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1answer
401 views

The image current due to moving charges and a current carrying thin wire

Suppose we have a plane conductor and positive charged particles of mass m are moving parallel to the plane conductor at a distance d. The trajectory can be assumed to be straight. An image current ...
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3answers
4k 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 ...
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0answers
35 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 ...
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2answers
51 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 ...
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0answers
21 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 ...
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2answers
176 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 ...
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1answer
114 views

Maxwell Stress Tensor at material boundaries

I am trying to grasp the meaning of the Maxwell Stress tensor $T_i^j$ at material boundaries. Concretely, I am trying to calculate the force between two waveguides. The results are given in an article ...
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2answers
218 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 ...
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2answers
171 views

Momentum around an accelerated electron

Assume that an electron is accelerated along the +x-axis. The electron will radiate electromagnetic energy and momentum in every direction. But it seems to me that the EM momentum it radiates in ...
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9answers
12k views
0
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0answers
42 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 ...
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3answers
174 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 ($E_x,E_y,E_z,B_x,B_y,B_z$). ...
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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 ...
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7answers
4k views

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 ...
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1answer
22 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 ...
1
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1answer
74 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 ...
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1answer
33 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 ...
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1answer
10 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 ...
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1answer
484 views

Induced electric field due to a moving wire

An infinite wire carrying a constant current $I$ in the $\hat{z}$ direction is moving in the $$y$$ direction at a constant speed $v$. Find the electric field, in the quasistatic approximation, at the ...
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0answers
31 views

How can there be E and B fields inside waveguides?

A hollow waveguide that is made of conducting material allows for the existence of an electromagnetic wave inside it which propagates from one end to the other. However, conductors are known to ...
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1answer
57 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 ...
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1answer
401 views

What are the boundary conditions for EM waves normally incident on the interface between two dielectric media?

An EM wave, amplitude $E_0$, frequency $\omega_0$, is incident upon a material with relative permittivity (dielectric function) $$\varepsilon \left( z \right) = \left\{ \begin{gathered}{\varepsilon ...
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2answers
784 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
234 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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0answers
32 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
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1answer
31 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
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1answer
21 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 ...
4
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1answer
78 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. ...
2
votes
1answer
207 views

Lagrangian of Non-Relativistic Charged Particle in a Magnetic Field

I'm trying to derive the Lagrangian for a non-relativistic charged particle under the influence of a magnetic potential. I'm assuming that $F=-\textrm{grad}(V)$ and so by the Lorentz force we have ...
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2answers
28 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 ...
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1answer
43 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 ...
1
vote
1answer
57 views

Can a charge moving in an open trajectory qualify as current?

It is sometimes said that a point charge is equivalent to an electric current. If it were a steady current, I should be able to find it from Ampere’s law or Biot-Savart’s law. Even if the current is ...
1
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1answer
28 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 ...
3
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1answer
126 views

Eddy currents on a conductors surface, and induced current flow around the loop both coexist?

The title seems confusing, because Eddy currents are induced currents... however, let me explain. Assume the following closed loop passing a uniform magnetic field like so: Now, this loop would ...
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0answers
31 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
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1answer
43 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 ...
1
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1answer
44 views

Induced EMF of this loop?

Consider a simple loop like so: And in-front of this loop are a series of wires that would cover the whole are of the loop, these wires are parallel to one another, and they have current flowing ...
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3answers
991 views

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. ...
1
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1answer
80 views

Force on a magnetic dipole due to a magnetic field

Imagine a solenoid which has current $i$ and is producing a magnetic field $B$ which equals $$B=\mu N i$$ Now, imagine we put a small cylindrical magnet at the end of the solenoid. Then because at ...
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0answers
35 views

Gauge invariance of quantum scalar field coupled to classical electromagnetic potential

I would like to quantize a scalar field that is coupled to a classical electromagnetic field $A_\mu$. More precisely, I start with the action (signature -+++) $$ S=\int ...
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14answers
2k 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 ...
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0answers
20 views

Surface electric current flows

All the models of electric current flow I have seen used in the texts I have seen are models where the current flows in a curve - let us call it $\gamma$ -, and for which, for example, the magnetic ...
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0answers
17 views

Voltage drop along electron beam

A focused electron beam represents a current and unless the charges (electrons) meet no resistance to their movement there should be a voltage drop along the length of the beam. So, assuming the beam ...
1
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0answers
45 views

Do gravitational waves produce real accelerations?

Do gravitational waves produce real accelerations? For example, if I have an electron and a gravitational wave passes by, will the electron emit electromagnetic waves according for instance to Larmor ...
1
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2answers
86 views

Non-standard representation of the free electromagnetic plane wave

The usual representation of a free electromagnetic wave in vacuum looks like this: The blue parts are the local electric field, while the green parts are the local magnetic field. The circularly ...
0
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1answer
34 views

Does an electromagnet use more energy when it is repelling another magnet?

Kind of a strange question. Is the amount of energy used to power an electromagnet directly proportional to the amount of work an electromagnet does? That is, if I were to power an electromagnet ...
3
votes
2answers
171 views

Relating Poyntings theorem to Lenz and Faraday's law?

In system's similar to a motor, where the armature begins to accelerate simultaneously there is induced $-\epsilon$ to reduce the applied current(hence the applied power $P(t)$ is also reduced), or ...
4
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1answer
3k views

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 ...
0
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1answer
178 views

potential inside a cylindrical shell in terms of the surface potential?

Given a potential distribution $V(\phi)$ at the surface of an infinite cylindrical shell, is there an easy way to derive the potential inside the cylinder. No charges or currents anywhere.
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0answers
31 views

One from Landau's Minimum (Macroscopic Electrodynamics)

A dielectric sphere with the electric and magnetic susceptibilities ε1 and µ1 is rotating with angular frequency ω in a constant electric field E~ in a medium, characterized by the parameters ε2 and ...