Questions tagged [classical-electrodynamics]

Classical electrodynamics is the discipline that studies electromagnetic phenomena – such as electric and magnetic fields, radiation, and the dynamics of charged bodies – in classical terms.

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Derivations of Maxwell equations

In my book of electrodynamics, the Maxwell equations are always used for specific conditions (electrostatics, magnetostatics, …). But nowhere I see a complete derivation of the equations. Maybe it ...
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Maxwell's equations, nonlinear media, and dynamic response

Maxwell's equations in the vacuum with electric permittivity $\epsilon_0$ and magnetic permeability $\mu_0$ are given as: $$\nabla \cdot \vec E = \frac{\rho}{ \epsilon_0}$$ $$\nabla \cdot \vec B = 0$...
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Does Jackson's result for the vector potential of current loop correct?

General form of Maxwell equation is given by $$ \nabla_\mu F^{\mu\nu} = 4\pi J^\nu $$ where $F_{\mu\nu}=\nabla_\mu A_\nu-\nabla_\nu A_\mu$ is the tensor of EM field. Then Maxwell equations can be ...
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1answer
66 views

Charged particle moving in magnetic field using cylindrical coordinate [closed]

It's knowen that a charged particle take a helix trajectory in a uniform magnetic field $B =B e_z$ I tried to study this problem using cylindrical coordinate and i get that $$F=q v ×B = m a$$ in ...
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157 views

Maxwell stress tensor for electromagnetic wave

Sorry if this is a naive question but I've been struggling in trying to proof this for a week. Consider an electromagnetic wave with wave vector $\vec{k}=k\hat{n}$, the Maxwell stress tensor can be ...
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Magnetic field $\vec{A}$ as momentum potential

I was reviewing some topics on electromagnetic field theory and I came across the following interesting assertion: the electromagnetic moment $P_{EM}$, which is defined in vacuum as: $$P_{EM}=\frac{1}...
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What is the answer to Feynman's Disc Paradox?

[This question is Certified Higgs Free!] Richard Feynman in Lectures on Physics Vol. II Sec. 17-4, "A paradox," describes a problem in electromagnetic induction that did not originate with him, but ...
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43 views

Question about the Lorenz gauge in classical electrodynamics

The Lorenz gauge is the gauge such that $$\nabla \cdot \mathbf{A} = -\mu_0\epsilon_0\frac{\partial\Phi}{\partial t}.$$ This condition dictates what $\lambda$ is in $$\mathbf{A}' = \mathbf{A} + \nabla \...
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Physics solely in terms of local observables

Practically all of the physics equations I've encountered are written in terms of what might be called "remote observables", such as the distances between objects in Euclidean space or between events ...
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120 views

Why can we pick the divergence of the vector potential? [duplicate]

I'm aware that the vector and scalar potential in E&M can be modified using a function $\lambda(t)$ in the following way: $$\mathbf{A}' = \mathbf{A} + \nabla\lambda,\;\; \textrm{ and } \;\;\Phi' =...
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Symmetry operations on an infinite uniform sheet of charge

My book has a section on symmetry operations. It says, (if the plane of charge is the yz plane) translation symmetry along the y-axis and z-axis implies that the electric field is constant if one ...
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On the applicability of Coulomb's law and the Biot-Savart law

Jefimenko's equations are $$\textbf{E}(\textbf{r}, t_r) = \frac{1}{4\pi\epsilon_0}\int \left[\rho\left(\textbf{r}', t_r\right)\frac{\textbf{r} - \textbf{r}'}{\left|\textbf{r} - \textbf{r}'\right|^3} + ...
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Could magnetic fields really be completely substituted by relativity and electric fields?

In many textbooks (especially those for undergraduate level), magnetic fields are described merely as a relativistic side product of electric fields when considering frames in motion relative to ...
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Green's function in a region between a conductor sphere and two charged spheres inside, with point charges inside of each

Please, help me. I have to find the Green's function in the following region, but I don't have any idea how to find it: I have a conducting spherical shell of radius a; in the center there are 2 ...
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3answers
115 views

Is Poynting vector conserved or Intensity conserved for reflection and transmission of electromagnetic wave?

When an electromagnetic wave meets a boundary, does energy conservation mean Poynting vector of reflected + Poynting vector of the transmitted wave is equal to Poynting vector of incident wave or just ...
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541 views

Why can the Lorenz gauge condition always be fullfilled?

Why is the Lorenz gauge condition always possible for classical electromagnetic fields? So far I can only understand the following: If we perform a gauge transformation $A\mapsto A'=A+\mathrm{d}\...
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114 views

Electromagnetic field tensor and antisymmetry

Why does the inner product between the four force (caused by the electromagnetic field tensor) and the four velocity equaling zero imply that the electromagnetic field tensor is antisymmetric? This ...
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4answers
279 views

Mathematics supporting the classical explanation of why the phase speed of light slows down in a medium

Consider the answer here by Chad Orzel which explains how a monochromatic light can slow down in a medium. He explains, You can think each of the atoms (of the medium) as being like a little dipole,...
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2answers
111 views

inverse square law and far-field radiation

This question is related to Feynman on inverse square law of EM radiation. It is basicly the same question except that I don't see that the question was ever answered, and I hope someone will answer ...
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1answer
42 views

Is the electric force that drives current equivalent to the Lorentz force acting on those currents?

Current flow ($I$) and the electric force responsible in moving the charges are proportional to the Lorentz force acting on those charge due to the magnetic field that the current flow produces, all ...
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35 views

Ampere's Law, Interface conditions for magnetic field

I'm failing to understand the derivation of the interface conditions for the tangential components of the magnetic field given her (based on d.j,griffiths) Ampere's law in integral form is given as $$...
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What are Towsend Coeffiecents exactly? And are there any tables out there to look them up?

My question is expecially for the gamma coefficent, does it depend from the air? And further how the material of electrodes is involved in Paschen's Law (Electric Arcs)?
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Is Faraday's law of induction valid for a partial conducting loop?

If a conductive loop is partial or incomplete(wrt. $A$), is Faraday's law of induction still valid? $$\varepsilon = -\frac{\delta \Phi_B}{\delta t}$$ Intuitively it seems possible to define the ...
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76 views

Energy of continious charge distribution

In the book of Griffith intro to electrodynamics, on page 94, the energy of continuous charge distribution is derived in the following way: W(total energy) = $\frac{1}{2} \int\rho V d\tau$, where $\...
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Time varying magnetic field, yielding two effects of induction?

$B_s$ is nonuniform, and it's generated from a movable source(e.g magnet or electromagnet). A rectangular loop of area $A$ is stationary. The variation of flux for this case is caused from the ...
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43 views

Induced emf from a time varying magnetic field & motion of charges simultaneously?

Due to the current flow, supplied by the battery, and the production of the magnetic field($-B\hat{k})$, A Lorentz force($f_L = IL\times B$) will accelerate the rod. My issue with this, is classical ...
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3answers
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The nature of current induction via time varying B & the interactions of different emf sources

1) If a conducting loop was placed in a time varying magnetic field, the changes of $B$ over some time, would produce and electric field as Faraday's law indicates(Regardless if there is a conductor ...
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Does classical physics allow a flow of electrons in vacuum to form a current?

My physics teacher today proposed this question as a homework. My view is that it does allow the current to flow classically.
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49 views

How is Poisson's Equation solved numerically?

This question is of pure interest. I would like to know, how a mixed boundary value problem like the following can be solved numerically: Lets say I have two conducting plates (not necessarily ...
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1answer
98 views

Transfer of Electrical Charges

I'm having a lot of trouble understanding how charges transfer exactly. Suppose I have 3 particles $a,b,c$, $a$ is negatively charged, $b$ is positively charged and $c$ is neutral. We let the charges ...
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2answers
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Can the magnetic field *always* be transformed away?

In the book, "Einstein's General Theory of Relativity..." by Øyvind Grøn and Sigbjorn Hervik, the following statement is made: "The Lagrangian density of an electromagnetic field is the energy-scalar ...
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Method of image charge for cylindrical conductor

I am simply puzzled that only for spherical and planar conducting surfaces the method of images is applied. Is it (really) impossible to find image charge or charge distribution which can simulate the ...
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4answers
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Does Coulomb's law hold as long as $\dot{\rho} = 0$?

Does Coulomb's law, $$\textbf{E}\left(\textbf{r}\right) = \frac{1}{4\pi\epsilon_0}\int \rho\left(\textbf{r}'\right)\frac{\textbf{r} - \textbf{r}'}{\left|\textbf{r} - \textbf{r}'\right|^3}dV',$$ hold ...
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3answers
229 views

Systematic expansion of $e^{i\vec{k}\cdot\vec{r}}$ in atomic physics in terms of Legendre polynomials and identifying different $l$ terms

In the context of light-matter interaction one often makes the approximation $e^{i\vec{k}\cdot\vec{r}}\approx 1$. Keeping higher order terms in $e^{i\vec{k}\cdot\vec{r}}$ give magnetic dipole, ...
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39 views

Fourier Transform of the Lienard Wiechert Fields and the retardation condition

If the Fourier Transform of the field as a function of space at a specific moment of time, $\vec{E}(\vec r , t)$, with respect to time gives us the field as a function of space at a specific frequency ...
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3answers
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Physical Interpretation of $\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} $

The differential's form of Gauss' Law is $$\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}. $$ This suggests that at every point in space, the the electric field $\vec{E}$ is determined by the charge ...
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26 views

Electric field produced by a moving charged particle above a planar dielectric interface

The electrostatic field of a single charged particle above a planar dielectric interface is a standard example given in many books (see example 4.4 in Griffiths or https://en.wikipedia.org/wiki/...
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Falling electric dipole contradicts equivalence principle?

Consider an electric dipole, with total mass $M$, consisting of charges $q$ and $-q$, separated by a distance $d$. The total mass $M$ includes the mass defect due to the negative electrostatic energy ...
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When a charge starts moving, does it's electric field change into magnetic field? [duplicate]

If the electric field does change into magnetic field, how does it happen? And if it doesn't happen, then what happens to the electric field?
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Question regarding charge and acceleration

From a stationary charge electrostatic fields arise. From a moving charge, magnetostatic fields arise. From an accelerating charge, EM waves arise. So i wonder -- what about a non-constantly ...
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1answer
173 views

Surface charge density from volume charge density [closed]

I'm working on a problem taken from Zangwill's Modern Electrodynamics, where I'm asked to derive the well known result of the electric field $\mathbf{\vec{E}(\vec{r})}$ both inside and outside a ...
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1answer
66 views

Are problems with self-energy of point charge in classical electrodynamics solved by field quantization?

Classical electrodynamics gives strange results when considering a moving charge in its self generated field (Abraham-Lorentz equation). Some 50 years ago there were many efforts and publications ...
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Which is the physical meaning of the evanescent wave?

I was reading that for an incident angle greater than the critical angle, there will be a total internal reflection. The cosine of the refraction angle is therefore an imaginary number. If we make a ...
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Could be possible to build a 4-vector in special relativity whose spatial component was the electric field E?

Hi everyone and sorry for my English. I would like to know if I can build a legitimate 4-vector as $E^\alpha=(E^0,\mathbf{E})$. I'd like you to check if my way is correct. 1- We already know that $\...
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1answer
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Poynting theorem in Landau and Lifshitz’ field theory book

In Landau & Lifshitz’s The Classical Theory of Fields, in section 31, they have proved the Poynting theorem (equation 31.6) in its integral form. In the footnote on page 76, they mention We ...
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344 views

How does the Lorentz force work for all velocities

At small velocities, the lorentz force in the boosted frame is approximately $F' = q(E + 2v \times B)$, where the one for the rest frame is $F = q(E + v \times B)$. How is this invariant if the two ...
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1answer
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Electrodynamics confusion - Hertzian dipole

I am studying a course in Electrodynamics and we are just covering retarded potentials and the Hertzian dipole. In my lecture notes, we have calculated the magnetic vector potential $A$ in the ...
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1answer
101 views

On the “Derivation of the Electromagnetic Lagrangian density”

In the most upvoted answer here : Deriving Lagrangian density for electromagnetic field, how do we know that equations (015) and (016) therein \begin{equation} \boxed{\: \dfrac{\partial }{\partial t}\...
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2answers
89 views

Doubt about current density [closed]

We are taught in electrodynamics classes that current density is a vector quantity while current is a scalar. I understand why current is a scalar and current density is a vector. But what's troubling ...
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56 views

Hamilton equations of motion for matter fields coupled to general relativity in ADM formalism

Do you know what are the Hamiltonian formalism analogs of the Klein-Gordon equation and/or the Maxwell equations in general relativity? Showing how these equations of motion for matter in the ...