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Difference between magnetic field strength and flux density?

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1. What is the difference and why does a constant separate them?
2. Anyone?
3. Flux density is directly proportional to mag field strength. I don't think you'll ever get a question asking you the difference between the two
Flux density is directly proportional to mag field strength. I don't think you'll ever get a question asking you the difference between the two
They do at university.
5. (Original post by JokesOnYoo)
They do at university.
6. (Original post by JokesOnYoo)

What is the difference and why does a constant separate them?
H is the auxillary field, B is the magnetic field. It plays a similar role in magnetostatics as the D (the electric displacement field) does in electrostatics.
I would urge you not to call them magnetic field strength and magnetic flux density.

is the free current passing through the loop
7. (Original post by langlitz)
H is the auxillary field, B is the magnetic field. It plays a similar role in magnetostatics as the D (the electric displacement field) does in electrostatics.
I would urge you not to call them magnetic field strength and magnetic flux density.

is the free current passing through the loop
Do you have a degree in Electrical engineering?
8. (Original post by JokesOnYoo)
Do you have a degree in Electrical engineering?
No I'm doing juniour honours electromagnetism this semester though
9. (Original post by langlitz)
H is the auxillary field, B is the magnetic field. It plays a similar role in magnetostatics as the D (the electric displacement field) does in electrostatics.
I would urge you not to call them magnetic field strength and magnetic flux density.

is the free current passing through the loop
Allow me to add a nice reference for those who are interested in the "origin of this confusion". Have a look at an article in AJP - B and H , the intensity vectors of magnetism written by John J. Roche
10. (Original post by JokesOnYoo)

What is the difference and why does a constant separate them?
Here, is the magnetic field due to a magnetic material, like a bit of iron, or some other material that can be magnetised - it's just the usual quantity that causes magnetic effects.

We're imagining a bit of iron sitting in the B field of a wire, and measuring the total B field near to (or inside of) the bit of iron. There are two components to the total B field:

1. The first field is just that of the B field of the wire as given by the Biot-Savart law. We can write this as:

is proportional to the current in the wire.

2. The second field is due to the magnetism arising from the action of 1. on the iron. We can have different effects here (ferro-, para-, dia- magnetism), and this generated field can either point in the same direction as (ferro-, para-) or in the opposite direction (dia-). So it can either increase or decrease the total field. We can write this as:

where is called the magnetisation. Loosely, is proportional to "currents" caused by the atoms of the material. (Quantum mechanics and intrinsic and orbital angular momentum are your friends, if you want the details - I can't remember them too well at the moment).

So we have:

It turns out that for many materials. So we can bundle the RHS up into a single quantity:

where . That's the quantity that they've given you, but as you can see it hides some details of the magnetisation of the material.

Essentially, is the proportionality constant that turns into , and is the proportionality constant that strengthens (or weakens) by the correct factor to account for the fact the some materials produce their own magnetic field when stuck in the B field of a wire.
11. (Original post by Eimmanuel)
Allow me to add a nice reference for those who are interested in the "origin of this confusion". Have a look at an article in AJP - B and H , the intensity vectors of magnetism written by John J. Roche
Thanks. That looks pretty interesting (well, you know, interesting for people like me...).
12. (Original post by langlitz)
H is the auxillary field, B is the magnetic field.
...
I would urge you not to call them magnetic field strength and magnetic flux density.
Why? These are pretty standard terms, so you need to know what they refer to.
13. (Original post by atsruser)
Why? These are pretty standard terms, so you need to know what they refer to.
It's an absurd name for them. B is the fundamental quantity so why not just call it the magnetic field?
14. (Original post by langlitz)
It's an absurd name for them. B is the fundamental quantity so why not just call it the magnetic field?
It's not clear to me why you call B the fundamental quantity - what is your definition of fundamental?

The reason that it's a good idea to learn the standard names is that it allows you to read all of the many, many books that use those names - there may be better names that could have been chosen, but you've got to learn the meaning of the ones that are already in use.
15. (Original post by atsruser)
It's not clear to me why you call B the fundamental quantity - what is your definition of fundamental?

The reason that it's a good idea to learn the standard names is that it allows you to read all of the many, many books that use those names - there may be better names that could have been chosen, but you've got to learn the meaning of the ones that are already in use.
"Many authors call H, not B, the "magnetic field". They then have to invent a new word for B: the "flux density" or magnetic "induction" (an absurd choice, since that term already has at least two other meanings in electrodynamics). Anyway, B is indisputably the fundamental quantity, so I shall continue to call it the "magnetic field," as everyone does in the spoken language. H has no sensible name, just call it "H"." Griffiths - Introduction to Electrodynamics

"The unhappy term "magnetic field" for H should be avoided as far as possible. It seems to us that this term has led into error none less than Maxwell himself..." Sommerfeld - Electrodynamics
16. (Original post by JokesOnYoo)

What is the difference and why does a constant separate them?
17. (Original post by langlitz)
"Many authors call H, not B, the "magnetic field". They then have to invent a new word for B: the "flux density" or magnetic "induction" (an absurd choice, since that term already has at least two other meanings in electrodynamics). Anyway, B is indisputably the fundamental quantity, so I shall continue to call it the "magnetic field," as everyone does in the spoken language. H has no sensible name, just call it "H"." Griffiths - Introduction to Electrodynamics

"The unhappy term "magnetic field" for H should be avoided as far as possible. It seems to us that this term has led into error none less than Maxwell himself..." Sommerfeld - Electrodynamics
I'm not finding these quotes any more convincing than your assertion, given that neither of them justifies their position. Until you tell me what you mean by one physical quantity being more "fundamental" than another, I have no idea on what basis you're deciding that B is fundamental than H.

I can think myself of a possible meaning: let's say that quantity P is more fundamental than quantity Q if there are some physical predictions than can be made using P that can't be made using Q. Now with that definition, I can't see that either plays the "fundamental" role - there's no physics that we can get out of B that we can't get out of H, in free space at least, since they only differ by a scale factor.

And we could also argue (some books do) that H is more fundamental than B since it depends only on the current in the wire, and the wire geometry, and not on the material in which we're measuring B, and thus H is the "cause" of B. I'm not sure how widespread this point of view is, however - I guess it's an engineering line of argument, rather than a physicist's.

And, of course, there's an argument that B isn't the "fundamental" magnetic field at all: a better contender for that is A, the vector potential, since it predicts physics that B doesn't (Aharonov-Bohm effect), and is used to construct Lagrangians and Hamiltonians with a magnetic component.

But none of this is worth much without knowing what definition you are using for the "fundamentalness" of a physical quantity. Without knowing that, it's impossible to say if you've got a sensible argument or not. (And on another note, I repeat the point that you still have to read books and speak to people who already use the terms that you dislike - you've got to learn to live with them.)

[edit: and of course, maybe we should say that E is the fundamental field, since we can always Lorentz-transform it into B ...]
18. (Original post by Neurology)
roger

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