Any physicists on the boards?

deludedgod
Rational VIP!ScientistDeluded God
deludedgod's picture
Posts: 3221
Joined: 2007-01-28
User is offlineOffline
Any physicists on the boards?

I’m trying to explain to a friend of mine the concept of electric displacement vector fields (D-fields) and magnetic intensity fields (H-fields). I’m so used to using them that I haven’t really thought of the conceptual definition for so long, but I guess it’s quite tricky to grasp because unlike electric, magnetic, polarization and magnetization fields, D and H do not have immediately clear physical meanings. We only introduce them to take bound charge and current respectively into account.

That’s why I’ve been finding it difficult to articulate in words precisely what D and H are. See what you think:

D, or the electric displacement field takes into account the fact that within a dielectric media, an electric field will induce a polarization density (P). The induced electric dipoles will tend to create a field which opposes the field that created them, thus reducing the density of electrostatic lines of flux that permeate the region of space in question. The source of these opposing fields are referred to as bound charges. The degree to which a dielectric media will reduce electrostatic flux lines is measured by its permittivity. Usually, however, instead of referring to absolute permittivity of a dielectric media, we refer to the relative permittivity. That is, the permittivity of the media as a ratio to that of a vacuum. Now consider an isotropic dielectric media as the simplest case. In such a case, there will be uniform density, hence the divergence of polarization will be zero. In this case, there is no net bound charge density and so the electric field is uniformly reduced by a factor of epsilon throughout the field due to the polarization. In this case, it is helpful to think of the electric displacement field as the “electric intensity”. In other words, it is directly related to the density of electrostatic flux lines that would be produced if the dielectric media was gone. The direct relation is a universal constant, the vacuum permittivity. Because of this, D and E do not have the same units.

You can use a variation of this line of thought in anisotropic media as well. If we have a field of non-uniform density, there will be a net divergence and hence a net bound charge. Because of this, the electric field is reduced by different factors in different regions. Since the divergence of P is a function of which is independent of the electric field, the polarization field is not a scalar multiple of E (in an isotropic media, it is, and the multiple is called electric susceptibility). Because of this, the only thing that makes physical sense is for epsilon to be a second rank tensor, which it is. However, in these cases, even though epsilon is a function of position, the same ratio still holds. Examining an infinitesimal volume with dielectric media (which, in the limit of volume, we assume is isotropic over that volume) we find that the field is still reduced by the same factor (epsilon). Everywhere in the field, D characterizes the intensity of the field by effectively removing the dissipation of flux lines by the media as a factor. This is useful because it means we can separate the effects of bound and free charges in producing electric fields in dielectric media. This only holds up to a point because as the electric field through a dielectric approaches the break-down point, the polarization no longer varies linearly with the electric field, and once it reaches break-down, the whole concept of a dielectric becomes meaningless anyway, but supposing that E is much less than the breakdown strength, you should be fine.

In magnetic fields, the same principle holds for the H field, but unfortunately, it can get much more complicated. In a manner analogous to bound and free charges producing fields, in magnetic materials, we can consider the loops of current due to electrons orbiting the nucleus as creating small permanent dipoles. It is helpful for you to think of the magnetization density field as a vector field whose vectors point in the direction of the generated south pole at that point from an orthogonal loop of current. It is a relatively simple exercise to demonstrate that the magnetization current (the bound current resulting from orbital motion) is the curl of the magnetization field. In other words, there will be no bound current in an isotropic magnetic media. This is exactly analogous to electric polarization density, which only generates bound charge in anisotropic media.

Please note that in most materials, there is no magnetism associated with the electron spin because of Pauli exclusion. With filled subshells, such materials have exactly zero net magnetic moment. We will consider paramagnetism and diamagnetism first, before ferromagnetism (which is more complicated). In general, the existence of magnetic domains in magnetizable materials will have the same effect as dielectric media responding to electric fields. Depending on electron arrangement, the media can either reinforce (paramagnetize) or reduce (diamagnetize) the applied field. Please note that because of Lenz’s Law, all materials will diamagnetize to some extent, including those that non-physicists think of as non-magnetic. Materials with unfilled shells will paramagnetize due to net moment. They will also diamagnetize, but paramagnetization is nearly always much stronger than diamagnetization, and overpowers it. In these materials, there is a relatively simple relationship between the magnetic field strength we permeate a material with and the degree to which they respond. A relatively simple way to understand this is to consider the magnetization density field (M) as denoting the relative dipole strength in a region. The net dipoles will align with the magnetic field and strengthen it by increasing the total flux density through the material.

For some materials, the response will be to reduce the field, and for others it will be to strengthen it, but in either case there is a constant linking the degree to which a field will be changed, and that is the relative permeability. For isotropic paramagnetic media, the number of dipoles aligned with the material is directly proportional to the flux density of the field that goes through it. Obviously, for a diamagnetizing response, this will be <1 (the material will retard the permeation of B), and for a paramagnetizing response, it will be >1 (the material will increase the permeation of B). In any case, just as with the D-field, we can in these cases view H as a “magnetic intensity” field. It is directly related to the magnetic field strength that would exist if the media was not there (the direct relation is the vacuum permeability, so H does not have teh same units as D). In these cases, it is helpful to think of B as the flux density through a region and therefore as a function of H. This is useful for engineering problems but is not advisable when studying electromagnetism in physics because in actuality, B is a more fundamental quantity than H. Of course, if the media is anistropic, than the permeability constant will be replaced by a rank 2 tensor, but the same relationship still holds. Remember that because of Stokes’ Theorem, the total bound current due to a uniform magnetization field will be equal to the line integral around the surface of the material.

 It might be visually helpful to consider the anisotropic media is being divided into infinitesimal blocks of isotropic media to represent a variable density field hence a variable magnetization field. In these cases, we can consider the magnetic intensity (H) as an independent quantity and the flux density (B) as a function of the intensity and depending on the media it permeates. But if we examine each individual little isotropic volume, we still find that B is related to H by this tensor which directly measures the degree to which the region will strengthen or weaken the field. Please note that permeability does not have to be either a constant or a tensor. It could be a non-constant scalar function of position. This will occur if a variable within a media does not alter the direction of the field lines through it but does alter it with varying intensity.

What makes magnetism more complicated than general electric materials is the property of ferromagnetism. Ferromagnetism is helpful in terms of understanding the H-field because ferromagnetic materials exhibit hysteresis. That is, the domains do not necessarily release once the magnetic field through them is released. So, we can increase the magnetic intensity through a ferromagnetic  material (H) and observe the resulting flux density through the material (B). This is where the quantity H becomes very useful because the magnetic field within a ferromagnetic material has no simple relationship with the magnetizing force. This is because the domains can align with each other and not just external fields and have a tendency to become stuck together, a tendency which varies with density, temperature, humidity, etc. That is why the magnetization of ferromagnets is in general, quite complicated. The hysteresis loop is useful here because it enables us to quickly grasp properties of the material we are magnetizing. If we apply a certain magnetizing force to a thoroughly demagnetized ferromagnet, then we will get a curve where the flux density increases with H. This is not linear because the increase in dipole alignment starts to slow down with increase in magnetizing force until it reaches the magnetic saturation. At this point there is no way to channel more magnetic flux through a material because all the dipoles are aligned with the field. If we start to ramp down the magnetic intensity to zero, the material will still have a flux through it because the domains have become permanently aligned. The amount of flux left in the material at the point where the intensity has been ramped down to zero is called the magnetic retentance and is a useful measure of permanent magnetization. In order to force the aligned dipoles to demagnetize, we must switch the direction of magnetic intensity until we reach a flux of zero. The magnetic intensity at this point is called the coercivity and is a useful measure of how strong a field we have to put through a magnet to demagnetize it.

If we continue to intensify H in the other direction past the coercivity point then we will reach a point of magnetic saturation again. This is equal and opposite to that in the other direction, and as we take the magnetic intensity to zero, we should find the flux to be equal and opposite to the coercivity.

I hope this helps.

 

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

Books about atheism


BobSpence
High Level DonorRational VIP!ScientistWebsite Admin
BobSpence's picture
Posts: 5939
Joined: 2006-02-14
User is offlineOffline
Hmm, I have an Electrical

Hmm, I have an Electrical Engineering degree from one of our local Universities (Univerity of Queenslant, St Lucia), so I do have a feel for the topic.

I haven't got time at the moment for a detailed discussion, and I might need a little time to refresh myself on some of the details, but let me briefly describe how I understand these terms.

The electric field is expressed in volts/meter, and the resultant 'displacement field' also called 'electric flux density' can be expressed as coulombs/meter^2, IOW electric charge density on a surface, either a 'real' surface such as a metal electrode or a notional surface intersecting an electric field. So if I apply a certain voltage across a parallel plate capacitor, that voltage, together with the physical separation of the plates, define the E in the air space between the plates. The charge density 'induced' on the plates will correspond to B. The effect of dielectric material gets more complicated.

Similarly with magnetic fields H is the 'magnetizing' field, in ampere/meter, which may be directly a function of an electric current flowing in a wire and the geometry of the current path. The magnetic flux density B is a function of H and the magnetic properties of the material occupying the space influenced by field H.

In each case, I think of E and H as the driving 'force', and D and B are measures of the effect of those applied 'forces'.

Anyway, have to go now.

 

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

From the sublime to the ridiculous: Science -> Philosophy -> Theology


deludedgod
Rational VIP!ScientistDeluded God
deludedgod's picture
Posts: 3221
Joined: 2007-01-28
User is offlineOffline
Thanks. That's how I would

Thanks. That's how I would articulate it.

Quote:

In each case, I think of E and H as the driving 'force', and D and B are measures of the effect of those applied 'forces'.

Wait. You mean D and H as the driving forces and E and B as the effects.

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

Books about atheism


BobSpence
High Level DonorRational VIP!ScientistWebsite Admin
BobSpence's picture
Posts: 5939
Joined: 2006-02-14
User is offlineOffline
deludedgod wrote:Thanks.

deludedgod wrote:

Thanks. That's how I would articulate it.

Quote:

In each case, I think of E and H as the driving 'force', and D and B are measures of the effect of those applied 'forces'.

Wait. You mean D and H as the driving forces and E and B as the effects.

Well, I think of applying a voltage across something, which defines a field which drives charge to move and manifest as a electric current, or accumulate as complementary charge on opposite plates of a capacitor. Most electrical circuits are designed to be driven from a source of more-or-less constant voltage, so my Elec. Engineering background leads me to think of it this way.

I can imagine a current-driven circuit, which injects a flow of charge into the wires, but I still think of a field E (Volt/m) driving charge, which maps to D (Coulomb/m^2).

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

From the sublime to the ridiculous: Science -> Philosophy -> Theology


deludedgod
Rational VIP!ScientistDeluded God
deludedgod's picture
Posts: 3221
Joined: 2007-01-28
User is offlineOffline
Since my background is

Since my background is physics, not engineering, I tend to think of D and H as related to the total field minus the effect of polarization and magnetization respectively. If the problem occurs solely in a vacuum, then D and H no longer become useful quantities. Likewise, if we are dealing with conducting media, then we never use D because conducting media don't create polarization density fields. They are only useful in the context of magnetizable and dielectric media.

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

Books about atheism


Answers in Gene...
High Level Donor
Answers in Gene Simmons's picture
Posts: 4214
Joined: 2008-11-11
User is offlineOffline
Hey DG, if your friend

Hey DG, if your friend is not following your explanation, perhaps that comes from him not having quite as much background as you are crediting to him.  In that case, you would probably want to go back to something more basic for a warm-up.  Knowing how far back to go is something that only you can determine but even so, perhaps he is missing part of your explanations because he does not already have a more fundamental model fully internalized.

Honestly though, what material which I have written on this subject has been more for the pop-sci crowd and I have to assume that they usually know next to nothing. So my material tends to be much more basic than where you are going with your friend.

 

So one way that I tend to start people is with fluid dynamics. Everyone knows about the standard rubber balloon and a balloon with a knot tied in can be likened to a battery sitting on a table. If they can handle the concept of the air pressure in a balloon, they they basically already have a handle on the voltage in the battery, they just needed someone to provide the model for them to make the connection.

 

Obviously, your friend is past that level but if you can determine what he does need to get to the point where he can follow what you wrote up above, then you should have no problem after that.

NoMoreCrazyPeople wrote:
Never ever did I say enything about free, I said "free."

=


BobSpence
High Level DonorRational VIP!ScientistWebsite Admin
BobSpence's picture
Posts: 5939
Joined: 2006-02-14
User is offlineOffline
I can understand H as the

I can understand H as the 'magnetizing' field which I see it is sometimes labelled as. It makes sense to me for B as the fundamental field, particularly since it defines things like the force experienced by a charge moving thru a magnetic field, without involving 'permeability' which describes the reaction of a material to an applied magnetizing field H.

Similarly, E seems to be the fundamental in the same way in defining force on a charge.

I think of force, velocity, charge, as the fundamentals, with permeability and permittivity as properties of the medium. So on that basis, yes, E and B are the 'fundamental' fields, D and H are the driving fields, directly related to charge and charge flow (current) respectively.

 

 

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

From the sublime to the ridiculous: Science -> Philosophy -> Theology


deludedgod
Rational VIP!ScientistDeluded God
deludedgod's picture
Posts: 3221
Joined: 2007-01-28
User is offlineOffline
I am confident that he will

I am confident that he will follow it. Strictly speaking, he already knows exactly what D and H are. It takes only fundamental knowledge of vector calculus and field equations to derive them mathematically from the physical descriptions of E,B,P and M (which are easy to understand since they have precise physical meanings). The tricky thing with D and H is that many students of physics, especially in electromagnetism, like being able to visualize their mathematical results, and D and H don't really have clear physical meaning (by "clear physical meaning" I mean an exact statement of the quantity being measured. E, for example is the "force per unit charge" and P is the "electric moment per unit volume" ) so it's hard to visualize them. The next best thing is to be able to articulate what they are in words. That was the nature of the request.

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

Books about atheism


HisWillness
atheistRational VIP!
HisWillness's picture
Posts: 4100
Joined: 2008-02-21
User is offlineOffline
deludedgod wrote:The next

deludedgod wrote:

The next best thing is to be able to articulate what they are in words. That was the nature of the request.

It's funny - I took electromagnetics in second year (brutal course!) and I was absolutely stumped when I read your post. I don't think I've ever really thought of the concepts outside of the math, other than the obvious mechanical ones. I would have been stuck for an answer myself.

Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence


Eloise
TheistBronze Member
Eloise's picture
Posts: 1808
Joined: 2007-05-26
User is offlineOffline
deludedgod wrote:I&rsquo;m

deludedgod wrote:

I’m trying to explain to a friend of mine the concept of electric displacement vector fields (D-fields) and magnetic intensity fields (H-fields). I’m so used to using them that I haven’t really thought of the conceptual definition for so long, but I guess it’s quite tricky to grasp because unlike electric, magnetic, polarization and magnetization fields, D and H do not have immediately clear physical meanings. We only introduce them to take bound charge and current respectively into account.

That’s why I’ve been finding it difficult to articulate in words precisely what D and H are. See what you think:


 

I think you've made it too perfect, DG, what your friend is most likely looking for is buried in a list of rule exceptions.

 

I would start with just one definition and then smooth and straighten any misconceptions afterwards. For example.

D= eps0 + P

where eps0 is the permittivity of free space  and P is the polarisation of the medium.

Permittivity of free space is basically how much current will flow through the space external to your dielectric surface. On the dielectric surface the charge is polarised, I like to think of this as though the charge were coiling up like a spring in each unit of surface on the medium -- this reflects the dielectric medium's capacity for storing electrostatic charge.  So the displacement field then is a measure of the current coiled up in the medium plus the free space and this is all expressed as an amount per unit of area.

What I think is difficult about the physical meaning is that the electric displacement field is defined to be on the surface of the media, easily enough imagined, but then surface is defined as the sum of two spaces that are never conceived of oustide of physics.  Where we normally think of a surface in the abstract sense that is reflected by basic euclidean geometry, and take it for granted that this is a precise and accurate definition of a surface it is actually Maxwell's vortices that are more like reality.

So then the basic interpretation of D is that a current on a dielectric surface is spread out over these  two "spaces" and there is D much current in a unit area of atoms in a free space. This can correspond directly to E but doesn't necessarily do so.

Theist badge qualifier : Gnostic/Philosophical Panentheist

www.mathematicianspictures.com


deludedgod
Rational VIP!ScientistDeluded God
deludedgod's picture
Posts: 3221
Joined: 2007-01-28
User is offlineOffline
Quote:D= eps0 + PWait. You

Quote:

D= eps0 + P

Wait. You mean:

D=E(eps0)+P

 

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

Books about atheism


Eloise
TheistBronze Member
Eloise's picture
Posts: 1808
Joined: 2007-05-26
User is offlineOffline
deludedgod wrote:Quote:D=

deludedgod wrote:

Quote:

D= eps0 + P

Wait. You mean:

D=E(eps0)+P

 

Ugh, Yeah, oops.

Theist badge qualifier : Gnostic/Philosophical Panentheist

www.mathematicianspictures.com


Eloise
TheistBronze Member
Eloise's picture
Posts: 1808
Joined: 2007-05-26
User is offlineOffline
Feel free to disagree with

Feel free to disagree with me, DG. I mean, a lot of people don't consider electric displacement to have any actual physical correspondence at all, and almost everyone would equate saying reality corresponds to the vortices in Maxwell's Lines of force with resurrecting aether.

Basically, I've said something really controversial and all I get in return is silence?

Theist badge qualifier : Gnostic/Philosophical Panentheist

www.mathematicianspictures.com


BobSpence
High Level DonorRational VIP!ScientistWebsite Admin
BobSpence's picture
Posts: 5939
Joined: 2006-02-14
User is offlineOffline
I think the 'P' there refers

I think the 'P' there refers to the surface charge, not current, equivalent to the P(olarization) of the dielectric material.

J is for current.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

From the sublime to the ridiculous: Science -> Philosophy -> Theology


Eloise
TheistBronze Member
Eloise's picture
Posts: 1808
Joined: 2007-05-26
User is offlineOffline
BobSpence1 wrote:I think the

BobSpence1 wrote:

I think the 'P' there refers to the surface charge, not current, equivalent to the P(olarization) of the dielectric material.

J is for current.

This is why you clear up the misconceptions afterward. Keeping a tight rein on how you use every unit you mention comprimises the consistency of the visual that you are building of the concept, and you get perfectly precise but unenvisionable reams of text. You could try saying the same thing while picking out all the nits, but then you'd have the same problem DG is having.  Or you can just accept that all our conceptualisations are flawed, but still useful.

 

Theist badge qualifier : Gnostic/Philosophical Panentheist

www.mathematicianspictures.com


deludedgod
Rational VIP!ScientistDeluded God
deludedgod's picture
Posts: 3221
Joined: 2007-01-28
User is offlineOffline
Normal 0

I would agree that D doesn’t have any physical meaning. That’s why this is quite difficult to articulate. The term “displacement current” doesn’t mean anything either and is a throwback to the fact that Maxwell’s idea of light as stresses in the ether was incorrect. Even though D doesn’t have a physical meaning the way E, B, M and P do, it does measure something. Purely from a mathematical standpoint, D has a direct relationship, at any point in space, between the “real field, (in other words, E is the real physical thing that you can measure) and D corresponds to the “intensity” of the field that is directly related to the field independent of the media (which E is not). This is kind of obvious when we think about it, since:

D=εij·(ε0E)

Here, εij maps out a second rank tensor field whose components correspond to the degree and direction in which P retards E, which is not a scalar multiple of E provided that the media is anisotropic. Mathematically, you should understand why we need to use a tensor field and not a scalar which varies with position but don't bother trying to visualize it. The effects of ranks greater than 1 (vectors) are impossible to picture in your head.

And yes, to be absolutely clear, P is the polarization density of the material. For an isotropic media, by Gauss’ Theorem, this will be equivalent to the surface charge density on the boundary of the material (in accordance with the boundary conditions on D).

PS This discussion is purely in the context of classical electromagnetism

 

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

Books about atheism


BobSpence
High Level DonorRational VIP!ScientistWebsite Admin
BobSpence's picture
Posts: 5939
Joined: 2006-02-14
User is offlineOffline
Eloise, I must confess I

Eloise, I must confess I find your explanations much harder to understand than DG's....

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

From the sublime to the ridiculous: Science -> Philosophy -> Theology


deludedgod
Rational VIP!ScientistDeluded God
deludedgod's picture
Posts: 3221
Joined: 2007-01-28
User is offlineOffline
Hey, thanks.Ferromagnetics

Hey, thanks.

Ferromagnetics really hammer this point home. In transformer design, for example, one must consider how much flux one can channel per magnetizing force applied externally. In other materials, this situation is easy because the two have a direct relationship. For a ferromagnetic, we will want the hysteresis loop to be quite small (because when you play with the mathematics for long enough, you realize that the integral of the dot product of B and H corresponds to the energy of the magnetization cycle). If it takes a lot of magnetic energy to coerce or retain or saturate the material, then it doesn't channel flux very efficiently. What makes this important? Well, the B-field cannot distinguish sources of magnetic field. It is a completely superposable vector field which adds the external magnetic field with those of all the dipoles that are aligned in the material. What H does is remove the consideration of the M-field. This is very useful when designing transformers because the important thing is how much magnetic energy we have to put in the first place to channel flux. Measuring B doesn't actually tell us this because B doesn't distinguish external and internal magnetic fields.

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

Books about atheism