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Results tagged with electromagnetism
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user 36793
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.
2
votes
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 …
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1
vote
Accepted
Lorentz invariance of wave equation
Firstly, wave equations in a relativistic field theory need not be Lorentz invariant. They are Lorentz covariant i.e., unchanged in form under a Lorentz transformation. The wave equation for the elec …
- 27.2k
3
votes
Accepted
Symmetry properties of the scalar potential and the vector potential
Recall the relations $\textbf{E}=-\boldsymbol{\nabla} V(\textbf{r},t)-\frac{\partial}{\partial t}\textbf{A}(\textbf{r},t)$ and $\textbf{B}=\boldsymbol{\nabla}\times \textbf{A}(\textbf{r},t)$. Now, $\t …
- 27.2k
3
votes
Do we need a bounded domain for the Laplace equation to have a non-zero solution $u$?
I'm not sure that I understand what you mean by "bounded domain". This is an answer based on what I understand from the question.
To solve Laplace's equation uniquely, you have to specify either the …
- 27.2k
2
votes
Mass term in Maxwell's Lagragian for Electromagnetism
The fact that $m^2A_\mu A^\mu$ is both Lorentz invariant tells that this term is an allowed term in the Lagrangian. But it does not explain why $m^2 A_\mu A^\mu$ represent the mass term.
The reason …
- 27.2k
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vote
What can Maxwell's Equations tell us about permanent magnets/ how are permanent magnets and ...
but can the equations tell us anything else about the magnetic fields of permanent magnets on their own, i.e. without interactions with a wire/current, or how such fields arise?
Permanent magnets …
- 27.2k
4
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3
answers
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Radiation gauge and choice of the gauge function
In electrodynamics, the scar potential $\phi$ and the vector potential $\textbf{A}$ satisfy the equations $$\frac{\partial}{\partial t}(\boldsymbol{\nabla}\cdot\textbf{A})+\nabla^2\phi=-\frac{\rho}{\e …
- 27.2k
2
votes
2
answers
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Current loop and direction ambiguity of the magnetic moment
Consider a circular loop in the XY-plane which carries a current $I$. Then it behaves as a magnetic dipole with moment $\textbf{m}=I\int d\textbf{S}$ where $\int d\textbf{S}$ is the area of the loop …
- 27.2k
2
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2
answers
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Can the electric field be made to penetrate the bulk of a metal?
When an external electric field $\textbf{E}_\textrm{ext}$ is externally applied to a metal, the free electrons move opposite to the direction of the field inside the metal and create an internal field …
- 27.2k
3
votes
1
answer
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Why does the magnetization vanish in diamagnetic material in absense of an external magnetic...
Though essentially present in all substances, diamagnetism is a much weaker effect and therefore, often suppressed by relatively strong opposite effects, like paramagnetism. This effect is exclusively …
- 27.2k
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answer
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What is the precise/defining mathematical behaviour for Meissner effect?
This video derives the Meissner effect $$\textbf{B}(x)=\textbf{B}(0)e^{-x/\lambda},$$ by reducing the equation, $$(\nabla^2-\lambda^{-2})\textbf{B}(\textbf{r})=0\tag{1}$$ into its one-dimensional coun …
- 27.2k
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2
answers
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Why do naturally occurring ferromagnetic materials contain a large number of domains?
Why do naturally occurring ferromagnetic materials (e.g. a piece of iron) contain a large number of domains rather than a single domain, and hence, carry no net magnetization? So the question is basic …
- 27.2k
8
votes
3
answers
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How do Maxwell's equations uniquely determine ${\bf E}$ and ${\bf B}$ despite no. of equatio...
Maxwell's equations in free space are given by $${\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 …
- 27.2k
1
vote
1
answer
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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 …
- 27.2k
2
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3
answers
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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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