Flux density

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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?

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"Tom Del Rosso" wrote in news:racu90\$svq\$ snipped-for-privacy@dont-email.me:

90 degrees of other than Kevin Bacon?
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H is independent of material in the volume around which the core is wound - it is the magnetising force. B is the magnetic field produced by this magnetising force which does depend on the material around which the coil winds.

In a higher-permeability material the same H produces a higher B than it does in a low permeability material.

```--
Bill Sloman. Sydney```
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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 ```
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B is flux density: wrap a loop of wire around a given cross-sectional area, 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 ```
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Huh, I'm not sure. The physics types (I think Purcell and Feynman) pointed out in the ~60's, that they (the physicists) had been using B and H kinda wrong. And it was B that was the 'real field' Real in that F=q*(E + v x B), it's the E and B fields that give the force. D and H are useful computational fields.

At least that's my limited understanding, George h.

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Yeah, I was taught second year E&M out of Purcell's book. Sort of the physics student's version of the New Math--as Tom Lehrer famously sang, "It's so easy, so doggone easy, that only a child can do it!"

The major mistake there ISTM was that Faraday's law became a complete

*deus ex machina* rather than (as was actually the case) the key to the whole subject.

Cheers

Phil Hobbs

```--
Dr Philip C D Hobbs
Principal Consultant ```
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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.

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"Tom Del Rosso" wrote in message news:raf445\$1vt\$ snipped-for-privacy@dont-email.me...

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 ```
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We need more Tom Lehrer!

Yeah IDK. After reading Feynmans take on it... (He just uses with E and P (polarization) fields for Electro-statics and then uses B and M (magnetization) for magnetic fields... But he rewrites the magnetic field equations so that M looks more like P. It made things a bit easier for me to get. And that's how I tend to think about it now.

George H. Purcells E&M book is a beautiful too.

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And then there's the Aharonov-Bohm effect, where the phase of the electron wave function couples to the magnetic vector potential even in field-free regions. Vector potential was previously thought to be a calculating convenience as well.

Cheers

Phil Hobbs

```--
Dr Philip C D Hobbs
Principal Consultant ```
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I had one of those effects. But I went to a doctor for a shot and got over it.

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Yeah, I'm a bear of little brain, and am happy with the idea that potentials are more 'fundamental' than fields. At least for stationary charges the potential is easier to calculate. :^) I'm not as sure about calculating the vector potential... but almost anything has to be better than Amperes law.

George H.

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"Tom Del Rosso" wrote in news:racu90\$svq\$ snipped-for-privacy@dont-email.me:

Here is a good start, though it begins much earlier than the info you want. Still a pretty good instructor.

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Pity about the side effects. ;)

Cheers

Phil Hobbs

```--
Dr Philip C D Hobbs
Principal Consultant ```
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Strange, men usually see a doctor to get a pill to increase their potential.

Tim

```--
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design ```
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What's shocking is that I have more potential than I can use.

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I represent that remark.

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John S wrote in news:ralp99\$d5q\$ snipped-for-privacy@dont-email.me:

These are the times that try men's holes.

These are the times that try men's poles.

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This gentleman has a great nuts-and-bolts on the whole topic (and a great electronics page in general)...

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He unravels the units, demystifies the magic, etc., etc. Recommended.

Cheers, James Arthur

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