General > General Technical Chat
Questions for those who know electromagnetism better than I do
Slartibartfast:
--- Quote from: CatalinaWOW on August 20, 2021, 04:15:17 am ---You can use Maxwell's equations for this, but for a DC current the magnetic field is given simply by Ampere's law.
--- End quote ---
Do you realise that Ampére's Law is nothing else but the (in usual counting) fourth Maxwell's equation?
CatalinaWOW:
--- Quote from: Slartibartfast on August 23, 2021, 11:14:25 pm ---
--- Quote from: CatalinaWOW on August 20, 2021, 04:15:17 am ---You can use Maxwell's equations for this, but for a DC current the magnetic field is given simply by Ampere's law.
--- End quote ---
Do you realise that Ampére's Law is nothing else but the (in usual counting) fourth Maxwell's equation?
--- End quote ---
Of course. And you can the prove to yourself that the time derivative of a DC current is zero and write it looking like the original Ampere's Law which is accessible to those with less math background.
You realize that you can use Maxwell's equations to do circuit analysis. But most folks find the simplified equations of Kirchoff are adequate and far easier to solve.
rstofer:
--- Quote from: Slartibartfast on August 23, 2021, 11:08:37 pm ---
--- Quote from: rstofer on August 20, 2021, 03:27:51 am ---You wind up dealing with Maxwell's Equations and NOBODY wants to go there voluntarily. Three people in history have understood Maxwell's Equations: Maxwell, Feynman and Einstein. The rest of us just think we know what is going on.
--- End quote ---
You're trying hard to be silly here, aren't you?
--- End quote ---
Yes and no. I remember Field Theory as the most difficult and least interesting course I had to take. I will take the opportunity to avoid Maxwell's Equations at every opportunity. Yes, intuitively, I understand them (with a few minutes review) but the math can get really ugly.
--- Quote ---
Maxwell's equations really aren't that difficult to understand, particularly the local (i.e. differential) version. The global (integral) version is a bit harder, but more practical in some situations.
--- End quote ---
Slartibartfast:
--- Quote from: CatalinaWOW on August 24, 2021, 04:19:00 am ---
--- Quote from: Slartibartfast on August 23, 2021, 11:14:25 pm ---
--- Quote from: CatalinaWOW on August 20, 2021, 04:15:17 am ---You can use Maxwell's equations for this, but for a DC current the magnetic field is given simply by Ampere's law.
--- End quote ---
Do you realise that Ampére's Law is nothing else but the (in usual counting) fourth Maxwell's equation?
--- End quote ---
Of course. And you can the prove to yourself that the time derivative of a DC current is zero and write it looking like the original Ampere's Law which is accessible to those with less math background.
--- End quote ---
I'm not sure what you're referring to. The time derivative of current does not enter anywhere. Are you talking about so-called "displacement current"? That name is misleading, it is not a current, but a varying electric field.
AFAIK the only difference between the "original" and later version of Ampére's Law is the inclusion of the time derived electric field in the latter. That the time derived electric field is zero, is trivial in the given situation, and does not need proof.
--- Quote ---You realize that you can use Maxwell's equations to do circuit analysis. But most folks find the simplified equations of Kirchoff are adequate and far easier to solve.
--- End quote ---
That includes me, of course. But the analogy is a poor one: Kirchhoff's are derived from Maxwell's, but Ampère's IS one of Maxwell's.
I'm always amused when guys declare Maxwell's are too difficult to deal with, but then go and happily use Gauss' Law (1st and 2nd of Maxwell's), or Faraday's Law (3rd Maxwell's), or even Ampére's Law (4th), and claim that's a simplification. As simplification goes, the situation given by the topposter in fact calls for using the Biot-Savart law, which is the general solution of Ampére's Law (which by itself is a differential equation) in the given situation.
Wikipedia has a quite decent article on Maxwell's. It's well written IMHO, and very accessible, at least when excluding the advanced parts (e.g. relativistic, i.e. manifest Lorentz invariant formulation, and the classical limit of quantumelectrodynamics).
Slartibartfast:
--- Quote from: CatalinaWOW on August 20, 2021, 04:15:17 am ---Many texts and online resources give solutions for a cylinder were the current density is uniform in the cross section of the cylinder. But they never discuss whether the current density would be uniform.
--- End quote ---
That's because there isn't much to discuss. In the general case it is not uniform, of course. The case that is usually assumed if talking about a uniform current density distribution needs:
0.) a DC current. With AC, effects related to skin effect destroy the uniformity.
1.) the conductor to be the shape of a generalised cylinder (i.e. size, shape, and orientation of crosssection constant along it's length).
2.) uniform conductor's material (more specifically, constant conductivity across the conductor's volume).
3.) the electric potential to be constant across the end surfaces.
That's it. If any of these are violated, the current densitiy in the best case is only approximately uniform. Violation of more than one can be made such that their effects on the current uniformity cancel, but that's a very tricky business.
Navigation
[0] Message Index
[#] Next page
[*] Previous page
Go to full version