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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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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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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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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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51 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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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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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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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
117 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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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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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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118 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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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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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 [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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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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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
104 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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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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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
30 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
84 views

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
123 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
132 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
47 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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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
79 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
48 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
156 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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2answers
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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
45 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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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
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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
67 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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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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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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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
415 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
245 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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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 ...