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- Tom Del Rosso

May 24, 2020, 4:47 am

Reviewing stuff I forgot during lockdown, this is one thing I never got.

H is amp-turns/meter, and having distance in the denominator suggests

that it is also a measure of flux density (but without the core

influences). So why is B defined as flux density, as if that

distinguishes it from H?

H is amp-turns/meter, and having distance in the denominator suggests

that it is also a measure of flux density (but without the core

influences). So why is B defined as flux density, as if that

distinguishes it from H?

--

Re: Flux density

On 2020-05-24 00:47, Tom Del Rosso wrote:

It's just a definition. In Gaussian units (rationalized CGS-ESU), B is

quoted in gauss and H in oersted, but there's no actual dimensional

difference, i.e. mu is dimensionless.

Cheers

Phil Hobbs

It's just a definition. In Gaussian units (rationalized CGS-ESU), B is

quoted in gauss and H in oersted, but there's no actual dimensional

difference, i.e. mu is dimensionless.

Cheers

Phil Hobbs

--

Dr Philip C D Hobbs

Principal Consultant

Dr Philip C D Hobbs

Principal Consultant

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Re: Flux density

of uniform flux density B, and you get B*A flux in that loop (which if the

flux is changing, you can do Faraday's law, etc.). Who knows what current

flows in the wire.

Conversely, put some current into a loop of a given perimeter, and you have

some magnetic field intensity H within it (give or take geometry, of

course). Who knows how much flux that took.

In space, the ratio of these two happens to be mu_0. Or at the terminals of

the loop, its inductance: H == V.s / A. For general materials, use mu =

mu

___0 * mu___r, and the effective cross sectional area A_e and effective path

length l_e.

Tim

--

Seven Transistor Labs, LLC

Electrical Engineering Consultation and Design

Seven Transistor Labs, LLC

Electrical Engineering Consultation and Design

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Re: Flux density

Tim Williams wrote:

I think Phil understood best what I meant, but all the answers (except

Kevin Bacon) contributed something helpful. Thanks so much.

A few things.

Where do you measure l_e?

What is V_s?

And you seem to be relating inductance H to mu, but isn't that a whole

different H? Inductance doesn't depend on current for one thing.

I think Phil understood best what I meant, but all the answers (except

Kevin Bacon) contributed something helpful. Thanks so much.

A few things.

Where do you measure l_e?

What is V_s?

And you seem to be relating inductance H to mu, but isn't that a whole

different H? Inductance doesn't depend on current for one thing.

Re: Flux density

In general, you'd calculate it by integrating over space, in such a way that

you get the average of magnetic path lengths, weighted by their

contributions to total flux. I guess that's a ratio between some Maxwell

equations but I can't think which ones at a glance.

When mu_r >> 1, the path is essentially all in the core (or gaps between

core pieces), so is the mean circumference of the core. l_e is almost

exclusively used with cores, since it isn't very meaningful elsewhere...

Same for A_e, the effective area is the core cross section. You can define

it easily enough for helical geometries (solenoid, toroid, whatever) as

well, but you'll always get an inductance greater than calculated because

there's leakage between turns as well as the main (intended?) field.

V.s is the product of volts and time, flux (webers). (Notice I consistently

used underscore to denote subscript.)

I bring up inductance because we're often concerned with circuit parameters

(volts, amps, winding flux, inductance), or what makes them up (inductivity

(inductance / turn^2), flux per turn, amp-turns), as well as the fields and

other bulk properties (flux density, magnetization, permeability).

I like to treat turns as their own unit, to keep track of whether I'm

talking about circuit values (turns cancel out), core values, or fields.

The thing about dimensional analysis is, you can always add dummy units and

track them through the operation -- a helpful tip just for hand-working

algebra -- but it's a lot harder to remove units, and doing so may invite

confusion (I would perhaps suggest avoiding the cgs system until one is very

comfortable with fields).

Yes, magnetization symbol is H (bold H if you're talking about vectors), and

the henry unit is H, one must be careful not to confuse the two. I usually

use "==" to denote unit equivalence, and a regular "=" to denote

mathematical equivalence.

Also I tend to refer to H as magnetization, even though that's the built-in

magnetization M (i.e., a permanent magnet). What I mean is "magnetic field

intensity" but ain't no one got time fo' dat.

Also also, inductance does vary with current, for practical ferromagnetic

cores -- that's one reason why we're interested in tracking the total flux

(circuit flux * turns / A_e = B), or sometimes magnetization (circuit

amperes * turns / l_e = H), in magnetic component design.

If you're more interested in fields in general, than component design, you

can ignore much of the circuit-oriented values.

Tim

--

Seven Transistor Labs, LLC

Electrical Engineering Consultation and Design

Seven Transistor Labs, LLC

Electrical Engineering Consultation and Design

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Re: Flux density

In my experience, l

___e and A___e are very close to the expected mechanical

dimensions -- i.e., cross section of the wound limb(s), mean circumference

of expected path. I don't think that's necessary, and is in part a

consequence of conventional shapes being well behaved -- compact,

symmetrical, optimized for cost and performance.

Also, v

___e ~= l___e * A_e, which I'm not sure has to necessarily be true.

(There could be vestigial core features that don't magnetize, so the core

volume is greater than the active volume; but then, it's

___effective___volume,

so that wouldn't be counted anyway?).

And when you bring nonlinearity into things... As magnetization rises:

mu

___eff falls, A___e rises some (fringing fields), l_e rises some (because the

inside track saturates first, especially inside corners, pushing the active

volume outwards).

The changes in mu

___eff and A___e partially oppose, so it's not immediately

obvious how to separate them; since they're both effective parameters, we

might just assume one or the other remains constant instead, and measure the

other as the combination.

These are hopefully effects we can ignore... which for power application,

yep, no problem. For signals, well obviously you want to keep the

magnetization low to avoid distortion, frequency shift, etc. Some airgap

helps ballast changes in core mu, which would otherwise be rather sensitive

(not to mention, to temperature as well as signal level).

Tim

--

Seven Transistor Labs, LLC

Electrical Engineering Consultation and Design

Seven Transistor Labs, LLC

Electrical Engineering Consultation and Design

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