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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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Classically, how would an electron orbiting a proton in a perfectly circular orbit emit photons? [duplicate]

Obviously, with quantum mechanics, we know particles don't really orbit in electric fields. From what I know, clasically, Bremsstrahlung radiation would occur if an electron was deflected or ...
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Why does a surface charge experience electrostatic pressure from its own field?

In Griffiths he mentions that a surface charge experiences a force in the presence of an electric field, but then he specifies that a force experienced by the surface is one due to its own electric ...
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How to calculate induced emf of moving rod?

I have the following exercise: A copper rod with length L is moving on two frictionless conducting rails, in a distance a from an very long straight conductor. The rods resistance: R. Ignore any self ...
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Magnetic forces and change in the type of kinetic energy

I have been thinking about magnetic forces and how they do no work. When looking at the definition of work, it makes sense as the Magnetic forces only change the direction. My other approach to try ...
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Electromagnetic Lorentz invariant apparent violation

We know that the scalar product $$\vec{E}\cdot \vec{B}$$ is a relativistic invariant in any inertial frame of reference. This made me pose the following question: Suppose we have a charged filament ...
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Radiation of a charged particle

Take a uncharged particle. It hits a resting charged particle. Will the charged particle radiate then?
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Harmonic dependence of magnetic field and scalar potential

I was reading a book about electrodynamics. the book said we shall now consider the special case when 'the scalar potential' and the field component depend harmonically on the $z$ coordinate (...
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Pre-metric electrodynamics: additional symmetry of the tensor density

I am currently reading this paper. How can I prove (eq. 7 of the paper) that if we assume $$ \chi ^{abcd} = \chi ^{cdab}$$ this leads to $$ F \wedge \# F' = F' \wedge \# F $$ and vice versa? $F$ ...
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How can we prove that light is an Electromagnetic wave? [duplicate]

In many books it is written that light is an electromagnetic wave, as we know there does not exist any oscillator that can oscillate an electron with a frequency of light. My question is, how can we ...
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Charge distribution in a sphere in uniform field

So my teacher was telling about how if we place an uncharged conducting sphere inside a uniform electric field , the charges so distribute that the E field inside them becomes zero. He told us that ...
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signal propagates in unequal length (or bended) transmission line

Suppose I have a square wave signal generated from a signal generator and its outputs are connected to the two terminals of a paired PCB traces (left side of the picture below). The other end of the ...
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Does a moving charge interact with the magnetic field it produces? [duplicate]

So the title cuts my question a bit short. If a moving point charge produces a magnetic field, does the magnetic field it produces affect it? And let's suppose a moving charge is moving in a region ...
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Deriving Jefimenko's equations in Fourier space

From the Fourier-transformed Maxwell equations we have, with some algebraic manipulation, $$\mathbf{E}=\frac{1}{|k|^2}\left[\mathbf{k}\frac{\rho}{\epsilon_0}-\mathbf{k}\times k_0\mathbf{B}\right]$$ $$\...
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What would happen if I bring an electron near a conductor

What would happen if I bring an electron near a conductor Charges should be induced, but since a charge cannot be smaller than that of an electron.... Edit :This is not a homework question. I had a ...
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Momentum transfer due to Thompson scattering

This is an interesting problem regarding on momentum transfer of electromagnetic waves at a relativistic limit. Here we consider Thompson scattering, but the results could be well applicable to other ...
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Maxwell's equations UPML in FDTD with inhomogeneous media

I'm looking at matching the UPML (uniaxial perfectly matched layer) defined in Taflove&Hagness' Computational electrodynamics to an inhomogeneous media (inhomogeneous w.r.t. both $\varepsilon$ and ...
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$* d * $ operator — Digest the (differential/geometry) meaning

I like to digest better: the $* d * $ operator in Maxwell differential form equation the $* D * $ operator in Yang-Mills differential form equation We already knew that in Maxwell differential ...
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Microscopic explanation for Hooke’s law

This figure shows the force between two atoms - at separation d there is no repulsive or attractive force, but for separation between d and the minimum, there is an approximately linear increase ...
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What is the force corresponding to Lamor's formula for EM radiated power?

The rate at which electromagnetic energy is radiated is given by Lamor's formula. What is the corresponding rate at which momentum is radiated and hence force to this?
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The issues when thinking about the magnetic flux law as being universal in modeling

$$ \varepsilon = -\frac{\partial \Phi}{\partial t} =-\frac{\partial (BA)}{\partial t} $$ Any instance of considering the emf induced in a system, I usually think of the flux law first, I intensely ...
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What are the electric and magnetic fields of an arbitrarily moving point charge assuming instantaneous field propagation for simplicity? [closed]

I could find an equation for the magnetic field. It is called the Biot-Savart law: $$ {\vec{\pmb{B}}} = \frac{\mu_0}{4\pi} \cdot q \cdot \frac{1}{r^2} \cdot \left( {\vec{\pmb{v}}} \times {\hat{\pmb{r}}...
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Repulsive force from charge accumulation in a capacitor plate?

During a charged state of a capacitor (Regardless of the type of capacitor), Simple parallel plate: .png Parallel plate with dielectric material in the gap: ]3 Supercapacitor: How is the ...
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Why is it that magnetic fields(or any field)not move in space? [closed]

When I imagine a magnetic field produced by a magnet, or the electric field produced by a charge, I've learned that the fields are stationary, however, their value(across space) changes. If I placed ...
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What does Maxwell's equations predict for the propagation of EM waves converging to a point?

Maxwell's equations model EM radiation as propagating away from an accelerating charge. Suppose instead the propagation of this EM radiation is reversed and presented as a source-free boundary ...
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Electromotive force in the presence of non-steady currents

Griffiths's Introduction to Electrodynamics states $$\mathcal E = \oint \mathbf f \cdot d\mathbf l$$ In which $$\mathbf f = \mathbf f_s + \mathbf E$$ Where Griffiths describes the summation as ...
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Using the Lorentz force equation twice to model to different phenomena?

In a rail system, can I apply Lorentz force separately to: Derive the work required to move the charges(motion of current); Derive the kinematics relative to the rod's motion; All stemming from: $$ ...
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In electrodynamics, why do we say $\mathbf J = \sigma \mathbf E$ and not $\mathbf J = \sigma (\mathbf E + \mathbf v \times \mathbf B)$?

Griffiths notes it's because charges have an extremely low $\mathbf v$, so it's essentially an approximation, but aren't charges meant to be electrons? How can they be moving slowly? I usually think ...
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Relationship between the: Power supply's electric force for current flow, and Lorentz force equation for electric force?

$$ F = qE + qv \times B$$ For the Lorentz force relevant to a current carrying wire, that is caused by the motion of a wire w.r.t to an exterior magnetic field $B$, the second term($qv \times B$) on ...
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Displacement currents, aren't really currents?

I'm confused with this definition of displacement currents within capacitors via Wikipedia: However it is not an electric current of moving charges, but a time-varying electric field. It's a ...
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Energy-momentum tensor of the electromagnetic field

I have to derive the electromagnetic energy-momentum tensor from Noether's theorem and translation invariance. Due to translation invariance and gauge transformation: $$\delta A_\mu= a^\nu F_{\mu\nu}$$...
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Griffiths Electrodynamics Problem 9.39: How can $\sin(\theta_T)$ be greater than one?

When an electromagnetic wave strikes an interface between two linear media, Snell's law states that $\frac{\sin(\theta_T)}{\cos(\theta_I)} = \frac{n_1}{n_2}$ where $\theta_I$ is the angle of incidence,...
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Diffraction by induced quadrupoles

This is a very interesting problem that I've been struggling to solve for a week, so I decided to ask for some orientation, as I think it could also be of interest for the community. Let's consider a ...
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Invariance of Maxwell action

I have to show that the Maxwell action $$S=-\frac{1}{4}\int d^4x F^{\mu\nu}F_{\mu\nu}\,$$ is invariant under translation: $\delta_aA_\mu=a^\nu \partial_\nu A^\mu$ with $a^\mu$ as arbitrary and ...
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How do we know that electric charges are invariant?

According to tparker at Why charge is Lorentz invariant but relativistic mass is not? So there are two different ways to generalize the mathematical form of Coulomb's law to make it ...
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Subarea within a changing magnetic flux?

If I were to introduce a boundary area $\tau$: And after sometime $t$, I introduced a constant magnetic field(let's imagine it spawned suddenly and ignored the change in flux from $t_o$ $\rightarrow$ ...
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Effects generated from a supercapacitor placed in a time varying external magnetic field?

The diagram above, showcases the simple outlook of a supercapacitor's interior and combining it with a full circuit loop. If an exterior magnetic field is introduced in all the operating states of a ...
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Is the relative number of electric field lines between two charges proportional to the difference between those two charges?

Let us consider a system of two unlike charges and suppose that the magnitude of the positive charge is greater that of the negative charge and call them a and b respectively. If that(asked in the ...
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The Electromagetic Tensor and Minkowski Metric Sign Convention

I am trying to figure out how to switch between Minkowski metric tensor sign conventions of (+, -, -, -) to (-, +, +, +) for the electromagnetic tensor $F^{\alpha \beta}$. For the convention of (+, -,...
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Difference in the direction of propagation of em wave [duplicate]

How are kx-wt and kx+wt in terms of the direction of the wave. I have been stuck at this or an hour, still can not find a definitive answer.
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Deriving current density from charge density

Sorry for the naive question, but in Jackson's book in Electrodynamics, exercise 9.10, they give the charge density for the transition of hydrogen from 2p to 1s, $$\rho=\frac{2e}{\sqrt{6}a_0^4}re^{-...
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Dipole Inside Cavity of A Spherical Conductor

Consider the following case: There is a short electric dipole placed arbitrarily inside a spherical cavity inside a solid,uncharged conducting sphere We need to find electric field at a point ...
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How can direction of electric field due to a moving charge be from the present position of charge?

According to Maxwell's Equations, the electromagnetic waves in vacuum travel at the speed of light $c$. While solving Maxwell's equations using Lorenz gauge conditions (or basically evaluating scalar ...
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The Meaning of Electromagnetic 'News' in Griffiths Book

In the Introduction to Electrodynamics book, by David J. Griffiths, 4th edition, page 60, the author makes the following statement: "it is not the position, velocity, and acceleration of Q right now ...
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Electric field of a line of Charge on it axis using electric potential

We have a line of charge with length $L$ and charge density $\lambda$ and we want to find its Electric field on a point $p$ with distance $d$ from one end of it using potential. I drew a picture like ...
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Energy momentum tensor of EM field written in symmetric form

I'm reading A. Zee's book, Einstein Gravity in a Nutshell. In problem 7 of chapter IV.2, it is said that the energy momentum tensor of the electromagnetic field \begin{align} T^{\mu\nu}=\eta_{\lambda\...
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How to calculate Average Electric Field for a microscopic filed in dielectric?

In Griffith's book in The chapter of Electric Fields in Matter (The field inside dielectric) , He has considered the Sphere of Radius R and for the inner dielectric element He used the field as $$\...
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Constants of motion of an electron in a harmonic electromagnetic field in free space

I have encountered a question in Classical Electrodynamics, as below: In free space, an electron, initially at rest at $z=0$, is subjected to an intense laser field $\vec E=\hat x A \cos(\omega t-...
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Why can infinite planes be approximated as Gaussian surfaces?

A little background: I'm an undergraduate studying Electrodynamics, currently in Chapter 8 of Griffiths. A question I came across (8.4 part a for those curious) asks for a calculation of the force ...
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Coulomb forces in String Theory

In QED electrostatic forces are mediated by field theoretic effects known as virtual "particles" if I am not mistaken, but I don't know how string theory explains electrostatic interactions between ...
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A changing magnetic field passes through a wire loop but the loop itself is not in the field. Is an EMF induced in the loop? [duplicate]

$$\nabla \times \vec{E} =-\frac{\partial{\vec{B}}}{\partial{t}}$$ Applying Stokes' theorem: $$\oint_{loop} \vec{E} \cdot d\vec{l}=\int_S -\frac{\partial{\vec{B}}}{\partial{t}} \cdot d\vec{S}$$ ...