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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What causes electron to orbit the nucleus in an atom? [closed]

What causes the electron to orbit the nucleus? Which is the force that causes it to do so? Is it related to the Electro - Magnetic force? .
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Why are the classical electron radius, the Bohr radius and the Compton wavelength of an electron related to each other?

Using the definition of the fine-structure constant $\alpha = \frac{4 \pi \epsilon_0 \hbar c}{e^2}$ and the Compton wavelength of an electron $\lambda_c = \frac{h}{m_e c}$ the classical electron ...
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1answer
167 views

What is the intensity of this light?

I am struggling with a derivation that calculates the cross sections for Mie scattering and since the incident light is considered to be a x-polarized plane wave I thought that we would have $$I_i = \...
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electric field of unpolarized light after reflect?

Reflection and transmission (Fresnel equation) of polarized light are treated in many optics or electromagnetism books. If $E_s$ and $E_p$ is incident electric field with s-polarization and p-...
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How do I calculate electric fields due to currents of magnetic dipoles?

Short version of my question: Do dipole currents cause fields? I think currents of aligned magnetic dipoles cause an electric field, but I don't know how to calculate this field except in the ...
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1answer
225 views

Can inertia be explained by Bremsstrahlung?

Considering that on the atomic level objects consists of densely spaced positively and negatively charged particles, does not the acceleration of those objects lead to Bremsstrahlung of those ...
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2answers
364 views

Applicability of the concept of voltage in electrodynamic circuits

In electrostatics, we have $$\nabla \times \vec{E} = 0$$. Hence, we can define a scalar potential $V$, where $$\vec{E} = -\nabla V$$. We know from Faraday's law that $$\nabla \times \vec{E} = -\frac{\...
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Mie Scattering for spheres with constant dipole moment

I was wondering whether there exists a theory that describes Mie Scattering for spheres that have a constant dipole moment. Since there are theories that describe Mie scattering in the case of a ...
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1answer
1k views

General solution to the Helmholtz wave equation with complex-valued frequency in cylinderical coordinates

The Helmholtz equation is expressed as $$\nabla^2 \psi + \lambda \psi = 0$$. This equation occurs, for eg., after taking the Fourier transform (with respect to the time coordinate) of the wave ...
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1answer
71 views

What are the properties of the Electromagnetic wave $E=E_0e^{-i\omega t}$

My question is, whether this definition $E=E_0e^{-i\omega t}$ includes that it is a plane wave, since I am confused by the fact that we do not have any dependence on the position. So about what kind ...
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1answer
611 views

Understand equations of a conducting sphere

Can somebody explain to me, when the following two equations (equations 2.48 and 2.50 in this document) are applicable and what $\Phi_s$ and $\Phi$ actually are? The thing is, I want to find general ...
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146 views

Potential energy: Electric field two spherical charges

I want to determine the potential energy of two equally charged spherical charges by using the equation: $V_{pot}= \int_V \frac{1}{2} \epsilon_0 E^2 dV$ and therefore I was wondering what I has to ...
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1answer
226 views

Electric dipole, error in calculation

Currently I am calculating the dipole moment of a metal sphere in a uniform electric field $E_0$ in z-direction. From here I know that the charge density look at page 15 is given by $ 3 \epsilon_0 ...
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Electric field screening for arbitrarily formed charge

if I have a not necessarily homogenous electric field of a charge distribution in an electrolyte and i want to find out what the electric field at some position in the electrolyte is. is there any ...
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Properties of electric field

I have the following vector field: $E=E_0(-sin(\phi),cos(\phi),0)^T$ and $E_0$ is some constant. Does anybody here have an idea what this electric field does to a metallic sphere that is in it? ...
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Two charges in a medium where different permittivity is adjacent

I was thinking about the following: Assuming that you have NON SPHERICALLY SYMMETRIC charges and they are both in medium 1. Does it make a difference(whereby I am referring to the total force) if ...
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Maxwells Equation from Electromagnetic Lagrangian

In Heaviside-Lorentz units the Maxwell's equations are: $$\nabla \cdot \vec{E} = \rho $$ $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + \frac{\...
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1answer
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Meaning of terms and interpretation in the electric multipole expansion

In section 3.4.1 of Griffiths' Introduction to Electrodynamics, he discusses electric multipole expansion. He derives the formula or the electric potential of a dipole, which I follow, but right ...
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1answer
416 views

Electromagnetic tensor in CGS units

To write the electromagnetic field tensor in CGS units I just have to kick off the c-s from the SI tensor right? I know this is a stupid question but I need a reliable answer.
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2answers
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Vector plus vector equals scalar ? (Nabla operator)

A quick question that is currently bothering me. I have the following equation: $\mathbf{E}+\frac{\partial \mathbf{A}}{\partial t} = -\nabla V$ My question is, how can the right side, being a ...
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1answer
622 views

What is the direction of an accelerated particle due to a variation of magnetic field?

Let an ion of charge $q$ and mass $m$ traverse a circular orbit of radius $R$ under the influence of a uniform magnetic field $\mathbf{B}=B(r)\,\hat{\boldsymbol{z}}$, where $r$ is the distance from ...
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What is the time component of velocity of a light ray?

If we have a light ray $x^\mu$ with velocity $c$, what is $c^0$ (the time component)?
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1answer
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Difference between Poynting vector and energy flux density?

Are those two terms the same, or...? My book says that the Poynting vector is an energy flux density given by: $$\mathbf{S} = \frac{1}{\mu_{0}}(\mathbf{E} \times \mathbf{B})$$ So that alone should ...
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2answers
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Find E and B from vector potential

I have a vector potential given by: $\mathbf{A}(x,t) = \mathbf{e}_{y}\frac{1}{2} e^{-(x-ct)^{2}/{4a^{2}}}$ Now, the question is "Determine the E and B under the condition that the scalar potential ...
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0answers
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Boundary Condition for Perfect Conductor in Uniform Magnetic Field

When I was studying the perfect conductor scattering (Section 10.1) in Jackson's book, I was confused by the calculation for magnetic dipole induced by the incident wave. He simply said like "set the $...
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Is classical electromagnetism a dead research field?

Is classical electromagnetism a dead research field? Are there any phenomena within classical electromagnetism that we have no explanation for?
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Can we measure an electromagnetic field?

As far as I can check, the Aharonov-Bohm effect is not -- contrary to what is claimed in the historical paper -- a demonstration that the vector potential $A$ has an intrinsic existence in quantum ...
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When can a center of mechanical momentum frame be found for an electromagnetic system?

In classical mechanics, a center of mechanical momentum frame can always be found for a system of particles interacting with one another locally. For an electromagnetic system where the charges ...
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2answers
425 views

Magnetostatics of Current-Carrying wire

A question has been nagging at me about Faraday's Law as related to a wire with a constant current: If you have a circular loop of wire with some small resistivity, connected to a battery so that it ...
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2answers
642 views

Coulomb gauge fixing and “normalizability”

The Setup Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as $$ A_\mu\to ...
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An example which contradict to Newton's 3rd law?

Let a,b be two charged particles. $$\vec{r}_a(0)=\vec{0}$$ $$\vec{r}_b(0)=r\hat{j}$$ $$\vec{v}_a(t)=v_a \hat{i}$$ $$\vec{v}_b(t)=v_b\hat{j}$$ In which both $v_a$ and $v_b$ $<<c$. Then $$\...
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Noether's first theorem and classical proof of electric charge conservation

How to prove conservation of electric charge using Noether's first theorem according to classical (non-quantum) mechanics? I know the proof based on using Klein–Gordon field, but that derivation use ...
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1answer
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Classical (or semi-classical) interpretation of photoelectric effect?

This site says that "it has recently been proven that the photoelectric effect can be interpreted classically (or at least semi-classically) in non-particle, wavelike terms". Is anyone familiar with ...
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Force on Earth due to Sun's radiation pressure

I have been asked by my Classical Electrodynamics professor to calculate the force that the Sun exerts in the Earth's surface due to its radiation pressure supposing that all radiation is absorbed and ...
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3answers
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What does the * mean in spherical harmonics?

In Jackson's book about classical electrodynamics, this formula comes up: $$q_{lm} = \int \mathrm d^3 x' \, Y^*_{lm}\left(\theta', \phi'\right) r'^l \rho\left(\vec x'\right)$$ What does that $^*$ ...
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Non-linear dynamics of classical hydrogen atom [duplicate]

Possible Duplicate: Non-linear dynamics of classical hydrogen atom I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom. Taking ...
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2answers
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Non-linear dynamics of classical hydrogen atom

I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom. Taking into account Newton equations for the electron and the proton and Maxwell ...
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1answer
185 views

Conducting surface inside conducting surface

Let's say there's a closed conducting surface. Then by Gauss's Law the E field bound by the surface must equal the charge inside. There's no charge inside, so the E field cancels. This is a Faraday ...
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1answer
487 views

What happens to electrons in an open circuit?

In the Physics classes, the professor did an experiment using de Van de Graaff generator, by which he held a neon tube radially outward to the V d Graaff dome, and the neon lit up. I understood that ...
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Magnet and energy conservation

If we consider a steel ball falling under gravity in a cup (potential well) and being stopped at the bottom by an obstacle then energy conservation implies that the gravitational potential energy has ...
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What is the answer to Feynman's Disc Paradox?

[This question is Certified Higgs Free!] Richard Feynman in Lectures on Physics Vol. II Sec. 17-4, "A paradox," describes a problem in electromagnetic induction that did not originate with him, but ...
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3answers
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Why do electrons around nucleus radiate light according to classical physics

As I navigate through physics stackexchange, I noticed Electron model under Maxwell's theory. Electrons radiate light when revolving around nucleus? Why is it so obvious? Note that I do not know ...
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1answer
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Semiclassical QED and long-range interaction

I'm interested in the (very) low energy limit of quantum electrodynamics. I've seen that taking this limit does not yield Maxwell equations, but a quantum corrected non-linear version of them. If ...
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3answers
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Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation?

In Physical Review Letters, there was a paper recently published: Masud Mansuripur, Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation, Phys. ...
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1answer
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Question on 1st order Lagrangian Derivation in Faddeev-Jackiw Formalism

I'm looking at this reference (sorry it's a postscript file, but I can't find a pdf version on the web. This paper describes a similar procedure). The topic is the Faddeev-Jackiw treatment of ...
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Do Maxwell's Equations overdetermine the electric and magnetic fields?

Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and $\vec{B}=(B_x,B_y,B_z)$...
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Boundary conditions / uniqueness of the propagators / Green's functions

My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields. It is well known that the Green's function for the Laplace ...
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6answers
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How do we visualise antenna reception of individual radiowave photons building up to a resonant AC current on the antenna?

I am a chemical/biological scientist by trade and wish to understand how quantum EM phenomena translates to our more recognizable classical world. In particular, I want to get a mechanistic picture ...
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Interaction of matter with EM fields

For the interaction between electromagnetic fields and matter, when do we have to include quantization of the EM field and when we can ignore it? when do we have to include quantization of atomic ...
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1answer
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Is there a Newton's third law for the em field?

There is a momentum associated with the em field that ensures the conservation of total momentum for a system of interacting charges. Can the same be done in an analagous way to ensure Newton's ...