Magnetic Reluctance: Examining Its Validity in Toroidal Solenoids

[htg]

Is the concept of magnetic reluctance correct?
If so, then the flux of magnetic induction in a toroidal solenoid, whose half length of core has relative permeability = 10, and the other half has relative permeability = 1000 or 10000 will be almost the same in both cases. Has anyone verified it experimentally?

 

[marcusl]

This is basically correct. The principal is used all the time in ferrite pot cores--see the picture here http://www.mag-inc.com/products/ferrite-cores/ferrite-pot-cores"
The coil bobbin fits over the post, and a second identical core fits over the first until the mating surfaces touch. Ferrites have permeabilities of thousands, but the overall reluctance can vary over an order of magnitude depending on the flatness and cleanliness of the mating surfaces, how much pressure is applied, etc. This is obviously untenable for an electronic circuit.

To fix this, the posts are ground a little short so as to leave a precision air gap of a some thousandths of an inch. Since the gap has permeability one, the overall reluctance is set by the gap thickness independent of the core permeability or quality of mating surfaces. This gives highly accurate and reproducible performance.

 

[htg]

I have serious doubts if the concept of magnetic reluctance is correct. Since magnetization is caused by orientation of micro domains, I propose to talk about:
1) H = Hfree, the intensity of magnetic field due to free currents (in conductors wound around a core)
2) Hbound, the intensity of magnetic field due to bound currents (due to magnetization)
3) Htotal = Hfree + Hbound
4) B = MuZero * Htotal
Such a conceptualization leads to a different picture which also enables one to talk about Hbound of a permanent magnet (something beyond the reach of the generally used conceptualization of description of magnetic fields).
ALSO, consider a horseshoe electromagnet with a ferromagnetic core. It seems clear to me that magnetization acts like additional ampere-turns, so B in the air gap between the poles should be very significantly different in the case of permeability of the core = 1000 vs 10 000.

 

[Bob S]

See equation (7) and derivation in thumbnail. For a toroid of radius R, if half the toroid is an air gap, then G = πR. The denominator of Eq (7) is the reluctance.

Bob S

 

[htg]

I do not know what thumbnail you are referring to.
What about B in the air gap of a horseshoe electromagnet mentioned above?

 

[marcusl]

Such a conceptualization leads to a different picture which also enables one to talk about Hbound of a permanent magnet (something beyond the reach of the generally used conceptualization of description of magnetic fields).

The difficulty you are having in conceptualizing permanent magnets is not a failure of classical E&M theory, which treats magnetic phenomena quite successfully.

ALSO, consider a horseshoe electromagnet with a ferromagnetic core. It seems clear to me that magnetization acts like additional ampere-turns, so B in the air gap between the poles should be very significantly different in the case of permeability of the core = 1000 vs 10 000.

Clear or not, magnetization does not "act like additional ampere-turns." Suggest you study a little further. We at PF can recommend some texts that you may find useful.

What about B in the air gap of a horseshoe electromagnet mentioned above?

B in the gap will be nearly identical in both cases.

 

[htg]

If magnetization does not act like additional ampere-turns, then the widely known theory of magnetization by orientation of magnetic domains must be false.

 

[Bob S]

I do not know what thumbnail you are referring to.
What about B in the air gap of a horseshoe electromagnet mentioned above?

Here is the post again, with thumbnail.

See equation (7) and derivation in thumbnail. For a toroid of radius R, if half the toroid is an air gap, then G = πR. The denominator of Eq (7) is the reluctance. Note that for very high permeability, the magnetic field in the air gap is independent of the permeability. This effect is very well known, and included in electromagnet design.

Bob S

 

[htg]

At least for a small gap, equations 4 and 5 contradict the Gauss' law.

 

[htg]

Clear or not, magnetization does not "act like additional ampere-turns." Suggest you study a little further. We at PF can recommend some texts that you may find useful.


B in the gap will be nearly identical in both cases.

I want to consider H significantly below the saturation field intensity. Will the B in the air gap of a horseshoe electromagnet, whose core permeability is 1000 or 10 000 be nearly the same in both cases?

 

[Bob S]

At least for a small gap, equations 4 and 5 contradict the Gauss' law.

Div B = 0
B longitudinal at gap is continuous
H longitudinal is not continuous

Bob S

 

[htg]

When you look at the microscopic mechanisms of magnetization, it is clear that both H and B have to be continuous. What you say seems to be generally accepted, but it is pretty clear that it is not true.

 

[marcusl]

Ah, what a dilemma. You are certain of yourself, but what to do about all mainstream physicists and Nobel laureates of the past 150 years who must be wrong?