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Questions for those who know electromagnetism better than I do
sandalcandal:
--- Quote from: bsfeechannel on August 30, 2021, 07:36:57 am ---
--- Quote from: CatalinaWOW on August 30, 2021, 06:05:24 am ---capacitors and inductors violate two of your conditions for use of k l and kcl.
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Not if you treat them as lumped components, in which case the circuit path will be between their terminals, away from their internal varying fields.
--- End quote ---
To add to that. The "inductance" used in KVL and lumped element analysis (the common/typical type of circuit analysis taught in EE) is more precisely described as "partial inductance" which is different to the more generalised mutual-inductance and self-inductance as it is formalised in Physics studies.
This is a good (but quite heavy) paper going over derivation of the lumped element "inductor" model from first principles Maxwell's equations using a partial inductor model: http://eagle.chaosproject.com/sandbox/acstrial/newsletters/summer10/PP_PartialInductance.pdf
Edit: This level of analysis starts to get important for people doing high performance power electronics as well as RF black magic. At the point the lumped element modelling starts needing excess work to keep going, you tend to just go to FEA of the field equations rather than keep attempting analysis using lumped elements.
gcewing:
--- Quote from: Slartibartfast on August 27, 2021, 06:41:05 pm ---
--- Quote from: imo on August 25, 2021, 09:28:56 am ---My first lecture on "EM Field Theory" started with an intro given by the professor - "..do you really think the electrons transfer the energy from the power station to your household?
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An exceedingly silly rant, if it really happened. Of course the marching electrons (a.k.a. current) need the electric field (a.k.a.) voltage, to, as the multiplicative product, deliver the power.
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What he was probably getting at is that the power doesn't travel through the wires, it travels through the electromagnetic field surrounding the wires. See https://en.wikipedia.org/wiki/Poynting_vector
iMo:
The fact the "individual electrons" are marching in metals with a speed of a lazy ant, is not so obvious among the folk. Thus the marching electrons (like a water streaming in a pipe) themself cannot transfer power or energy in such a setup. The power is transferred via the e-field, where the field is strongest near the conductor's outer surface and spreads out over the entire universe, with decreasing intensity. The energy transfer inside a conductor is almost zero as the e-field in the conductor is almost zero. The conductor thus only gives the "direction" to the energy transferred by the surrounding field.
In order to calculate the "current" you have to integrate individual field contribution of each electron over the entire space surrounding the conductor. The Poynting's vector shows the direction and the strength of the field.
The energy/power from a battery to a lamp is transferred outside (along) the wires, with highest energy density just above the conductor's surface. When the conductor shows some "resistance" it means Poyinting's vector points towards the conductor's surface and you get energy losses like heat (because the outside field propagates itself with speed of light, but the speed of the field entering the conductor drops down significantly).
For example in a coaxial cable we hams often use the energy is transferred (mainly) in the dielectric between the outer and inner conductor, not in the copper.
Slartibartfast:
--- Quote from: T3sl4co1l on August 28, 2021, 02:34:51 pm ---
--- Quote from: EPAIII on August 28, 2021, 11:16:02 am ---Now, the magnetic flux (field strength) in a closed path surrounding a conductor. I think it is important to differentiate between two types of closed paths that can surround a conductor with a DC current. One such closed path would be the classical path of equal field strength. This is what we envision when we see the classic pattern of iron filings on a piece of paper that the conductor passes through and which are called by the simplistic phrase "magnetic lines of force". This type of path is, by definition a path of uniform field strength.
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If you'll permit this one indulgence -- strength is "line" density, not the path itself.
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If you're honest, then you'll admit that his definition - path of equal field strength - is more well-defined than using "line density", a concept which you critisise yourself in the following.
--- Quote ---I never liked the idea of "magnetic lines of force" anyway. There's no such thing as a line, you can't count them
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Sorry I have to say this is not entirely correct. In high-temperature situations you cannot count them, but in a type II superconductor the field condenses into separate flux lines, which in every respect behave like what your imagination expects of field lines. Every line creates a little vortex, which can be imaged and counted. Here is a scanning SQUID microscopy picture of magnetic field lines in a thin superconducting YBCO film.
Cheers Peter
Slartibartfast:
--- Quote from: EPAIII on August 29, 2021, 01:39:01 am ---Boy, I really wish I had some references on hand about how this "cloud" of electrons inside a conductor behaves. With no current flow I can easily see how their attraction to the nuclei of the metal atoms will keep them "bound" to those atoms and their charge density will be approximately uniform.
But once a current does start to flow, and I am primarily considering a DC current at this point, then those bonds are effectively broken and, as is obvious from the very fact that a current IS flowing, those electrons are much freer to wander about.
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This picture is wrong.
The periodical positioning of the nuclei (a.k.a. lattice) forces the available energy levels into bands. In metals, the electrons with the highest energy go into the so-called conduction band, where they have sufficient energy to roam freely. For these electrons, there is no bond, even without an external electric field, without any net current flowing.
--- Quote ---They will move from one atom to the next and while in flight between atoms,
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No, they don't. As I said, they don't hop from atom to atom, but roam freely.
You may be confusing this with conduction by holes in doped semiconductors. Since a hole away from an atom does not make sense, here the "hopping picture" is appropriate.
Cheers Peter
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