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2
votes
1answer
110 views

Expression for maximum energy transfer to electron by fast moving charge

Suppose a charge $q = +Z e$ is moving along positive $+x$ direction with electron below $x-$axis and the charge is moving fast enough to consider electron at rest, then what is the maximum value of ...
2
votes
5answers
263 views

Is the canonical momentum conserved when a particle moves in magnetic field?

Here is a question about the canonical momentum that I had asked some days ago, but I still have one point that I am not understand. Considering a particle moves in a magnetic field with charge $q$ ...
1
vote
1answer
185 views

Frequency of rotating coil

Given a coil initially in the x-y plane, rotating at angular frequency $ \omega $ about the x-axis in a magnetic field in the z-direction. This uniform time varying magnetic field is given by $B_z ...
1
vote
2answers
130 views

A question about canonical momentum and arbitrariness for potential in magnetism

The following question confuses me: There exists magnetic field $B_z =- \beta x$ where $x > 0$, and a particle is incident from origin point $(0,0)$ with pisitive charge $q$, mass $m$, and ...
2
votes
3answers
173 views

Why do surfaces act like barriers for electrons?

Say you have a conductor, filled with free electrons. The nuclei have a weak pull on the valence electrons so they are moving around in the conductor. But the electrons don't leave the solid. If you ...
0
votes
0answers
125 views

Field inside a conductor?

If the above image is a cross section of a conductor, the field at the point shown is not zero. So the field inside a conductor is not zero at all points. You could argue that the electrons would ...
3
votes
1answer
188 views

Is Newton's third compatible with retarded Lorentz force?

In Griffiths Introduction to electrodynamics it is said that Newton's third law is not valid in electrodynamics, but, in the example given, the it does not consider the retarded values for the fields ...
1
vote
1answer
132 views

What happens to a conducting ring when exposed to an electric field?

It might be a silly question, but one of my friends just got asked this question at an oral exam, and he could not answer it, and didn't receive the answer either (Or at least he forgot). And I've ...
1
vote
0answers
175 views

Complex polarizability of a dielectric sphere in a homohenious electric field

It is well known that complex polarizability of uniform dielectric sphere with radius $r$ and complex permittivity $\hat\epsilon_{in}(\omega)$ placed in a medium with complex permittivity ...
0
votes
1answer
62 views

Objects made up of electrons?

Say you have a neutral rod, and you bring a positively charged rod beside it (call the side the charged rod is brought near side A and the other side side B). The electrons from the side B will start ...
3
votes
1answer
188 views

Lorentz force equation from relativistic Lagrangian

The relativistic Lagrangian is given by $$L = - m_0 c^2 \sqrt{1 - \frac{u^2}{c^2}} + \frac{q}{c} (\vec u \cdot \vec A) - q \Phi $$ I need to derive, $\displaystyle \frac{d\vec p}{dt} = q \left( \vec E ...
0
votes
2answers
126 views

is action integral Lorentz invariant?

I need to find the Lagrangian for charged particles in EM fields considering relativistic effects. Is action integral Lorentz invariant. $$A = \int_{t_1}^{t_2} L (q_i, \dot q_i, t) dt $$ According ...
2
votes
1answer
48 views

Is charge 'localization' implicit in the idea of current?

If it was possible for charge to assume arbitrary densities, like we often see electrostatic exercises, and one could spread charge density uniformly over a ring, then how one would, theoretically, ...
3
votes
1answer
186 views

Missing terms in Hamiltonian after Legendre transformation of Lagrangian

Short question Given any Lagrangian density of fields one could possibly conceive, is it the case that after one has performed a Legendre transformation, if the Hamiltonian is then expressed in terms ...
0
votes
0answers
44 views

Is it physically realistic to have an electric field and polarisation density but no displacement field?

Given a Lagrangian density that describes a classical dielectric in interaction with the EM field, I found the Euler-Lagrange equations, and in the case of the electric field, worked through to find ...
1
vote
1answer
100 views

Can the electric field — always — be derived from the potential?

After studying the definition (& derivation) of the potential to an electric field and the Poisson equation I'm currently wondering whether the following is possible: Can one give an example of ...
4
votes
2answers
142 views

In Jackson's expression for the electrostatic Green function, why is the Laplacian taken with respect to the primed coordinates?

Jackson writes, The function $1/|\mathbf{x} - \mathbf{x}'|$ is only one of a class of functions depending on the variables $\mathbf{x}$ and $\mathbf{x}'$, and called Green functions, which satisfy ...
3
votes
1answer
124 views

Did the Goudsmit-Uhlenbeck analysis of spin consider relativity?

It's frequently mentioned in introductory quantum mechanics texts that Goudsmit and Uhlenbeck conjectured that the magnetic moment of an electron was due to angular momentum arising from the electron ...
3
votes
1answer
101 views

Motion in a Paul trap: $2n$th harmonic with larger amplitude than $n$th harmonic

Using a Paul trap, we captured the motion of a light charged particle (based on a rotating potential applied by AC current). Our rotational frequency was 50 Hz, and so when used FFT on the data, we ...
1
vote
1answer
186 views

Traditional Kirchoff voltage law in AC circuit?

The traditional (not taking into account phasor addition or complex addition) application of Kirchoff Voltage law, i.e. $\Sigma\Delta V=0$ along a loop, does not work for AC circuits. We can sum the ...
0
votes
0answers
60 views

Explanation of the classical coupling of the Higgs Field to Electromagnetism

I'm interested in learning about the classical coupling of the Higgs Field to Electromagnetism. There are numerous sources explaining the Higgs mechanism quantum mechanically, i.e. How does the Higgs ...
4
votes
1answer
290 views

Is there a Hamiltonian for the (classical) electromagnetic field? If so, how can it be derived from the Lagrangian?

The classical Lagrangian for the electromagnetic field is $$\mathcal{L} = -\frac{1}{4\mu_0} F^{\mu \nu} F_{\mu \nu} - J^\mu A_\mu.$$ Is there also a Hamiltonian? If so, how to derive it? I know how ...
8
votes
2answers
255 views

What is the mechanism by which magnetic fields do work?

I've seen some conflicted answers to this question in texts and on the web, in the case of a dipole, for example. Do magnetic fields do work directly, or is it their induced electric fields that do ...
0
votes
1answer
349 views

How is bound charge and free charge possible?

I am studying Introduction to electrodynamics by Griffiths and I came along a concept I cannot seem to understand properly. The concept of free charge AND bound charge. I do not understand how we can ...
2
votes
2answers
121 views

What is the area in Faraday's law if we have only a piece of metal moving in a magnetic field?

If a piece of metal of length $l$ is moving with a speed $v$ in a region where there is a uniform magnetic field $B$ perpendicular to it, there will be a potential difference across its terminals ...
-1
votes
1answer
40 views

Scalar Field of a long thin wire

Given the situation that $B=-\nabla A$ where B is magnetic field and A is some Scalar Field. How can I calculate the scalar field, A. We are dealing with current free region, here. I know we can ...
2
votes
2answers
152 views

Illegal gauge condition in electrodynamics

Just a quick sanity check here: I'm preparing a tutorial for a class on classical electrodynamics and I wanted to show an example of a gauge condition which leads to a contradiction, so I simply ...
3
votes
1answer
177 views

Orthogonality between $\vec{E}$ and $\vec{H}$ waves with space-dependent amplitudes

I am able to prove in a few lines that the electrodynamic field vectors $\vec{E}$, $\vec{H}$ and $\vec{S}$ are all orthogonal to each other considering that $\vec{E}$ and $\vec{H}$ are coherent plane ...
4
votes
1answer
173 views

How does light pass through rough glass?

Light incident on a rough surface will be diffuse after passing it. Angular intensity depends on the grinding of the glass surface. I'm trying to find information about the scattering indicatrix of ...
5
votes
2answers
382 views

Electrostatics/ magnetostatics: why is $\int_\text{all space} d\vec r \; \nabla \cdot(\vec A \times \vec B)$ equal to 0?

I'm reading electrodynamics notes and come across that: $$\int_\text{all space} d\vec r \; \nabla \cdot(\vec A \times \vec B)=0$$ in case of magnetostatics and: $$\int_\text{all space} d\vec r \; ...
4
votes
2answers
338 views

What is the magnitude of the force on a charged particle due to electromagnetic radiation?

Suppose there is an electromagnetic wave moving forward in the $\mathbf{\hat{k}}$ direction. Its electric/magnetic field components are given by: $$\mathbf{E} = E_0 \sin(kz - \omega t) ...
5
votes
1answer
92 views

Classical EM neglects electron recoil?

Imagine two electrons $A$ and $B$ at rest. Electron $B$ is at a vertical distance $r$ above electron $A$. Let us assume that the electrons are constrained to move on horizontal rails. At time $t=0$ ...
0
votes
2answers
119 views

Drift Speed and Current in Two Different Inertial Frames

We have a long, cylindrical wire carrying a constant current I in an inertial frame. At a distance of R from the center of the wire, the magnitude of magnetic field is $μI/2πR$. What is the magnitude ...
1
vote
1answer
93 views

Accelerated charge inside sphere (again!)

Sorry to go on about this scenario again but I think something is going on here. Imagine a stationary charge $q$, with mass $m$, at the center of a stationary hollow spherical dielectric shell with ...
1
vote
1answer
48 views

Is there a heuristic argument for the expression $ \textbf{g} = \frac {\mathbf{S}}{c^2}$?

Electromagnetic momentum density and the Poynting vector are related by the simple expression: $$ \textbf{g} = \frac {\mathbf{S}}{c^2}$$ It can be rigorously derived from Maxwell's equations, but is ...
3
votes
0answers
94 views

Accelerated electromagnetic system leads to divergent calculation?

Consider the above system comprising a pair of oppositely charged parallel plates, connected by a rigid rod of length $r$, constrained to move in the x-direction. The forces on the plates from the ...
4
votes
2answers
313 views

When studying electrodynamics do we assume Maxwell's Equations or derive them?

This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then ...
0
votes
1answer
185 views

Gauss's / Divergence theorem in Classical electrodynamics for the Electric field [duplicate]

Can somebody explain the proof of Gauss's theorem / divergence theorem taking the vector as electric field $$\iiint(\nabla\cdot\vec E)\mbox{ d} V=\iint \vec E \cdot\hat{n} \mbox{ d} ...
1
vote
0answers
70 views

Time derivative to energy equates $0$

Following up on a related question. This implies that, From the reference we can write \begin{align*} E(\lambda) &= I_F [g_\lambda ] + I_K [f_\lambda , g_\lambda ] + I_V [f_\lambda ] \\ & ...
1
vote
0answers
43 views

Question about “quadrupole radiation” vector potential formula derivation

I tried to get an expression for $\mathbf A (\mathbf x )$ in quadrupole approximation. After some transformations of Liénard–Wiechert vector potential I got, as in many books, $$ \mathbf A \approx ...
2
votes
1answer
207 views

Why is there no (time derivative of charge density) in the $B$ field in Jefimenko's equations?

I was going through Griffiths chapter on potentials and fields just to brush up on a few old things. He gets to Jefimenko's equations by this general path: Maxwell's equations Introduce scalar and ...
7
votes
4answers
452 views

Why does electric field intensity $E$ can be uniquely determined by its divergence and curl? [duplicate]

My question is, the number of following equations $$\nabla\cdot E=\frac{\rho}{\varepsilon}$$ $$\nabla\times E=-\frac{\partial B}{\partial t}$$ is 4 while the number of unknown variables ...
-3
votes
1answer
4k views

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? .
3
votes
3answers
743 views

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 ...
4
votes
1answer
106 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 = ...
2
votes
1answer
194 views

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 ...
6
votes
3answers
613 views

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 ...
1
vote
1answer
168 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 ...
4
votes
2answers
112 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} = ...
2
votes
0answers
72 views

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 ...