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I need some help in understanding the relationship between

**B**and

**H**fields and their "physical" meaning (helps me visualize problems). I'll try to be as clear as possible about my current knowledge and my questions:

- "Fields" do not exist, they are just a mathematical parametrization of the Force (or any) vector generated by a certain body at a point in space and time. For instance, if the force between two (punctual) charges is:

[itex]\vec{F} = \frac{q_1 q_2 \vec{r_{1,2}}}{|\vec{r_{1,2}}|^3}[/itex]

then we can define a__mathematical__relationship F/q2 that we call "Field" (in this case E) so then we can generalize the force made by q1 in space to any charge q2.

- From what I gather H fields, H being the Magnetic Intensity field, are independent from the material they are in and depend only on the generating current, distance and geometry of the wire that generates it (ampere's law).

- [itex]\nabla \cdot \vec{B} = 0 [/itex] since magnetic flux density is defined as [itex] d \phi = \vec{B} \cdot d \vec{S}[/itex] and there are no magnetic monopoles. Magnetic flux [itex]\phi[/itex] is also fictional but it's still a flux and therefore we can define [itex]\vec{B} [/itex]. (Gauss' Law for magnetism)

- Magnetic field density is also defined for every material and point in space as:

[itex] B = \mu _0 ( H + M ) = \mu _0 (1 + \chi _m) H[/itex] (and I REALLY don't understand this one)

Then my questions are:

1.- Which field is conserved in a magnetic circuit with big reluctances (and why)?

2.- What's the physical meaning of the reluctance?

3.- How is it possible for ferromagnetic materials to have a B saturation point? (and this one really puzzles me). I mean, if B = (1+x)*H*mu0 then how can it stop increasing when I increase H (or the magnetic field generating current). Does the excess flux surround the material?

and finally:

4.- If I have a magnetic circuit formed by a ferromagnetic material (initially demagnetized) and I want to generate a certain flux (in Webers) then which field is constant across the circuit, B or H? (I have the B-H curve of the material, now I just need to know which one is constant across the circuit since there's an air gap).

It's a long set of question but I'd really appreciate it if you could help me (and I'm sure thousands of other people have the exact same questions)

Thanks a lot!!!