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1answer
81 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 ...
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3answers
175 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 ...
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9answers
669 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 ...
2
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1answer
43 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 ...
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0answers
12 views

Where does 1/Gamma characteristic angle come from in EM Radiation?

Very curious as to where this angle comes from? It describes the peak of radiation for almost all radiation regimes, but I am having a difficult time seeing where it comes from. Also, the physical ...
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0answers
22 views

How does displacement current come about? [duplicate]

I know that displacement current is due to time-varying electric field and its not an electric current. But then, is it charge that is actually being displaced?
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0answers
22 views

Why is radiation at the relativistic limit characterized by 1/gamma angle?

Trying to think of a reason as to why? Also, the factor that radiation is zero on axis? I haven't been able to resolve these two fundamental principles in my head :(
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1answer
56 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
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1answer
42 views

How is Transition Radiation different from EM waves crossing a boundary?

Just confused my self again :(. Transition radiation is the radiation produced when a charge crosses a boundary between two dielectric materials (http://en.wikipedia.org/wiki/Transition_radiation). As ...
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0answers
51 views

Quantum frequency vs classical frequency and Energy dependence

I recently realized what seems to be a contradiction in what is called "frequency" for light, and would enjoy some clarification of some more educated mind on the matter, thanking you in advance for ...
4
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1answer
129 views

Soft Bremsstrahlung: why $\hat{k}\cdot\mathbf{v}= \mathbf{v}'\cdot\mathbf{v}$?

On page 181 in Peskin & Schroeder they say that we consider the integral (intensity) $$\tag{1}\mathcal{I}(\mathbf{v},\mathbf{v}') = ...
3
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1answer
52 views

Time reversal invariance and boundary conditions in electrodynamics

This is really several related questions... The equations of classical electrodynamics are time-reversal invariant. However, when we solve the equations for a particular system of charges it is ...
1
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1answer
76 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 $\frac{d\phi}{d z}$ ...
3
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2answers
112 views

Can the $\vec H$-field have non-zero divergence? Does an $\vec H$-field monopole exist?

We know that, $\vec \nabla \cdot \vec B=0$ but $\vec \nabla \cdot \vec H\neq 0$, if $\vec \nabla \cdot \vec M \neq 0$. Does it mean that, in those cases $\vec H$-field has poles although $\vec ...
1
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1answer
63 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 ...
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2answers
295 views

The problem of self-force on point charges

Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, ...
2
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1answer
85 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 $l=1$). ...
1
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1answer
97 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 ...
0
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1answer
212 views

Lorentz transformation for electric and magnetic fields

How do derive the following transformation rule (J.D. Jackson third Edition 11.10) for electric and magnetic field? $$\vec E' = \gamma \left( \vec E + \vec \beta \times \vec B\right) - ...
2
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1answer
92 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
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4answers
181 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
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1answer
163 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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2answers
113 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
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3answers
145 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 ...
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0answers
119 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
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1answer
126 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
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1answer
115 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 ...
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0answers
126 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
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1answer
58 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 ...
2
votes
1answer
148 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
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2answers
102 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
46 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
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1answer
165 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 ...
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0answers
42 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 ...
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1answer
97 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
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2answers
135 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
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1answer
77 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
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1answer
91 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
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1answer
139 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 ...
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0answers
57 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 ...
3
votes
1answer
207 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 ...
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2answers
236 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
208 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
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2answers
104 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 ...
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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
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2answers
137 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 ...
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1answer
153 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 ...
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1answer
150 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 ...
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2answers
376 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
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1answer
293 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) ...