As for the math and the physics involved, I think that the reason of our disagreement is mostly about description of reality, let me explain, we have two ways:
i) Using Classical Electrodynamics up to its limit of validity, when it abandon us we can use some concepts from Quantum Mechanics, e.g. to explain magnetic permeability of ferromagnetic materials, quantum vacuum, etc.
ii) Using Quantum Electrodynamics.
As this is an audio forum, ii) is out of the table, except perhaps for some little details.
Assuming that we have a continuous medium of magnetic permeability μ >>1, is valid the approximation
(1/ μeff) ≈ ( l + lG μ ) / l μ ≈ (1/μ) + (lG / l) ≈ (lG / l)
Sorry, but I don’t see any distributed gap within the material, because it is a continuous medium; remind you that the idea to define μeff is for an equivalent ungapped core with a continuous magnetic field H that follows the constitutive relation
B = μeff H
In other words, if you like to continue talking about the nothing, you must abandon the idea of a discrete medium, otherwise I invite you to re-write the equations using QED.
Rats! More homework! 🙄
From Maxwell’s equations, the normal component of the electric field D at the interphase has a discontinuity
(D1 – D2) . n = 4 π σ
All charges into the capacitor are due to polarization, so no free charge, then
(D1 – D2) . n = 0
∇ x E = 0
E = - ∇φ
E = V / d
Then
E1 = V1 / d1 and E2 = V2 / d2
So we must solve
ε1 E1 – ε2 E2 = 0
E1 (d – d2) + E2 d2 = V
E1 = V / { d + d2 [(ε1/ε2) – 1]}
Now we can define an effective permittivity εeff, such that
ε1 E1 = ε2 E2 = εeff E
εeff = d ε1 / { d + d2 [(ε1/ ε2) – 1]}
Exactly the same form as the magnetic case as you predicted. Happy? 😀
Again, the idea to define εeff is for an equivalent ungapped dielectric with a continuous electric field E into a continuous media, that follows the constitutive relation
D = εeff E
And 1/εeff has nothing to do with the gap length distributed within the material.
No, for inductors/transformers, the energy will reach a maximum above which the losses due to the fringe field are more important, and energy begins to loose.
Yes, bingo! Two conducting parallel plane plates separated by a small distance d, divide the quantum vacuum, such that outside the plates, the possible harmonic oscillators are infinite and they can reach any λ, nevertheless, inside the plates, λ can reaches only the values d, d/2, d/3,…,d/n ; which are also infinite, but as rayma pointed out on post#1138 it is a different kind of infinite, and as a result, inside the plates there is a lower energy density, then it can store more energy.
Do you see? Your own assertion can only be explained with the concept of quantum vacuum, if you had "nothing" into the plates, things would be the other way round.
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Distributed gaps won't necessarily present external fringe. Why powdered
cores continue to be favored in some applications. And in gapped ferrites
with an obvious external fringing field: Remains lossless until it fringes
through an area of low resistivity (like a winding) able to support eddy
current. Though I suppose you could make for the extreme case of a
bar antenna, and declare purposeful radiation to be a fringe loss...
Permeability would be infinite without intrinsic distributed gaps. No such
solid materials exist, unless you live in a neutron star. Even then, doubt
the intrinsic gap goes away completely. Though a more significant huge
external gap completes the path outside...
Then again, why would a neutron anything present a magnetizing force?
And why are ferromagnetic materials able to exclude gap from the volume
they fill anyway?
cores continue to be favored in some applications. And in gapped ferrites
with an obvious external fringing field: Remains lossless until it fringes
through an area of low resistivity (like a winding) able to support eddy
current. Though I suppose you could make for the extreme case of a
bar antenna, and declare purposeful radiation to be a fringe loss...
Permeability would be infinite without intrinsic distributed gaps. No such
solid materials exist, unless you live in a neutron star. Even then, doubt
the intrinsic gap goes away completely. Though a more significant huge
external gap completes the path outside...
Then again, why would a neutron anything present a magnetizing force?
And why are ferromagnetic materials able to exclude gap from the volume
they fill anyway?
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By exclude gap, I could be asking exclude or short circuit quantum vacuum?
But then I have to ask why many solid materials that occupy space, certainly
for purpose of inductors, don't exclude this property at all?
My point about NOTHING has always been that it doesn't act like nothing.
Stop agreeing with me on that point. Making me go nutz. A short trip...
But then I have to ask why many solid materials that occupy space, certainly
for purpose of inductors, don't exclude this property at all?
My point about NOTHING has always been that it doesn't act like nothing.
Stop agreeing with me on that point. Making me go nutz. A short trip...
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I found this, and then immediately wished I hadn't:
http://www.oxfordneutronschool.org/2011/lectures/ARW_magnetism_Lecture_handouts.pdf
http://www.oxfordneutronschool.org/2011/lectures/ARW_magnetism_Lecture_handouts.pdf
Please don't twist my words, that I said is that a gap produce fringing fields, in fact, at the interface between the magnetic material and the gap, the tangential component of magnetic field B has a jump and it causes the fringing field.
Indeed, the way to reduce it is with a distributed gap, as you say.
As I said before
Even more, the Bohr–van Leeuwen theorem proves that magnetism is a quantum mechanical effect; it cannot occur in purely classical solids because electrons in a material do not interact with an applied magnetic field.
In other words, it has nothing to do with “intrinsic distributed gaps”
So far your assertion hasn't any support, nor from you, neither from any book or link.
I did my homework, and I hope you will do yours.
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We don't need a book or link to be correct in observing that "solids" are not solid.
And that the storage of magnetic or electric energy is a property of empty space.
Not a property of materials that facilitate a partial short-cut through empty space
within their volume. Electrical conductors, dielectrics, long-range ordered spins,
whatever. Your own math should have revealed to you the truth of this by now.
Fields: Much ado about nothing...
And that the storage of magnetic or electric energy is a property of empty space.
Not a property of materials that facilitate a partial short-cut through empty space
within their volume. Electrical conductors, dielectrics, long-range ordered spins,
whatever. Your own math should have revealed to you the truth of this by now.
Fields: Much ado about nothing...
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Since it appears that energy can only be stored in fields, I have to ask about
the one other thing that stores energy, matter. Is matter a field? I mean like,
is all that e=mc^2 stuff maybe the same energy as the pull of gravity exerted
against the whole universe?
And then matter might be moving (though thats relative), storing even more
energy. But is movement another field to store energy, or just more mass?
Or is mass (perhaps like spin) actually movement in some perpendicular or
toroidal direction we can't perceive? And then, is movement (to include the
part we don't see, perhaps relative universe average) the true field we
observe as gravity?
Photons exert a gravitaional pull without mass, but they do move...
I'm way outside my depth on this one. Feel free to shoot it down.
the one other thing that stores energy, matter. Is matter a field? I mean like,
is all that e=mc^2 stuff maybe the same energy as the pull of gravity exerted
against the whole universe?
And then matter might be moving (though thats relative), storing even more
energy. But is movement another field to store energy, or just more mass?
Or is mass (perhaps like spin) actually movement in some perpendicular or
toroidal direction we can't perceive? And then, is movement (to include the
part we don't see, perhaps relative universe average) the true field we
observe as gravity?
Photons exert a gravitaional pull without mass, but they do move...
I'm way outside my depth on this one. Feel free to shoot it down.
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Nevermind toroidal like spin. Would have observable polarizing consequences...
Lets just go with perpendicular motion (plus the part we can see), and shoot
that down.
Lets just go with perpendicular motion (plus the part we can see), and shoot
that down.
Much Ado About Nothing - The Nature of Reality
Apparently I'm not the first to abuse this phase to describe physics.
Apparently I'm not the first to abuse this phase to describe physics.
Agree.
Gedankenexperiment
Let's consider a diamagnetic material, 0<μ<1 with an external magnetic field B, in vacuum.
We must remember that energy density is given by
w = B²/ 8πμ
Then, into the vacuum is
w(vacuum) = B²/ 8π
w(diamagnetic) = B²/ 8πμ
w(diamagnetic) > w(vacuum)
In Quantum Mechanics, matter is a quantum field.
Diamagnetism in the form of large eddy currents probably doesn't count
except in the special case of a superconductor. But if room temp atoms
can be tricked to dance individual lossless orbital eddies. Then you might
have exception for storing a little more energy. In either case, there will
be a saturation limit. Beyond which, permeability strangely rises to 1.
I would call this "Agree"
---
Of course, flux would tend to just go around unless it has no other path.
You would practically have to pot the coil in the diamagnetic whatever.
except in the special case of a superconductor. But if room temp atoms
can be tricked to dance individual lossless orbital eddies. Then you might
have exception for storing a little more energy. In either case, there will
be a saturation limit. Beyond which, permeability strangely rises to 1.
I would call this "Agree"
---
Of course, flux would tend to just go around unless it has no other path.
You would practically have to pot the coil in the diamagnetic whatever.
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All materials are diamagnetic to a greater or lesser degree, then, we can choose the material to avoid complications with eddy currents in conductors or superconductors (plus Meissner effect), this is a thought experiment after all.
Me too.
October 1st, 2014, today. ...Is the universe expanding? ...And if so, to what?
Is man's brain part of the universe? ...And if so, is it also expanding? ...Or depleting?
...And to what?
Is man's brain part of the universe? ...And if so, is it also expanding? ...Or depleting?
...And to what?
To answer your questions:
- apparently, yes
- don't know, for it's current shape is unknown
- yes
- depends on the substance you're using..
- only if you suffer from Alzheimer's or if you have a hole in your skull 😛
I stopped doing drugs and drinking, heavily, years ago. Some of my poorest friends...are ex-heroinomane junkies.
Went to see my doctor yesterday; my heart is enlarged. ...It has expanded.
* This is a personal/medical issue; not to be expanded outside this thread.
Thank you for your cooperation.
Went to see my doctor yesterday; my heart is enlarged. ...It has expanded.
* This is a personal/medical issue; not to be expanded outside this thread.
Thank you for your cooperation.
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High pressure. Ambulance came last week, again. My blood is ok though, but my heart rate is a little high. Have to be monitored, and better life equilibrium.
And yes, my heart is enlarged. Other stuff too, like too much sex; I have to slow down.
Frank, the universe is truly expanding, and the world population as well.
Everything is just normal, following the natural flow of time and space.
And the humanity is becoming more and more robotic.
The world is larger than ourselves. And the universe is only a small part of the multiverse. And jazz is only one music genre.
All in all we all going to die soon or later, so might as well enjoy the little time we have on this planet, and get along with everyone else, no matter what our differences are and ages and experience and bank account sizes and what kind of audio gear and loudspeakers and all that blues.
Someday my princess will come.
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