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The classical theory of electric and magnetic fields, both in the static and dynamic case. It also covers general questions about magnets, electric attraction/repulsion, etc. Distinct from electrical-engineering.
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Is this case a failure of Stokes' theorem?
In the presence of a hypothetical magnetic point charge at the origin of coordinates, it turns out that an irremovable physical singularity of the vector potential ${\bf A}({\bf r})$ exists for any ch …
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1
answer
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What could be and how to come up with a mathematical formula for the local electric field in...
I asked a similar question here more than two years ago. I did not get an answer to my complete satisfaction. I would like to reiterate the problem again.
The local electric field of a monochromatic r …
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3
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Is the time evolution of physical fields unambiguous without fixing a gauge?
Context The origin of the question below stems from this lecture here by Raman Sundrum between $48.20$ to $51$ minutes.
Let at some initial instant $t_0$, the electric and magnetic fields (E and B) …
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How is Meissner effect consistent with the frozen field lines inside the superconductor?
And in fact, it is possible to lock magnetic field lines inside a superconductor if the magnetic field were applied before the material was cooled below $T_c$. This seems to suggest $B\neq 0$ insid …
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1
answer
263
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For the free electromagnetic field, is it possible make single gauge transformation to achie...
For any electromagnetic field, it is easy to impose the Coulomb gauge condition ${\bf\nabla}\cdot{\bf A}=0$. To start with, if ${\bf \nabla}\cdot{\bf A}_{\rm old}\neq 0$, the trick is to make a gauge …
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Reviewing an old argument about the number of DOFs of EM field
For free electromagnetic fields, it is possible to choose a gauge such that the scalar potential $\phi(t,{\bf x})=0$ and the vector potential ${\bf A}(t,{\bf x})$ satisfies the Coulomb gauge condition …
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3
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How do Maxwell's equations uniquely determine ${\bf E}$ and ${\bf B}$ despite no. of equatio...
Maxwell's equations in free space are given by $${\bf\nabla}\cdot\textbf{E}=0,~~{\bf\nabla}\cdot\textbf{B}=0$$
and
$${\bf\nabla}\times\textbf{E}=-\frac{\partial\textbf{B}}{\partial t},~~{\bf\nabla}\ti …
2
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Accepted
How can we do this tensor product $F_{\mu \nu}F^{\mu \nu}$?
Expand $F_{\mu\nu}$ and $F^{\mu\nu}$ and multiply. Since $\mu,\nu$ are summed over, in the next step, they can be interchanged so that $$(\partial_\mu A_\nu)(\partial^\mu A^\nu)=(\partial_\nu A_\mu)(\ …
2
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Accepted
Electric field lines and coordinates
The electric field $\textbf{E}_{\rm point}$ due to a point charge is spherically symmetric i.e. it does only depend upon how far you are from that charge. Such force fields are called central force fi …
2
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4
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What causes $A^{\mu\nu}_{\pm}=F^{\mu\nu}\pm i \tilde{F}^{\mu\nu}$ to have three independent ...
Both the elctromagnetic field strength tensor $F^{\mu\nu}$ and its dual $\tilde{F}^{\mu\nu}$ defined as $\tilde{F}^{\mu\nu}=\frac{1}{2}\epsilon^{\mu\nu\lambda\rho}F_{\lambda\rho}$ are examples of anti …
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Deviation from Linear response in metals and Ohm's law
In metals, Ohm's law is an example of a linear response i.e., $I\propto V$ where $I$ is the current (response) due to the applied voltage $V$ (external force). For metals, can we have a breakdown of l …
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Parity transformation property of $\epsilon^{\mu\nu\sigma\rho}$ and $F_{\mu\nu}$ (and $G_{\m...
The Lorentz invariant term $\epsilon^{\mu\nu\sigma\rho}F_{\mu\nu}F_{\sigma\rho}$ is not parity invariant. To show this one needs to find the parity transformation property of $F_{\mu\nu}=\partial_\mu …
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What would happen to the transverse nature of EM field if photon had a mass?
This is what happens for a Proca field. The corresponding "electric field" will not remain divergenceless i.e., $\boldsymbol{\nabla}\cdot\textbf{E}\neq 0$ but the corresonding "magnetic field" will re …
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2
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Why does hysteresis occur?
The existence of domains is a necessary condition for ferromagnetic materials to exhibit the phenomenon of hysteresis. But how are domains responsible for the phenomenon of hysteresis? What is the und …
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Physical implication of $\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\rightarrow -\textbf{E}...
An interesting observation to consider about the Maxwell's equation is that in absence of the sources, the equations are symmetric under the interchange $$\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\ …