The four fundamental fundamental equations of electromagnetism.
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1answer
181 views
Gravimagnetic monopole and General relativity
Review and hystorical background:
Gravitomagnetism (GM), refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein ...
4
votes
4answers
362 views
How to interpret the continuity conditions in the PDEs (for example, Maxwell equations) originated in physics?
I am currently working on PDEs in physics, mostly Maxwell equations. I am a mathematics graduate student, and this question has been haunting me for years.
In PDE theory, or more specifically the ...
33
votes
2answers
2k views
Why did Feynman's thesis almost work?
A bit of background helps frame this question. The question itself is in the last sentence.
For his PhD thesis, Richard Feynman and his thesis adviser John Archibald Wheeler devised an astonishingly ...
4
votes
3answers
457 views
can one introduce magnetic monopoles without Dirac strings?
To introduce magnetic monopoles in Maxwell equations, Dirac uses special strings, that are singularities in space, allowing potentials to be gauge potentials. A consequence of this is the quantization ...
3
votes
2answers
450 views
Does existence of magnetic monopole break covariant form of Maxwell’s equations for potentials?
Absence of magnetic charges is reflected in one of Maxwell's fundamental equations:
$$\operatorname{div} \vec B = 0 \text{ (1).}$$
This equation allows us to introducte concept of vector potential:
...
7
votes
3answers
736 views
Maxwell in multiple dimensions: What happens to curl?
I read this answer a while ago, and while thinking about $\nabla$, I realized something. Since the cross product can be written as a determinant, in higher dimensions we require extra vector inputs. ...
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vote
2answers
651 views
Conservation of Energy and the Poynting Theorem
Conservation of energy in an electrical circuit can be expressed by Ampere's law $$\nabla \times \textbf{B} = \mu_o
\textbf{J} + \epsilon_o \mu_o \frac {\partial \textbf{E}} {\partial t}$$ when ...
0
votes
2answers
170 views
Should $E$ and $B$ change with Gravity?
Lets examine a typical GR metric:
$$ds^2=g_{00}dt^2-g_{11}dx^2-g_{22}dy^2-g_{33}dz^2$$
The "d" going with ds has its correct meaning when the path is
specified with respect to a one dimensional ...
3
votes
3answers
1k views
Can the Lorentz force expression be derived from Maxwell's equations?
The electromagnetic force on a charge $e$ is
$$F=e(E+v\times B),$$
the Lorentz force. But, is this a separate assumption added to the full Maxwell's equations? (the result of some empirical ...
19
votes
6answers
2k 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 ...
2
votes
4answers
400 views
How is this classical “paradox” resolved in electromagnetism?
A magnet and a coil move relative to each other. In the frame of reference of the magnet, there is a magnetic field and consequently a force acting on the charges in the coil according to the Lorentz ...
5
votes
2answers
296 views
On Electromagnetic Self Energy
In the process of pair annihilation an electron and a positron annihilate each other to produce a pair of photons, conserving momentum and energy. As the oppositely charged particles approach each ...
3
votes
2answers
113 views
Derivatives of delta function and equation of continuity for a single charge…
For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are fiven by:
\begin{equation} \rho(\textbf{r},t)= ...
2
votes
2answers
353 views
A Paradox in Special Relativity
Two inertial frames K and k’ are considered. They are in relative uniform motion along the x-x’ direction with relative speed =v.
In the frame K’ we have a cuboidal piece of dielectric [at rest wrt ...
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votes
2answers
489 views
Do We Need Maxwell's Equations Since They Fail to Account for An Experimental Fact at Least in One Occasion?
This question is an outgrowth of regarding voltage and emf where @sb1 mentioned Faraday's law. However, Faraday's law as part of Maxwell's equations cannot account for the voltage measured between the ...
3
votes
3answers
2k views
Derivation of Maxwell's equations from field tensor lagrangian
I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = ...
