The four fundamental fundamental equations of electromagnetism.

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51 views

Maxwell Equations don't give unique Electric Field?

Consider the class of electric fields given by $$\mathbf{E}=\begin{cases} \ln (Cr)\hat{z} & 0\leq r < R\\ 0 & r> R \end{cases}$$ where $C$ is a constant and $r$ is the polar-distance ...
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45 views

Why must this boundary condition be met? (Electromagnetic wave at interface between two mediums)

My textbook says that The laws of Electromagnetic Theory (Section 3.1) lead to certain requirements that must be met by the fields, and they are referred to as the boundary conditions. ...
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212 views

Maxwell's equation in curved spacetime - how come? And experimental evidence?

I'm trying to understand the generalization of Maxwell's equations to curved spacetime. In FLAT (Minkowski) SPACETIME: If we define the "four-potential" as $$\ ...
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751 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 ...
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47 views

Do divergence and curl of Lorentz force have some physical meaning?

Time ago I started thinking about this: if we take the well known Lorentz Force expression, namely $$\mathbf{F} = q\left(\mathbf{E} + \mathbf{v}\times\mathbf{B}\right)$$ and we operate $\nabla\cdot ...
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69 views

Can a Set of “Maxwell's Equations” for Newtonian Gravitation be Derived from Newton's Force + Special Relativity?

When I learned about electromagnetism in my first year of undergraduate school, Maxwell's equations were derived roughly in the following way (see also here or in [1]): Gauss's law for a static ...
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50 views

Electric field from time varying charge density

Inside a cylinder of infinite length in $z$ axis, there is charge density $ ρ = cos(βz -ωt)$. I want to find the electric field and as far as i can understand we will get a radial component of $E$. ...
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56 views

Spectroscopy from a classical light wave or photon only?

In chemistry we mostly regard light/electromagnetic radiation as a beam of particles or photons. This is a very useful model to explain molecular excitations and ionisations from quantum interactions. ...
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123 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 ...
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189 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
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0answers
591 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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629 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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123 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 ...
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37 views

What does this coordinate transformation in the Wave equation mean?

My tutor derived the following of which I do not understand the transformations (2.1) and (2.2): $$\Delta\vec{E} - \frac{1}{c^{2}} \frac{\partial^{2}\vec{E}}{\partial t^{2}} = \frac{4\pi}{c^{2}} ...
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16 views

Time dependance of oscillating sheet of charge

I am working on a practice problem involving maxwells equations. We have an infinite sheet of charge density $\sigma$ in the x-y plane and it is oscillating as x= $\Re [x_0e^{-i\omega t}]$. I want to ...
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59 views

Distribution of current, charge and EM radiation from a centrally AC fed ball-shaped antenna

As far as I can understand, it is generally accepted that every classical electromagnetic phenomena can be explained by five equations: Maxwell's four equations and the Lorentz force law. However you ...
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68 views

What unit system puts a bunch of powers of ten in Maxwell's equations?

In what unit system can we get the Maxwell equation in the following form (section 1.2 from Lewin's book Advanced Theory of Waveguide) $$\nabla\times \vec E = -10^8\mu \frac{\partial \vec H} ...
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54 views

Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed?

Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed? It is clear that Maxwell's equations in themselves permit magnetic charges but what would their relativistic ...
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37 views

Boundary conditions for vector wave equations

Assume the time-harmonic case of Maxwell's equations, one can obtain the following vector wave equations: $$ ...
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34 views

How do I show $e_r$ and its first- and second time derivative?

What does a charge q moving in a circular orbit with a constant velocity (a "rotating charge") and a stationary observer that measures the E field look like? And how do I show $e_r$ and its first- and ...
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80 views

Aether/Ether in Electrodynamics?

From reading Maxwell's original papers on the formulation on the dynamics of electromagnetism, I saw that Maxwell kept mentioning aether in his paper. I know today in modern physics the Michelson ...
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40 views

Faraday's law in free space explaining away the constant vector?

Let's say that I have a plane electromagnetic wave travailing in free space, and I know the electric field part to be $\vec E$. If I am using Faraday's law to get the magnetic field part I will get ...
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195 views

Analytical solution to Maxwell's equations in 3D

I'm working on solving Maxwell's equation numerically and have implemented Yee's algorithm in Matlab. In order to check if the algorithm is implemented succesfully, I need an analytical solution to ...
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43 views

Can a charge moving in an open trajectory qualify as current?

It is sometimes said that a point charge is equivalent to an electric current. If it were a steady current, I should be able to find it from Ampere’s law or Biot-Savart’s law. Even if the current is ...
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122 views

Why did Heaviside eliminate the magnetic potential from Maxwell's Equations?

Maxwell's original equations had magnetic potential, but Heaviside eliminated this variable. What was the reason for Heaviside's removal of the magnetic potential?
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55 views

Does the anisotropic Fermat eikonal equation predict the extraordinary ray direction given by Poynting vector?

Does the anisotropic Fermat eikonal equation predict the extraordinary ray direction given by Poynting vector?
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75 views

How to solve the following set of equations (magnetohydrodynamics with anomaly term)?

Let's have system of equations: $$ \tag 1 [\nabla \times \mathbf E^{(1)}(\mathbf r , t) ] = -\frac{\partial \mathbf B^{(1)}(\mathbf r , t)}{\partial t} , $$ $$ \tag 2 [\nabla \times \mathbf ...
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65 views

Deriving Ampère's Circuital Law from Ampère's Force Law?

Ampère's force $d^2\vec{F_{21}}$ of current element $i_2d\vec{\ell_2}$ on $i_1d\vec{\ell_1}$ is$$d^2\vec{F_{21}}=-\frac{\mu_0}{4\pi}i_1i_2\frac{\hat{r}}{r^2}\left[2(d\vec{\ell_1}\cdot ...
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133 views

Were Maxwell's equations first formulated by McCullough?

Some years ago, I heard a talk about a an Irish or Scottish physicist named McCullough who had formulated Maxwell's equations several years before Maxwell. This fellow was recognized for his work, ...
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586 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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52 views

Do these steps demonstrate that acceleration of charged particle is proportional to current?

One formulation of Maxwell's Gauss Law for electric field is: $$\bigtriangledown E = 4 \pi k \rho $$ This can be worked into the Divergence Theorem as follows: $$\int\int_{A} F_\perp \:dA= 4\pi k ...
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86 views

One more time about the connection of Weyl tensor and gravitational waves

There is differential identity with Weyl tensor and energy-momentum tensor: $$ D^{\lambda}C_{\lambda \alpha \sigma \beta} = 4 \pi G \left(D_{\sigma}T_{\alpha \beta} - D_{\beta}T_{\alpha \sigma} + ...
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80 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 ...
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108 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 = ...
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812 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 ...
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39 views

Explanation about the speed of light according to Maxwell from the book : “ A brief History of Time”

I just started reading Hawking's book: " A brief history of time" and there is a section that I don't understand referring to the speed of light moving through the "ether". In the second chapter, ...
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22 views

Displacement current in a capacitor

I recently learned about the concept of displacement current in a capacitor. I've understood the basics - mainly understood the reason why it was introduced. However, is it purely a mathematical ...
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0answers
18 views

Relation between displacement current, dielectric and time varying Electric field

I know that displacement current is produced in dielectric material due to dipole moment. I also know that displacement current is produced by time varying electric field (according to maxwell ...
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29 views

When can I use Helmholtz equation for electraomagnetic wave

The complete Maxwell wave equation for electromagnetic field using the double curl operator "∇×∇×". Only when the transverse condition is hold, this operator can equal to the Laplace operator and form ...
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20 views

Purpose of magnetic charge and current density

I am aware that introducing a magnetic charge density and a magnetic current density makes Maxwell's equations much more symmetric. But in what situations/problems is this beneficial? Could someone ...
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35 views

Deriving Maxwell's equation from the Lagrangian of an electromagnetic field with a charge density $\rho$

I want to derive Maxwell's equation from the Lagrangian of an electromagnetic field with a charge density of $\rho$ The Lagrangian is given by ...
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0answers
64 views

Magnetic monopole using differential forms

I'm trying to understand the different variations of the Maxwell's equations using differential forms. The Maxwell's equations are $$dF=0\\ *d*F=J$$ where $F$ is the electromagnetic tensor ($F=dA$) ...
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31 views

derivation of the electic displacement D

I've been revising Maxwell equations recently and tried to prove that the electric displacement $ \mathrm{\nabla \cdot D = 0}$ in the electrostatic approximation ($\mathrm{E = - \nabla} f$). My steps ...
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27 views

RF cavity Field Maps using Poisson Superfish

This may be a slightly obscure question but I'm trying to use Poisson Superfish to generate field maps for single cell of an ILC SRF Cavity. There are examples in the documentation for radio ...
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25 views

Effective Medium

Please consider the following problem : A plane wave of wavenumber k is incident on an infinite slab which is inhomogeneous in the z direction. Also assume harmonic time dependence and that the ...
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0answers
19 views

In electrostatics, what is the actual relation between flux density and flux

I know, in magnetostatics, unit of flux in webers. And unit of flux density B is webs per metre square. its clear. Now in electrostatics, unit of flux is volts metre. And unit of flux density D is ...
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71 views

Would a super conductive insulation completely prevent the propagation of a magnetic field from a wire where it is wrapped around?

I have limited understanding about super conductors and see them as expelling magnetic fields purely due to eddy currents produced without resistance opposite the magnetic field. I have read that ...
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23 views

Single slit diffraction treated as a differential equation

I want to find the values of electromagnetic fields that result from single slit diffraction. This should be possible by solving maxwell's equations for appropriate boundary conditions. But I'm not ...
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36 views

Two equal charges accelerating parallel to each other

Let's say constant acceleration for simplicity. Ignore possible logistic concerns, such as what is accelerating them or how they stay in path. Lets just assume they are in a conduit made of a solid ...
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33 views

Pefectly electrically conducting Neumann boundary conditions

I have a rather subtle question regarding necessary boundary conditions. To solve Maxwell's source-free equations as an initial boundary value problem in a volume $\Omega$ bounded by a perfectly ...