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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2answers
57 views

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
105 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
128 views

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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2answers
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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
140 views

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
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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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41 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
127 views

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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27 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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504 views

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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20 views

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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1answer
80 views

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
222 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
67 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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312 views

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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5answers
424 views

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
107 views

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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2answers
350 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
36 views

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
108 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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0answers
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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 ...
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1answer
68 views

Empty container with pinhole - an assumption for a black body

I know that a black body is a hypothetical perfect absorber and radiator. It emits EM radiation with different intensities. But my doubt is, how can an empty container with a pinhole be considered a ...
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1answer
31 views

Mechanical and electrical power of discharging a capacitor

I want to find the power of completely discharging a capacitor with capacitance $C$ during a time interval $\Delta t$. Using the mechanical definition of power as the rate of change of energy $W$ ...
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0answers
19 views

Textbooks that can help me understand the basics of electrostatics and its mathematics [duplicate]

I am currently reviewing electrostatics in classical electrodynamics. I get to know the different mathematics behind each concept. Now, for mastery, I am looking for books that has detailed ...
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1answer
170 views

Best text books for reference (dynamic-electromagnetic systems)? [duplicate]

For modeling,design and optimization purposes relative to electrodynamic systems, what text book(s) would be ideal? I'm a mechanical engineer, and during my undergrad I used David J. Griffiths ...
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1answer
200 views

What is azimuthal symmetry? [duplicate]

What is azimuthal symmetry? When to use azimuthal symmetry and and how to know whether the problem has azimuthal symmetry or not?
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1answer
50 views

Electric quadrupole - tensor identity

In classical electrodynamics, we introduce the electric quadrupole moment $$D^{ij}\equiv\int y^i y^j \rho \mathrm{d}^3y$$ and its reduced (trace-less) version $$\mathcal{D}^{ij}\equiv D^{ij} - \frac{1}...
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1answer
29 views

Is Poynting's theorem derived from Faraday & Lenz law?

Is Poynting's theorem dependent on Faraday & Lenz law? It's an eloquent equation that shows the electrical to mechanical conversion(and vice versa), but I assume that it heavily rely's on the ...
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3answers
607 views

Kirchhoff's Voltage Law in a General Electromagnetic Field

Recently, Prof. Walter Lewin and YouTuber ElectroBOOM started a discussion about KVL, after Dr. Lewin claimed that KVL did not hold in the presence of an magneto-dynamic field. I would argue that Dr. ...
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2answers
53 views

Why charged particles moving in an electric field deflect less at higher velocity?

According to coloumb's law, particles of the same charge should experience the same force, however, when moving at higher velocities, they deflect less. Can this be explained in terms of classical ...
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1answer
86 views

Retarded time in Larmor's formula

Let $q$ be the charge of a particle whose motion is $\mathbf y(t)$; let $\boldsymbol \beta = \dot {\mathbf {y}}/c $. Let also $\mathbf x$ be a point in space, and $r=|\mathbf x|$, $\mathbf n = \mathbf ...
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1answer
50 views

Angular momentum of a circualr polarized EM wave

In an exercise, I am being asked to compute the angular momentum of a circularly polarized wave. The wave is defined by the four potential: $$\Phi^\mu(x^\nu) = \text{Re} \left\{ \varepsilon^\mu e^{...
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2answers
195 views

Hanging two charged sphere by a light string

NB: This is not a homework question. I am not searching for any solution of a math problem. I found something incorrect to do always in the nature of two charged pith balls hanging from a light ...
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1answer
50 views

Electrodynamics : Problem with Notations for fields $\vec{(\vec{r},t)}$ and $\vec{B}(\vec{r},t)$(complex and real notations)

I'm sutyding a course on electrodynamics and am stuck on a few lines I can't make sense of. The professor uses $$\vec{E}(\vec{r},t) = \vec{U_0} cos (\vec{k}\cdot \vec{r} - \omega t + \phi)$$ (so far, ...
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2answers
38 views

Reaction forces in electrodynamics

Consider two conducting plates, at different potentials so as to set up an electric field. A charged particle is released in the field. The particle experiences a force for sure, but is there a ...
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1answer
71 views

Conceptual question on volume current density and derivation of the continuity equation

The expression for the volume integral of the volume charge density is $\int_{V} (\nabla \cdot\vec{J}) d\tau = -\frac{d}{dt} \int_{V} \rho d\tau = -\int_{V} (\frac{\partial \rho}{\partial t}) d\tau$...
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3answers
98 views

Is $F^{\mu\nu}F_{\mu\nu}$ equivalent to $A^{\mu}\nabla^{\alpha}\nabla_{\alpha}A_{\mu}$ for $U(1)$ gauge field lagrangian?

The two seem to yield the same equation of motion is why I asked. Where of course the standard notation for exterior forms applies $dA=F$. We all know how the field strength tensor plays into the ...
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2answers
73 views

Magnetic force under change of reference: Do Maxwell's equations hold?

Suppose I have a uniform magnetic field through all of space $$\textbf{B}(x,y,z)=\hat{\textbf{z}}$$ and a charge $q$ moving at a velocity of $v\hat{\textbf{x}}$. In this frame of reference, a magnetic ...
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0answers
39 views

Relativistic Resistors

I would like to simulate what happens if you move electric circuits at relativistic speeds. At first, I would like to check the resistor. If I move a wire in the simplest case with speed $v$ along ...
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1answer
71 views

Question about when the Biot-Savart law holds

Is the condition $\dfrac{\partial\textbf{E}}{dt} = \boldsymbol{0}$ sufficient and necessary for the Biot-Savart law to hold? If it's sufficient but not necessary, under what other conditions does the ...
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1answer
33 views

Behaviour at an interface plane wave

I have this example diagram that was given in one of my lectures and I am just going through what the equation given actually mean and calculating some results from the equation. Which are the angle ...
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5answers
22k views

Method of calculating eddy currents of a conductor, is this correct?

I have a conductor with volume $V$, passing a magnetic field($B$) with velocity($v$): I'm trying to calculate the Eddy currents to figure out the magnitude of the drag force($F_d$) generated the Eddy'...
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1answer
323 views

Surface current density confusion

From Griffiths' Intro to electrodynamics: Now I'm confused about 3 things: 1) What is the 'mobile' surface charge density? Isn't the surface current density itself the 'mobile' surface charge ...
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1answer
50 views

Why does potential appear to differ between classical and relativistic mechanics? [closed]

As far as we know the Einsteinian mechanics is the modification of Newtonian mechanics for very fast relativistic speeds. But if Einstein's mechanics are used in low speeds, it'll give the same ...
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1answer
107 views

Coaxial cable with infinite return conductor

If a coaxial cable has a coaxial return conductor with infinite outer radius, will the return conductor experience a voltage build-up due to current flowing through it, or will it stay on ground ...
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1answer
83 views

Induced EMF in metamaterial

I am reading JB Pendry's original paper on metamaterials (Magnetism from Conductors, and Enhanced Non-Linear Phenomena) and I am really having some trouble understanding just a few of his mathematical ...
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1answer
83 views

Equation for the field of a magnetic dipole

In my electrodynamics class, my professor derived the equation for the field of the magnetic dipole $$\vec{B}(\vec{r})=\frac{\mu_0}{4\pi}\frac{1}{r^3}[3(\vec{m}\cdot\hat{r})\hat{r}-\vec{m}]+\frac{2\...
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2answers
381 views

Electromagnetic stress tensor is only traceless in 4D?

The electromagnetic stress tensor $F_{\mu \nu}$ is as we all know traceless in 4 dimensions. With $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$ and $A = (A_0,A_1,A_2,A_3)= (\phi, A_1, A_2, ...