But if we get far from the magnetic field, shouldn't it be weaker? Shouldn't the divergence of the field be positive? If ...
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59 views

Deduce magnetic field based on electric field

I'm learning Maxwell's electromagnetic equations and i can't wrap my head around this problem: Given the volume $x\in [0,1], y\in [0,1], z\in [0,1]$, electric field $\vec E(x,y,z,t)$ and material ...
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0answers
328 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 ...
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293 views

Sommerfeld radiation conditions for an electromagnetic field

There is some confusion in the definition of Sommerfeld radiation conditions for an electromagnetic field, which are related to the asymptotic behaviour of the field for a distance $r \to \infty$ ...
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2answers
81 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 ...
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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 ...
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107 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 ...
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Which form of Maxwell's equations is fundamental, in integral form or differential form?

I am not sure which form of Maxwell's equations is fundamental, integral form or differential form. Imagine an ideal infinitely long solenoid. When a current is changing in time, can we detect ...
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Electromagnetism duality theorem

Concerning Electromagnetism, textbooks often refer to the Duality Theorem. Sometimes it is presented like this: ¬ęConsider the Maxwell's Equations (with phasors) and a known field $\mathbf{E}_1$, ...
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280 views

What is the physical significance of the Dipole Transformation of Maxwell's Equations?

The Question Given Maxwell's equations of the form \begin{align} \bar{\nabla}\times \bar{B} = \dfrac{4\pi}{c} \bar{J} + \partial_0 \bar{E} \\ \bar{\nabla}\times \bar{E} = -\partial_0 \bar{B} \\ ...
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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?
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101 views

How to do this index notation differentiation?

I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ? $$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} ...
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1answer
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How can KVL & KCL be derived from Maxwell equations?

How can KVL (Kirchhoff's Voltage Law) & KCL (Kirchhoff's Current law) be derived from Maxwell equations in lumped circuits?(Lumped network : if $d$is the largest dimension of the network and ...
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1answer
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How can electrons move along the conductive wire? ( seems to be a paradox )

Tangential components of the electric field across an interface between two media, with no impressed magnetic current densities along the boundary of the interface, are continuous. So: $ n \times (E_2 ...
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3answers
179 views

Question about units of mass, $M = (L^{3})(T^{-2})$?

In section 5 of the "Preliminary: On the measurement of quantities" chapter (page 3) in "A treatise on electricity and magnetism" Maxwell uses, total length, $s=mt^{2}/{2r^{2}}$to show that ...
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3answers
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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} ...
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2answers
120 views
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1answer
164 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 ...
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3answers
293 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 ...
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2answers
791 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 ...
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358 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 ...