# Questions tagged [classical-electrodynamics]

Classical electrodynamics is the discipline that studies electromagnetic phenomena – such as electric and magnetic fields, radiation, and the dynamics of charged bodies – in classical terms.

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### What is the force corresponding to Lamor's formula for EM radiated power?

The rate at which electromagnetic energy is radiated is given by Lamor's formula. What is the corresponding rate at which momentum is radiated and hence force to this?
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### The issues when thinking about the magnetic flux law as being universal in modeling

$$\varepsilon = -\frac{\partial \Phi}{\partial t} =-\frac{\partial (BA)}{\partial t}$$ Any instance of considering the emf induced in a system, I usually think of the flux law first, I intensely ...
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### Electromotive force in the presence of non-steady currents

Griffiths's Introduction to Electrodynamics states $$\mathcal E = \oint \mathbf f \cdot d\mathbf l$$ In which $$\mathbf f = \mathbf f_s + \mathbf E$$ Where Griffiths describes the summation as ...
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### In electrodynamics, why do we say $\mathbf J = \sigma \mathbf E$ and not $\mathbf J = \sigma (\mathbf E + \mathbf v \times \mathbf B)$?

Griffiths notes it's because charges have an extremely low $\mathbf v$, so it's essentially an approximation, but aren't charges meant to be electrons? How can they be moving slowly? I usually think ...
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### Displacement currents, aren't really currents?

I'm confused with this definition of displacement currents within capacitors via Wikipedia: However it is not an electric current of moving charges, but a time-varying electric field. It's a ...
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### Relationship between the: Power supply's electric force for current flow, and Lorentz force equation for electric force?

$$F = qE + qv \times B$$ For the Lorentz force relevant to a current carrying wire, that is caused by the motion of a wire w.r.t to an exterior magnetic field $B$, the second term($qv \times B$) on ...
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### Energy-momentum tensor of the electromagnetic field

I have to derive the electromagnetic energy-momentum tensor from Noether's theorem and translation invariance. Due to translation invariance and gauge transformation: $$\delta A_\mu= a^\nu F_{\mu\nu}$$...
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### Griffiths Electrodynamics Problem 9.39: How can $\sin(\theta_T)$ be greater than one?

When an electromagnetic wave strikes an interface between two linear media, Snell's law states that $\frac{\sin(\theta_T)}{\cos(\theta_I)} = \frac{n_1}{n_2}$ where $\theta_I$ is the angle of incidence,...
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### How do we know that electric charges are invariant?

According to tparker at Why charge is Lorentz invariant but relativistic mass is not? So there are two different ways to generalize the mathematical form of Coulomb's law to make it ...
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### The Electromagetic Tensor and Minkowski Metric Sign Convention

I am trying to figure out how to switch between Minkowski metric tensor sign conventions of (+, -, -, -) to (-, +, +, +) for the electromagnetic tensor $F^{\alpha \beta}$. For the convention of (+, -,...
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### Invariance of Maxwell action

I have to show that the Maxwell action $$S=-\frac{1}{4}\int d^4x F^{\mu\nu}F_{\mu\nu}\,$$ is invariant under translation: $\delta_aA_\mu=a^\nu \partial_\nu A^\mu$ with $a^\mu$ as arbitrary and ...
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This is a very interesting problem that I've been struggling to solve for a week, so I decided to ask for some orientation, as I think it could also be of interest for the community. Let's consider a ...
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### Effects generated from a supercapacitor placed in a time varying external magnetic field?

The diagram above, showcases the simple outlook of a supercapacitor's interior and combining it with a full circuit loop. If an exterior magnetic field is introduced in all the operating states of a ...
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### Dipole Inside Cavity of A Spherical Conductor

Consider the following case: There is a short electric dipole placed arbitrarily inside a spherical cavity inside a solid,uncharged conducting sphere We need to find electric field at a point ...
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### Subarea within a changing magnetic flux?

If I were to introduce a boundary area $\tau$: And after sometime $t$, I introduced a constant magnetic field(let's imagine it spawned suddenly and ignored the change in flux from $t_o$ $\rightarrow$ ...
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### Is the relative number of electric field lines between two charges proportional to the difference between those two charges?

Let us consider a system of two unlike charges and suppose that the magnitude of the positive charge is greater that of the negative charge and call them a and b respectively. If that(asked in the ...
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### 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. ...
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### 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" is: ...
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### Difference in the direction of propagation of em wave [duplicate]

How are kx-wt and kx+wt in terms of the direction of the wave. I have been stuck at this or an hour, still can not find a definitive answer.
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### Energy momentum tensor of EM field written in symmetric form

I'm reading A. Zee's book, Einstein Gravity in a Nutshell. In problem 7 of chapter IV.2, it is said that the energy momentum tensor of the electromagnetic field \begin{align} T^{\mu\nu}=\eta_{\lambda\...
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### 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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### Symmetries of the Hamiltonian of a charged particle in a uniform magnetic field

Consider the Hamiltonian of a charged particle of charge $q$ in a uniform magnetic field $\textbf{B}=B\hat{\textbf{z}}$ is given by $$H=\frac{(\textbf{p}-q\textbf{A})^2}{2m}$$ where $\textbf{p}$ is ...
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### Concerning the energy stored in electromagnetic fields

How do we know that $$u = \frac{1}{2}\left(\epsilon_0E^2 + \frac{1}{\mu_0}B^2\right)$$ gives the energy density of electromagnetic fields? Is it a postulate of classical electrodynamics? Griffith ...
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### A changing magnetic field passes through a wire loop but the loop itself is not in the field. Is an EMF induced in the loop? [duplicate]

$$\nabla \times \vec{E} =-\frac{\partial{\vec{B}}}{\partial{t}}$$ Applying Stokes' theorem: $$\oint_{loop} \vec{E} \cdot d\vec{l}=\int_S -\frac{\partial{\vec{B}}}{\partial{t}} \cdot d\vec{S}$$ ...
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### Facing a paradox: Earnshaw's theorem in one dimension

Consider a one-dimensional situation on a straight line (say, $x$-axis). Let a charge of magnitude $q$ be located at $x=x_0$, the potential satisfies the Poisson's equation \frac{d^2V}{dx^2}=-\frac{\...
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### Are the microwaves in an ECRIS plane polarized?

Or randomly polarized? Are the photons in phase, like in a laser or maser? What is the theory behind how an electron in an ECRIS responds to a microwave photon?
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### Space translation of coordinates, classical field theory

Consider the Lagrangian density $L = -\frac{1}{4}F_{\mu\nu}F^{\mu \nu}$ with $F_{\mu \nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}$. After deriving the Euler-Lagrange equations for this ...
In the following exercise: I concern myself with the validity of my interpretations of (b). Here I am more confident slightly. The divergence of the current density is merely $- d \rho / dt$, so as ...
### Deriving magnitudes for $\mathbf J$ and $\mathbf E$ from the shape of a conductor
In the following exercise: I have no idea how to infer the magnitude of $\mathbf J$ nor $\mathbf E$ given the shape of the wire. The only clear thing to me here is that A, B and C all have different ...