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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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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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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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Application of the Flux-law for an incomplete loop?

1) The application of the flux law, to a circular or rectangular loop is simple. However, what if the loop was incomplete? If there is a change in flux caused from either the deformation of the loop'...
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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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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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Surface charge density from volume charge density [on hold]

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
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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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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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Lagrangian Mechanics - Charged particle in magnetic field [closed]

A particle of mass $m$ and charge $Q$ moves in the equatorial plane ($θ=π/2$) of a magnetic dipole, where the vector potential of the dipole is given by $$\mathbf{A} = \dfrac{\mu \sin \theta }{4 \...
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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
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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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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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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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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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2answers
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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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1answer
25 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
28 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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1answer
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Why does electric field undergo a discontinuity when we cross $any$ surface charge $σ$?

According to Griffith's book on electrodynamics, electric field always undergoes a discontinuity when crossing a surface charge $σ$. I do understand that in certain cases like the surface of a ...
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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
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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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Magneto-optics: relative permittivity (and permeability) tensor for diamagnets and paramagnets

Currently, i am reading about magneto-optic effects from the book Modern magnetooptics and magnetooptical materials by Zvezdin and Kotov. In this book, examples of relative permittivity tensors (...
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1answer
51 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
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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
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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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1answer
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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
42 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
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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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2answers
48 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
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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
23 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
29 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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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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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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2answers
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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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1answer
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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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2answers
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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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1answer
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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
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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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3answers
195 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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1answer
66 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
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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
48 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
65 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
102 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, ...
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2answers
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Retarded potentials with a dirac delta fail to give Lienard-Wiechert

In the derivation of the Liénard-Wiechert potential the expression for the retarded potential is given $$\varphi(\mathbf{r}, t) = \frac{1}{4\pi \epsilon_0}\int \frac{\rho(\mathbf{r}', t_r')}{|\mathbf{...
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1answer
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Is it enough to assume $F_{\mu\nu}\to 0$ at infinity but not $A_\mu$ to derive the equation of motion?

Suppose the the Lagrangian $\mathscr{L}$ of the free electromagnetic field is augmented with the term $$F_{\mu\nu}\tilde{F}^{\mu\nu}=\partial_{\mu}(\epsilon^{\nu\nu\lambda\rho}A_\nu F_{\lambda\rho}).$$...
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1answer
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Classically, if the magnetic moment of a particle is aligned with a time-varying magnetic field, can its spin flip?

Consider the time-varying magnetic field: $$ \mathbf{B}=B \tanh{\Big(\frac{t}{\tau}\Big)}\hat{\mathbf{z}}. $$ If the magnetic moment (which is proportional to the angular momentum) of a particle at $...
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1answer
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Question about the definition of magnetostatics

From my understanding, magnetostatics is defined to be the regime in which the magnetic field is constant in time. However, Griffiths defines magnetostatics to be the regime in which currents are "...
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1answer
21 views

Calculating force between stationary magnets and a drum with applied magnets

Im working on a school project using stationary magnets to cause the rotation (torque) of a drum with magnets adhered to it. I have skimmed through an electrodynamics textbook but I am finding it ...
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3answers
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How does the Schrödinger model of the hydrogen atom take into account radiation friction?

When one first encounters quantum mechanics, he learns about Bohr's model of the hydrogen atom and one of his biggest problems - electrons were accelerating and not emitting EM radiation (which is ...