The four fundamental fundamental equations of electromagnetism.
19
votes
6answers
1k 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 ...
32
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 ...
3
votes
2answers
437 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:
...
1
vote
1answer
297 views
Special Relativity: Transforming Maxwell's equations
I'm working through Einstein's original 1905 paper*, and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame.
The paper proceeds as follows:
...
5
votes
1answer
296 views
Are the Maxwell's equations enough to derive the law of Coulomb?
Are the 8 Maxwell's equations enough to derive the formula for the electromagnetic field created by a stationary point charge, which is the same as the law of Coulomb?
If I am not mistaken, due to ...
6
votes
3answers
705 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. ...
3
votes
3answers
1k 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 = ...
2
votes
1answer
231 views
why is advanced radiation absent?
the Lienard-Wiechert green functions have future and past null cones of radiation. Maxwell equations allow for a continuous range of mixtures between the retarded and advanced components, but we have ...
2
votes
1answer
201 views
Electrodynamics and the Lagrangian density
Could anyone tell me what equations can I obtain from the Lagrangian density
$${\cal L}(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i,\,\,A_{i,j})~=~\frac{1}{2}|\dot A+\nabla\phi|^2-\frac{1}{2}|\nabla \times ...
5
votes
3answers
176 views
Faraday's law - does the induced current's magnetic field affect the change in flux?
I've had this conceptual problem with Faraday's law and inductance for a while now.
Take the example of a simple current loop with increasing area in a constant field (as in this answer). So ...
4
votes
4answers
355 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 ...
2
votes
2answers
341 views
Electron model under Maxwell's theory
I was not able to recall my memories, so:
What is the formula that states the frequency of electrons revolving around nucleus is equal to the frequency of light (or photon) emitted (or radiated)?
(I ...
1
vote
1answer
113 views
Determine the flow and amplitude equation for thermal energy (with Del operator)
It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
-7
votes
2answers
480 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 ...
