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Ampere's law

Anonymous Thu 11 Jun 18:05:13 2020 No.11786598 View Reply Original Report

Quoted By: >>11786972 >>11787000 >>11787032

Hello,

Not homework. Just something that has been bothering me.

If iron "guides" magnetic fields by its high permeability, then it would affect the B-field reading around the contour shown in the image. In this case, the B-field reading would show 0 (or very close to it), which would imply that there is no current passing the enclosed area defined by the contour, which is false.

Where is the error in my reasoning?

Anonymous

Anonymous Thu 11 Jun 2020 18:22:13 No.11786638 Report

Quoted By: >>11787141

Could it be that the iron is not actually concentrating the field created by the current in the conductor? That you would be getting the same B-field readings as you would without the iron, keeping Ampere's law consistent?

Anonymous

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Anonymous Thu 11 Jun 2020 19:22:58 No.11786816 Report

Quoted By: >>11787141

First off, thanks OP for posting this, interesting thought experiment. I myself have been reviewing electromag myself recently, particularily in cases where we must break the assumption that the divergence in the B or A field is 0.

It appears under that equation that the ferromagnetic wrapping would in a way tied the hands and feet of the charge carrier as it attempts to progress down the wire. If a current is measured after surviving this wrapping, there must be more to the story.

Perhaps the reasoning is too be found in later on in that wiki. equation related depicts the countour integral of the B field as composed of two terms, one a buffet of current densities, the other, it appears, an expression of the electric fields propagation in time with the appropriate constants of the media

Anonymous

Anonymous Thu 11 Jun 2020 20:13:00 No.11786972 Report

Quoted By: >>11787139 >>11787141 >>11787189

>>11786598
Instead of iron, imagine a superconducting torus around the wire (the wire runs through the doughnut hole).
How would the current move on the surface of the torus to cancel the induced magnetic field?
It would move opposite to the current flow of the wire at the inner diameter and in the same direction at the outer diameter.
Could it cancel all of the magnetic field (inside and outside the torus)?
No.
If you stretch the torus along the doughnut hole axis, you would get two superconducting cylinders (one at the surface of the wire and one at the outer diameter).
The current on the inner cylinder would be opposite to the current in the wire and the current on the outer cylinder would be in the same direction as the wire.
What would these two currents need to be in order to minimize the total magnetic field energy of all of space?

Anonymous

Anonymous Thu 11 Jun 2020 20:21:06 No.11787000 Report

Quoted By:

>>11786598
You can't have a ferromagnetic material block the magnetic field for exactly the reason you mention. Your assumption that it would block the field is wrong not Ampere's law

Anonymous

Anonymous Thu 11 Jun 2020 20:30:42 No.11787032 Report

Quoted By: >>11787054

>>11786598
I had a question similar to this, except the other way around. The Maxwell–Faraday equation states: $-\frac{\partial \mathbf{B}}{\partial t} = \nabla \times \mathbf{E}$ , but if you had an infinite (or even just toroidal) solenoid and a wire looped around it then the magnetic field would be entirely contained and never actually "touch" the wire, so would you still generate an EMF around the wire if you varied the field of the solenoid? I was told that you can solve this using vector-potentials, but was never given an explanation beyond that.

Anonymous

Anonymous Thu 11 Jun 2020 20:39:24 No.11787054 Report

Quoted By:

>>11787032
Yes it would still generate an EMF. The magnetic field is contained but there is a circulating electric field around the solenoid as the current in the solenoid is varied.

Anonymous

Anonymous Thu 11 Jun 2020 21:17:23 No.11787139 Report

Quoted By:

>>11786972
hmm, very intriguing line of reasoning indeed.
If i had to hypothesize, our two currents would need to be at a magnitude and direction of flow to 'help a brotha out' on those points of induction, give it the energy it needs to traverse that point in space without having to dispense itself as inductance.

Anonymous

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Anonymous Thu 11 Jun 2020 21:17:38 No.11787141 Report

Quoted By: >>11787168 >>11787228 >>11787290

>>11786638
Tested this with FEMM (figure), turns out that this is indeed the case. Ampere's law not debunked quite yet.

>>11786816
Hmm, interesting. In what sorts of situations would the divergence of B deviate from 0? I saw a video of the Royal Institution on magnetic monopoles, about creating them virtually.

>>11786972
This whole problem lead me to think about what exactly causes the "concentration" of the flux and it was something along the lines of this. If the iron can be though of as a torus around which a lossless current flows, then the fields can just be superpositioned on each other.

>The current on the inner cylinder would be opposite to the current in the wire and the current on the outer cylinder would be in the same direction as the wire.

Wouldn't it be the other way round? If the iron or superconducting cylinders were to produce an amplified field, then the inner cylinder's current would have to be in the same direction as the central conductor's current if judged with the curled right-hand rule.

Anonymous

Anonymous Thu 11 Jun 2020 21:29:29 No.11787168 Report

Quoted By: >>11787230

>>11787141
He's talking about a superconductor that wants to expel magnetic fields not a ferromagnet

Anonymous

Anonymous Thu 11 Jun 2020 21:42:27 No.11787189 Report

Quoted By:

>>11786972
First I let the inner cylinder current be equal and opposite to the outer cylinder current from continuity of current on the torus.
Using Biot-Savart for an infinite line, you get B(r) proportional to 1/r.
This also works for cylinders.
Computing the magnetic field energy requires integrating B^2 carefully (the currents only contribute to the magnetic field outside their cylinders).
I did this and found that the inner current is equal and opposite to the wire current and the outer current is equal to the wire current.
From outside the outer cylinder, it is as if there are no superconducting cylinders there.

Anonymous

Anonymous Thu 11 Jun 2020 22:02:11 No.11787228 Report

Quoted By:

>>11787141
Even the air is a pretty decent magnetic conductor as you can see. This makes it so Ampere's Law implies there can be no magnetic superconductors

Anonymous

Anonymous Thu 11 Jun 2020 22:03:31 No.11787230 Report

Quoted By: >>11787590

>>11787168
I'm actually talking about a superconducting ring that wants to trap magnetic field lines, not expel them.
If you wanted to trap an entire field line, put a superconducting cylinder around it.
If that field line is a circle, you end up with a superconducting torus.
If you want to trap a stack of these circular field lines, stretch the torus vertically.

Anonymous

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Anonymous Thu 11 Jun 2020 22:21:26 No.11787290 Report

Quoted By:

>>11787141
Sure, yeah, a kind gentlemen referred to some formalism as a dirac monopole, read this today
https://arxiv.org/ftp/physics/papers/0608/0608051.pdf
quite interesting, the equations describe an interesting deconstruction
>One may divide the electric(magnetic) fields in to two parts: the field which is due to the electric charges, E_e(B_e) and one which is due to the magnetic charges, E_m(B_m)

and abstracts another vector field G and scalar potential psi. I dunno quite yet, but it seems like it describes a higher recursive pattern electromagnetism than can be possibly be described (as this G field's divergence is gauged out to 0 as well)

I wish i had a list I could conjure up list as steady fact, but this set of observations and theories, (that royal institution monopole one as well) led me to conclude that perhaps something big of meaning was hidden perhaps in plain site, hidden behind the classic need to know basis of the education system, but that set is.

relativity and quantumness in electromagnetic fields, gravatars, tesla's writings on the 'death ray' and his energy transmission through the natural media patents, boron proton fusion with polodial plasma vortex, and yes the talk of US blackops ufo's

Anonymous

Anonymous Thu 11 Jun 2020 23:57:53 No.11787590 Report

Quoted By:

>>11787230
The superconductor expels magnetic fields, that's why putting a superconducting ring traps field lines going through the center. It's called the Meissner effect. Explaining that you are talking about a superconductor that expels magnetic fields rather than a ferromagnet that amplifies them also helps the person I was replying to understand why the effective current was flowing in the opposite way

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