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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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Pressure radiation using Lorentz force

We know from theory and experiment that an electromagnetic wave that incides on a surface will generate a radiation pressure normal to that surface as a result of the change in momentum of the wave ...
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How to correctly differentiate the Lienard-Wiechert four-vector potential to get the EM tensor?

The retarded 4-vector potential for a moving charge is given by $$ \left. \frac {eV^\alpha(\tau)}{V\cdot[x-r(\tau)]} \right|_{\tau = \tau_0} $$ where $e$ is the charge, $V$ the four-velocity, $x$ ...
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How do we find the surface charge density of a charged conductor?

It is mentioned in Feynman volume 2 that it is quite algorithmic , where the surface charge density is first guessed then check whether it is equipotential at the metal surface.. My question is for a ...
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Conservation of magnetic charge

It is well known that the electric charge of a system can be thought of as the Noether charge associated with isotropic large gauge transformations. That is, given Einstein-Maxwell theory $$S=\frac{1}...
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Questions about the energy density and momentum density in linear media

Precisely which energies are accounted for in the energy density of a linear medium given by $$u = \frac{1}{2}\left(\epsilon E^2 + \frac{1}{\mu}B^2\right)?$$ For example, is there a kinetic energy ...
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Pulsar distance estimation

This is quite an interesting problem in astrophysics so I thought it would be a good idea to ask here so we can archive the solution for future reference. Consider a pulsar that emits pulses of ...
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Energy-momentum vs charge-current

Is there a simple intuitive way to explain why energy-momentum density requires a tensor, while charge-current density is a vector? $\partial_{\mu} J^{\mu} = 0$ is a statement, in effect, that the ...
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Which forces violate Newton's third law of motion? [on hold]

Forces arising from magnetic fields do violate Newton's third law of motion under certain circumstances. What other forces violate the third law?
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Applying the Euler-Lagrange equations to Maxwell's Theory

In Prof. David Tong's notes, specifically on page 10, he gives the Lagrangian of Maxwell's theory to be $$ \mathcal{L} = -\frac{1}{2}(\partial_\mu A_\nu)(\partial^\mu A^\nu) + \frac{1}{2}(\partial_\...
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1answer
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Lorentz force within a flux tube

I know the formula for the Lorenz force exerted on a point charge $q$ moving with velocity $\vec{v}$ is given by $\vec{F} = q\vec{v} \times \vec{B}$. Now consider the flux tube with cross section $S$ ...
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Experiment to determine if a photon is emitted in one direction

I am currently puzzled over one aspect of the notion of photons regarding its property of being localized and having a direction (as opposed to the classical EM picture of a spherical wave). I have ...
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Changes in boundaries with the application of Faraday's law

Reviewing Faraday's law of an induced electric field due to a changing magnetic field $$ \nabla \times E = -\frac{\partial B}{\partial t}$$ In integral form via application of Stokes theorem: $$ \...
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Electromagnetic Angular Momentum: Problem with vector integrals

I found in the following reference (p. 10) an interesting decomposition for the electromagnetic angular momentum in terms of an orbital terms $\vec{L_{orb}}$ and an spin term $\vec{L_{spin}}$. However,...
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Polarization ellipse for an EM wave [duplicate]

In Chapter 7 of Jackson's book on Classical Electrodynamics, there's the following statement: Introducing the complex orthogonal unit vectors: $$\epsilon_{\pm}=\frac{1}{\sqrt{2}}(\epsilon_1\pm\...
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1answer
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Integral of the divergence of a vector field multiplied by the component of another vector field

In Forces in Molecules by Richard Feynman (Phys. Rev. 56, 340 (1939)), eq. (5) implies that $$\int(\nabla\cdot \textbf{F})E_\mu^\alpha dv=-\int F_\mu(\nabla\cdot E_\mu^\alpha)dv,$$ being $\textbf{F}...
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What is longitudinal and transverse component of electric field? [closed]

What is longitudinal and transverse component and how are they interpreted?
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1answer
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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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Electromagnetic wave in a prism

Imagine an electromagnetic plane wave entering perpendicular to one of the faces of a prism with the form of a triangle rectangle, which is made of a certain material of refraction index $n$. The wave ...
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2answers
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Is it possible to create EM radiation moving in an opposite direction to that from an accelerated charge?

The Lienard-Wiechert retarded solution to Maxwell's equations has the radiation fields diverging and propagating away from an accelerating charge; the advanced solution has radiation fields converging ...
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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
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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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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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2answers
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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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3answers
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Concerning the energy stored in electromagnetic fields

How do we know that $$u = \frac{1}{2}\left(\epsilon_0E^2 + \frac{1}{\mu_0}B^2\right)$$ gives the energy density of electromagnetic fields? Is it a postulate of classical electrodynamics? Griffith ...
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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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1answer
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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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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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Potential of a point charge and two parallel plates

I'm having trouble using the images method to find the electric potential of the following charge distribution. A point charge in front of two grounded parallel plates The problem is that in orde to ...
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2answers
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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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Does classical electromagnetism really predict the instability of atoms?

I will try to give a concise summary of what I wrote below. I understand that it is very long and apologize if I am wasting your time. I used the Liénard-Wiechert potential and the Lorentz force ...
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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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TMZ TME modes, clarification

I'm refering here to Taflove's "computational electrodynamcis, 3rd ed." He says Let us assume that the structure being modeled extends to infinity in the z-direction with no change in the shape ...
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1answer
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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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2answers
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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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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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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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4answers
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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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1answer
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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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3answers
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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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1answer
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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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1answer
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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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1answer
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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
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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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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 ...