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3
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1answer
65 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
126 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 ...
3
votes
1answer
136 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 ...
3
votes
2answers
194 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 ...
3
votes
1answer
79 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 ...
3
votes
0answers
81 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 ...
2
votes
2answers
124 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 ...
2
votes
2answers
166 views

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 ...
2
votes
1answer
43 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, ...
2
votes
1answer
69 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
2answers
733 views

What is the conserved canonical momentum for a relativistically moving charge in a static Coulomb electric field?

The canonical momentum is a fundamental conserved quantity from Noether's theorem for translational invariance of the Lagrangian. Yet I'm finding it very difficult to see its derivation, or even a ...
2
votes
1answer
75 views

Angular momenta of photon

$A^\mu$ can have multipole expansions in classical electrodynamics. This gives rise to dipole photon, quadrupole photon etc. For dipole photon $j=1$ (In electrodynamics books they write it as $l=1$). ...
2
votes
4answers
149 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 $q$ ...
2
votes
3answers
118 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 ...
2
votes
1answer
157 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 ...
2
votes
1answer
144 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 ...
2
votes
2answers
490 views

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 ...
2
votes
1answer
180 views

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 ...
2
votes
1answer
66 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
0answers
62 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 ...
2
votes
0answers
106 views

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 ...
2
votes
0answers
54 views

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 ...
2
votes
2answers
64 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 ...
2
votes
7answers
480 views

Metallic and glass sphere of same size released at a height

This question was in my exam today : A metallic and glass sphere of same size were dropped at same height. Which sphere would hit the ground first and why? I have thought about several things and ...
1
vote
1answer
111 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 ...
1
vote
1answer
64 views

Does the 1-D poisson's equation have monotonic potentials if $\rho=\rho(\phi(z))$?

I am solving the 1-D poisson equation: $$\frac{d^2 \phi}{dz^2}=-4\pi\rho(\phi)$$ with the additional requirement that $\rho(\phi(z=0))=0$. If I start by multiplying each side by $\frac{d\phi}{d z}$ ...
1
vote
1answer
90 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 ...
1
vote
1answer
106 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 ...
1
vote
1answer
45 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 ...
1
vote
1answer
226 views

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 ...
1
vote
2answers
217 views

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 ...
1
vote
2answers
35 views

If the net force on a current loop in a magnetic field is zero, why is torque independent of choice of origin?

Im trying to show that the integral over a closed loop of a crossproduct stays the same if I choose a different origin with $\overrightarrow{r}=\overrightarrow{r}\prime+\overrightarrow{r_0}$ and ...
1
vote
1answer
99 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
1answer
154 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 ...
1
vote
2answers
120 views

Integration constants in Maxwell's equations (ambiguousness?)

In classical electrodynamics, if the electric field (or magnetic field, either of the two) is fully known (for simplicity: in a vacuum with $\rho = 0, \vec{j} = 0$), is it possible to unambiguously ...
1
vote
1answer
50 views

electromagnetic induction. Does charge matter?

Just wondering. I know a negative electric charge moving though a coil will induce a voltage in the coil. My question is, would a positive charge, say an ion beam, moving though a coil also induce a ...
1
vote
2answers
103 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 ...
1
vote
1answer
82 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
314 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 ...
1
vote
1answer
212 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 ...
1
vote
1answer
78 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 ...
1
vote
4answers
275 views

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 ...
1
vote
0answers
18 views

Computing the Electric and Magnetic Field Distribution of a Funnel Waveguide

In our undergraduate E&MWaves class, we learned about a rectangular waveguide, and how to calculate the electric and magnetic field distribution throughout the waveguide using finite element ...
1
vote
1answer
106 views

Magnetic field of uniformly charged rotating hollow sphere

I want to compute the magnetic field due to a homogeneously charged, rotating sphere with radius $R$, angular velocity $\vec{\omega} = \omega\hat{z}$ and total charge $Q$. I want to use Biot-Savart ...
1
vote
1answer
75 views

Step in a proof that $\textrm{div} \ \mathbf{B} = 0$ from Biot-Savart's law

Notation: The magnetic field $\mathbf{B}$ generated by a point charge $e$ moving with velocity $\mathbf{v}$ is given by Biot-Savart's law $$\mathbf{B} = \frac{\mu_0 e\ \mathbf{v} \wedge ...
1
vote
1answer
23 views

Why is radiation for an ultrarelativistic charge zero on axis?

I attribute it to the fact that for an ultrarelativistic charge the field is contracted and essentially there are only fields in the transverse direction and nothing longitudinally (wrt the charges ...
1
vote
1answer
24 views

Far Field Diffraction of EM waves: what does the zero frequency signify?

If you have a system of independently radiating electrons/point-charges, the far field distribution of the EM waves can be approximated by the fraunhoffer diffraction integral, or simply by the ...
1
vote
1answer
72 views

The workings of the Hall effect?

I want to ask about the workings of the Hall effect. Why do the electrons come to rest on the edge of the wire? The magnetic field pushes them up, and the electric field pushes them forward. Shouldn't ...
1
vote
1answer
115 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 ...
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0answers
77 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 ...