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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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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431 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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255 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 ...
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99 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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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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324 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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101 views

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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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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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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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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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 ...
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1answer
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What is an electromagnetic plane wave?

On Wikipedia: In the physics of wave propagation, a plane wave (also spelled planewave) is a wave whose wavefronts (surfaces of constant phase) are infinite parallel planes. In my understanding, an ...
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Doing work against back emf

Brushing up on my understanding of electrodynamics, using Griffiths Introduction to Electrodynamics(4th ed), I'm always questioning the magnitude of "energy" required/consumed in the process of doing ...
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Can inhomogeneity in the medium accelerate particles

Suppose I have a charge which is moving in through a medium with constant velocity. Now, what will happen to the charge as it encounters an inhomogeneity in density? whether it will accelerate or ...
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How do you classify current density?

When talking about the electromagnetic field one usually thinks of: the electric field described locally by its intensity $\vec{E}$ and its flux density $\vec{D}$, the magnetic field described ...
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21 views

derivative of the permittivity tensor

Good evening, If I derive $\partial_{k} \epsilon_{\mu i}E_{i} $ where $\epsilon_{\mu i}$ is the permittivity tensor, is it equal to $\epsilon_{\mu i} \partial_{k} E_{i} $? under what circumstances ...
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Voltage vs. EMF for a varying magnetic flux against an ohmic circuit

Suppose there is a circular wire, whose material is ohmic with uniform resistivity. If an increasing magnetic flux is applied to this "circuit", electric current will flow in one direction. Then by ...
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55 views

Phase Changes during Reflecion

I want to ask that whether there is any phase change during reflection of a P-polarised wave? I know that for a S- Polarised wave there is a phase change of 180° when wave travels from rarer to denser ...
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1answer
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deducting conservation of linear momentum in material media

Good evening, I'm trying to deduce the continuity equation for the fields and particles momentum , something like $\nabla \cdot (-\Pi) + \frac{\partial \vec{g}}{\partial t}=-f$ I should get that $\...
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Given an electromagnetic field in a frame of reference, find all other frames of reference where the electric and magnetic field are parallel

This is actually an exercise in Landau-Lifshitz's book. Their solution goes as follows. After we have found a frame of reference where $\mathbf E$ and $\mathbf B$ are parallel (let's call the common ...
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Divergence of Lienard Wiechert E-Field is not zero? (Violation of Gauss' law)

I wanted to see if the divergence of the lienard wiechert field follows Maxwell's equations (gauss' law): $$\nabla \cdot \vec{E} = 0$$ for $$ E(r,t)=\frac{e}{\gamma^2 R^2} \frac{n-\beta}{(1-n\cdot\...
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2answers
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How can electromagnetic waves heat non-conducting media?

According to this source, the divergence of the poynting vector is related to the total energy density of an electromagnetic wave, which is (locally) expressed as $$-\nabla\cdot S=EJ+(E\frac{\partial ...
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$\mathcal{\underline{J}}(\underline{r},t)=\rho(\underline{r},t) \underline{v}(\underline{r},t)$ from Maxwell equations

In classical EM theory one can use the following equations as independent: $$\nabla \times \mathcal{\underline{E}}(\underline{r},t)=-\frac{\partial \mathcal{\underline{B}}(\underline{r},t)}{\partial ...
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Understanding the Maxwell stress tensor for unidirectional electrostatic fields

The Maxwell stress tensor for electrostatic fields only is given by, $\sigma_{ij} = \epsilon_0(E_iE_j - \frac{1}{2}E^2\delta_{ij})$. Here $\vec E$ denotes the total electric field at a point in the ...
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2answers
66 views

Is the current density not uniquely defined?

Given I know how the charge distribution $\rho(\vec{x}, t)$, I can define a vector $\vec{j}$ that is supposed to show the flow of this charge distribution. To do that, $\vec{j}$ only has to suffice \...
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46 views

Electric field energy contribution of proton to its inertia

Quoting from the book Introduction to elementary particles by Griffiths. Here two refers to proton and neutron. Heisenberg’ proposed that we regard them as two “states” of a single particle, the ...
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1answer
96 views

Motion of an electron near a proton [closed]

Statement of the problem: Consider an electron and a proton that are initially at rest separated $a$ meters. Do not take into account the movement of the proton, because its mass is much greater ...
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1answer
130 views

Derivation of curl of magnetic field [closed]

I am having trouble in one part of derivation of curl of magnetic field, from Biot-Savart law. The attached picture is from Griffiths - Introduction to Electrodynamics. I got all the parts, but only ...
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Reflection and transmission of general electromagnetic wave

Given is a source $S$ which produces an electromagnetic wave $E(x,y,z)$. The source is in vacuum. At z=0 there is an interface between vacuum and a perfect dielectric with $\epsilon$. The electric ...
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“Induced EMF is magnetic, or from an electric field” is the distinction important in analysis?

Their nature of induction is different, however, from relativity it seems that the two can be the same magnitude, in analysis of models relevant to EMF-induction is it important to identify that ...
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Does Electromagnetic Inertia has any relation with the emission of Electromagnetic Waves from Accelerated Charged Particles?

We know that Electromagnetic Fields have certain inertia in them. Lenz's Law is a good example to demonstrate Electromagnetic Inertia. Nature resists the change in the state of Electromagnetic Fields ...
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143 views

Prime coordinates in electrostatics/electrodynamics [closed]

If I know that my formula for potential is: $ V(r) = - \int \vec{E}(\vec r\prime)\cdot d\vec l\prime$. I am taking this us for potential; this can be worth for charge density; current density etc... ...
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Perturbative Techniques In Finding Electric Field of Symmetric Distributions

Lets say we have a uniform sphere of charges at the origin (at retarded time = 0) with some velocity and we are interested in the field at a point along the x-axis (normal to the surface of the sphere)...
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126 views

Is there an MKS unit system in which electric and magnetic fields have the same measurement unit?

I'd like to know if there's an MKS unit system in which electric and magnetic fields have the same measurement unit. I couldn't find anything like that on the internet. Does that system exist? Do ...
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255 views

How do we understand L C Oscillations (Inductor - Capacitor Circuit Oscillation) Intuitively?

How do we understand L C Oscillations (Inductor - Capacitor Circuit Oscillation) Intuitively? How to intuitively understand the Phase Lag and Imagine What is happening in the circuit exactly without ...
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How understand the stored energy due to magnetic field? [duplicate]

I'm confusing because in this book1 introduces the magnetic energy as mechanical work done by forced magnetic, but if magnetic force doesn't work, besides do who done work? Teruo Matsushita - ...
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1answer
79 views

Moving magnet and/ or conductor , should they be distinguishable?

If the two cases(moving the magnet, or moving the loop) would lead to the same physical consequence(same magnitude of induced emf & current), is it important to distinguish the cause when ...
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2answers
58 views

Is it right to say that magnetic field energy is created only by non-conservative electric field?

In all the examples of generation or existence of Magnetic Field energy I have seen so far, I couldn't find any example, where magnetic field energy is created without Non Conservative Electric field, ...
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Where does the Magnetic Field Energy come from, in case of a charged particle moving with constant velocity?

A charged particle moving with constant velocity creates Magnetic Field around it. If there is Magnetic Field, then there must be Magnetic Field Energy. The question is, where does the Magnetic Field ...
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81 views

Is the magnetic field energy around a current carrying wire is similar to the electric field energy associated with an isolated charge?

What I mean by this question is, as we say that the electric field energy around a charge is the self energy of the charge, similarly can we say that the magnetic field energy around a current ...
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4answers
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What do we mean by magnetic field energy? Does this magnetic field energy in a current carrying wire comes from the battery the wire is connected to?

Let me take an example to elaborate my question. Suppose we have a simple circuit with a battery (E) and a resistance (R). Current will be flowing in the circuit, I = E/R. Now, we know that that if ...
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Calculating Radiation Pressure from plane waves on Boundary Surface

Suppose we have an incident Electromagnetic plane wave $E_I = E_{0I} e^{i(k_1 z - ωt)} \hat{x}$ and $B_I = \frac1{v_1} E_{0I}e^{i(k_1 z - ωt)} \hat{y}$ heading towards a surface $z=0$ between two ...
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Electrodynamics,Laplace equation

Well the classical image charge problem in electrodynamics,clearly shows a slick way of dealing with some symmetric cases.But that seems somewhat a way of doing back calculations.So could anyone link ...
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1answer
72 views

A particle's dynamics near a solenoid

The image below shows a toroidal solenoid, on the $x-y$ plane, carrying a current $I$. At the origin there is a charge $q$ of mass $m$. At $t=0$ the current begins to decrease in magnitude. How is ...
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44 views

inconsistency in the magnetic filed of a solenoid?

Using Ampere's law, we can find that in the center of a striaght solenoid that carries a current $I$ and its turns density is $n$ there is a magnetic field $$B=\mu n I$$ parallel to the solenoid. ...
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47 views

Charged particle near a loop of varying current

Consider a loop of radius $R=1$ centered at the origin lies on the $x-y$ plane, carrying an electric current $I$. A point particle of charge $q$ is located initially at $(0,0,z)$ and at rest. The ...
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56 views

Lagrangian of Charged Particle Evaluated On-Shell

I am trying to calculate the Lagrangian of a charged particle in background gauge field evaluaed on-shell. Let $A^{\mu}(x)$ be a gauge field. The action of a charged particle in this background gauge ...
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Conservation law charge in plane-wave

When considering a charged particle in a plane-wave field, it is possible to show that the 2 following quantities are conserved $\boldsymbol{p}_{\perp} - e\boldsymbol{A}_{\perp}$ and $p_z - \gamma$ ...