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1
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1answer
65 views

Reflectivity and transmissivity greater than 1

In plasmonics, it is often seen that reflection coefficient and transmission coefficient are greater than 1. How is energy conservation valid in such cases?
0
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1answer
40 views

Any good electricity and magnetism books for highschool students? [duplicate]

I really want to learn about electricity and magnetism for a long time but never have gotten to it, are there are good books that are conceptual on the topic of electromagnetism? I do not know ...
1
vote
1answer
31 views

Why is the electric field perpendicular to a circuit zero?

Griffith briefly addresses the uniformity of the electric field in a wire using Laplace's equation by assuming that the electric field is always parallel to the wire (i.e. $\mathbf{E}\cdot\hat{n}=0$). ...
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0answers
36 views

What is Coulumb force at zero separation in classical picture [closed]

Assume a classical world. What would be force between 2 point charges if their separation tends to zero? Assume charges are static. My professor claimed it would be finite. I request you to ...
14
votes
5answers
2k views

How many photons are needed to make a light wave?

What is the smallest number of photons needed to make a "light wave"? In other words, how many (coherent?) photons start to exhibit classical behavior? For example, how many photons are needed to get ...
3
votes
0answers
50 views

Number of Independent postulates in Electrodynamics

We know that there are two ways to get charge conservation in electrodynamics by using the following action: $$S[A]~=~\int\! d^4x {\cal L},$$ $$ {\cal L} ~=~{\cal L}_{\rm Maxwell} + {\cal L}_{\rm ...
5
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0answers
57 views

Validity of gauge fixing in classical electrodynamics [duplicate]

I am working through Griffith, and was confused by some of the restrictions he imposed on the potentials in introducing the Coulomb and Lorenz gauge. It is easy to see that adding some arbitrary ...
0
votes
1answer
35 views

Multipole expansion of the electromagnetic field

In Jackson's Classical Electrodynamics, section 9.7, he develops the multipole expansion of the electromagnetic fields in terms of the vector spherical harmonics and the spherical Bessel and Hankel ...
1
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1answer
98 views

Is $A_\mu A^\mu=0$ a good gauge fixing? [closed]

I am taking a course in classical electrodynamics and I am facing this problem Prove that $A_\mu A^\mu=0$ is a good gauge fixing or not. If it is, there are residual gauge freedom? I know that, ...
2
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0answers
66 views

Confusion in reaction force of Ampere's Force Law [closed]

I am reading Maxwell's "A Treatise on Electricity and Magnetism" and I have some confusion in the following pages: The element ds is resolved into its components $\alpha$ and $\beta$;and the ...
30
votes
4answers
4k views

What is momentum really?

Wikipedia defines momentum as in classical mechanics: In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object. However, an ...
0
votes
0answers
45 views

Fine Structure and Fine Structure Constant - intuitive relation?

How does the fine structure and fine structure constant relate to each other, intuitively? I've seen $\alpha$ extrapolated as a term in energy calculations for fine structure, but is there a ...
0
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0answers
52 views

Confusion in the derivation of the potential of a magnetic shell

I am reading an old book on electromagnetism (THE MATHEMATICAL THEORY OF ELECTRICITY AND MAGNETISM) and I have some confusion in the following pages: First let me clarify what a "magnetic shell" ...
4
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1answer
100 views

Lagrangian density for Lorentz force of continuous charge distribution in external field?

It's frequently an exercise to derive the Lorentz force law for a particle with charge $q$ in an external electromagnetic field given by the following Lagrangian: $$L = -mc^2\sqrt{1-\frac{\dot{r}^2}{...
1
vote
1answer
39 views

differences of Aurora Borealis (North) vs. Aurora Australis (South)

I was wondering about the differences between the Northern vs. Southern lights: will one pole collect the positive charges, and the other the negatives? I know that the solar wind is composed mainly ...
0
votes
0answers
42 views

Deriving an equation in Maxwell's “a treatise on electricity and magnetism” [duplicate]

I am reading Maxwell's "a treatise on electricity and magnetism" and I need a derivation of formula 16 $\left(M=\iint\dfrac{\cos\varepsilon}{r}\mathrm ds~\mathrm ds'\right)$ (in the page below) using ...
1
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0answers
18 views

Variation of spin in the rest frame of an electron in an external magnetic field

In Jackson's Classical Electrodynamics, the equation of motion for the angular momentum $\textbf{s}$ of an electron in an external magnetic field is given by (eq. 11.101) $$\left(\frac{d\textbf{s}}{dt}...
0
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1answer
45 views

Correct Definition of Angular Momentum of a Charged Particle in an Electromagnetic Field? (Classical Mechanics) [duplicate]

What is the more correct definition of angular momentum $\vec{\mathbf{M}}$ in three dimensions? (I.e. classically/Lagrangian/Hamiltonian, not necessarily quantum or relativistic) $$\vec{\mathbf{M}}...
0
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0answers
21 views

Implication of breakdown of scale invariance for problems with intrinsic length or time scales?

According to Wikipedia article on scale invarince, the equations for electric (and magnetic) fields : $$\nabla^2\vec{E}=\frac{1}{c^2}\frac{\partial^2\vec{E}}{\partial t^2}\hspace{0.3cm}\text{and}\...
6
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2answers
107 views

Will accelerated observer see radiation from the charge that is at rest in observers's frame?

So I had a huge debate about this with my friends. Imagine that you are in a non-inertial frame of reference. For simplicity, assume that frame is accelerated along x-axis. You have held a charge in ...
5
votes
1answer
114 views

What is relationship between electromagnetic mass and rest mass?

Is there a direct equation which compares rest mass $m_°$ and electromagnetic mass $m_{em}$? Nothing on web I found. $m_{em} = \frac{4 E_{em}}{3c^2}$ 4/3 problem The final solution of the ...
0
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0answers
37 views

What is the physical meaning of a magnetic conduction current?

In electrodynamics, it is possible to have an electric conduction current, whereby $J=\sigma_e E$, with $J$ being the current, $\sigma_e$ the electrical conductivity and $E$ the electric field (this ...
0
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2answers
51 views

Calculating charge density $\rho(r)$ using Gauss law (both forms)

Below is a question given in my assignment. I tried applying Gauss law in both forms, differential and surface integral form. But both there is a difference by a factor of $2$. Is the differential ...
2
votes
1answer
59 views

Lorentz force in different reference frames?

I have been introducing myself to special relativity and relativistic electrodynamics, and became curious about the similarity of the electric and magnetic forces. I'm trying to show that the combined ...
0
votes
1answer
20 views

De-merits of the application of Laplace's Equation to find electrostatics potentials

QUESTION: What are the de-merits of the application of Laplace's Equation to find electrostatics potentials? Our professor told us that the answer was as follows: It can be used only when the ...
1
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2answers
51 views

How does always the magnetic field lag the elctric field in a conductor?

In conductor, the relation between the phase of the magnetic field $\delta_B$ and that of the electric field $\delta_E$ is given by $$\delta_B-\delta_E=\tan^{-1}(\frac{\beta}{\alpha})$$ where $\alpha$ ...
0
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0answers
18 views

Free charges inside a conductor and propagation of EM wave

In Griffith's book on Electrodynamics, while discussing the propagation of electromagnetic wave in a conducting medium, he set $\rho_{free}=0$. He argues that, any extra charge given to the conductor ...
-1
votes
1answer
45 views

Interpreting $\hat{e}_z$ in Maxwell's equations

I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\hat{e}_z$ comes from in the following equation: $ \frac{\partial{\vec{E}_t}}{\partial{z}}+i\frac{\...
1
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0answers
36 views

standard model classical limit [duplicate]

"The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known". Since it includes ...
1
vote
1answer
42 views

Probable mistake in the derivation of the vector form of Biot-Savart's Law

In the course of "Classical Electrodynamics", our professor stated Biot-Savart's Law as follows: $$\vec {dB}=\frac{\mu_0}{4\pi}\cdot \frac{i\vec {dl} \times \vec r}{r^3}$$ Then he proceeded to derive ...
0
votes
0answers
55 views

What is the difference between length and velocity gauge when it comes to a dipole approximation?

Lets say we have plane wave with $\vec E$ perpendicular to $\vec k$. The dipole term will come from $\vec A\cdot \vec p$. Is the electric field longitudinal in the length gauge for the dipole ...
1
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2answers
55 views

Is magnetic field of a uniformly moving charge constant everywhere?

As far as I understand, for the field of a uniformly moving charge, curl of $\mathbf E$ is zero everywhere. Since $\nabla \times \mathbf E = -\dfrac{\partial\mathbf B}{\partial t}$, magnetic field ...
0
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0answers
27 views

Lorentz invariance & Noether theorem of classical ED

I want to check invariance of the action under Lorentz boosts for classical electrodynamics. The action is $$S = \int \mbox{d}^4x F_{\alpha \beta} F^{\alpha \beta} $$ I assumed that the fields ...
0
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0answers
46 views

Gradient of Greens function

This question is about Jackson's equation (10.75) and (10.77) I don't know the step in between these two equations.I'm not sure what our unit vector $n'$ will be here and how can we take gradient of ...
0
votes
2answers
22 views

Electric charge and and cylindre

An electric charge is distributed with a uniform volume density $\rho$ in a cylindre with a radius $R$ and an infinite length. Our professor said the following: By symetry the electric field is ...
1
vote
3answers
180 views

Maxwell's equations - underdetermined - uniqueness

Maxwell's equations can be seen as two dynamical equations (the two curl equations), and two constraint equations (the two divergence equations). So we have 6 unknowns ($E_x,E_y,E_z,B_x,B_y,B_z$). ...
4
votes
1answer
28 views

Characterisation of passivity

I'm a mathematician trying to work on some problems involving metamaterials. I have some trouble to understand the notion of passive media. Informally, this means that (without sources), a medium ...
2
votes
1answer
115 views

How does Bremsstrahlung occur in a vacuumized particle accelerator?

In our electrodynamics course we have learned that accelerating a charged particle will lead to a loss of energy in the particle due to Bremsstrahlung. The exact amount of power radiated away is given ...
0
votes
1answer
11 views

A media in which the electrical displacement vector is not causal

I recently did an electrodynamics homework problem in which we showed that in a certain model (Lorentz-Drude), where the permittivity of free space $\epsilon$ was dependent upon the angular frequency ...
0
votes
1answer
59 views

relationship between torque and potential energy for electromagnetism

It is well known that the energy of a magnetic dipole in a magnetic field is taken as $U = - \bf{m}.\bf{B}$. The dipole also experiences a torque $\bf{\tau = m \times B}$. In classical mechanics the ...
2
votes
1answer
80 views

What causes electromagnetic waves to propagate in free space?

In free space, $\rho=0$ and $J=0$, so there are no electromagnetic sources/sinks. Maxwell's equations thus reduce to: $\nabla\cdot E = 0$ $\nabla\cdot B = 0$ $\nabla\times E = -\frac{\partial B}...
0
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0answers
35 views

Self Energy (Classical Electrostatics)

In classical electrostatics, the total energy is given by $W_T=\frac{\varepsilon_0}{2}\int_{\mathcal{U}}{\left|E(\vec{r}')\right|^2 \mathrm d\tau'}$ , while the interaction term is $$W_I = {\...
2
votes
1answer
45 views

Shape of Eddy Currents

I've always had this question and didn't know how to answer it - Why do eddy currents have the shape they do? Why are they circular eddies?
3
votes
1answer
26 views

Suitable boundary conditions magnetic field paradox

Consider a point charge $q$ situated at the origin, and a uniform magnetic field, covering all of space, pointing in the $z$ direction $\mathbf{B}=B_0\hat{\mathbf{k}}$. What happens when you turn off ...
5
votes
1answer
88 views

Ultraviolet catastrophe in a classical world

In the real world, the ultraviolet catastrophe doesn't happen because the quantization of photons modifies the classical behavior of light at frequencies comparable to and higher than the temperature. ...
0
votes
1answer
49 views

Relativistic Electrodynamics [closed]

What are the applications of relativistic electrodynamics I've been learning about it in a theoretical physics module however I don't understand what implications or uses it has in real life and haven'...
1
vote
2answers
38 views

How will the charges redistribute when a conductor is in contact with a uniformly charged material?

This is a conceptual question but it is just a bit tricky, Under the influence of E-field any charges that accumulates within the conductor redistributes to the surface. So when an uncharged ...
1
vote
1answer
52 views

Eddy currents of a thin wire vs. a large plate?

In many examples such as this: I noticed that most cases where Eddy currents are of focus, or have a considerable effect, would be with examples having a large conductive area perpendicular to the ...
0
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0answers
37 views

Definition of localized source in electrodynamics

I'd like to know the exact definition in classical electrodynamics of a localized source, e.g. localized charge density $\rho(\mathbf{r},t)$ or localized current density $\mathbf{J}(\mathbf{r},t)$. ...
0
votes
1answer
46 views

Evaluating the components of Maxwell's stress tensor

I was going through the Maxwell's stress tensor section of Introduction to Electrodynamics by Griffiths. In the example 8.2(screenshot below), I fail to understand how the equation 8.23 (in the ...