Flux density...

T

Tom Del Rosso

Guest
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?


--
 
\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote
in news:racu90$svq$1@dont-email.me:

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?
Click to expand...

90 degrees of other than Kevin Bacon?
 
\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote
in news:racu90$svq$1@dont-email.me:

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?
Click to expand...

90 degrees of other than Kevin Bacon?
 
On 2020-05-24 00:47, Tom Del Rosso wrote:
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?
Click to expand...
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
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com
 
On 2020-05-24 00:47, Tom Del Rosso wrote:
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?
Click to expand...
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
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com
 
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
Website: https://www.seventransistorlabs.com/

\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote in
message news:racu90$svq$1@dont-email.me...
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?


--
Click to expand...
 
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
Website: https://www.seventransistorlabs.com/

\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote in
message news:racu90$svq$1@dont-email.me...
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?


--
Click to expand...
 
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
Website: https://www.seventransistorlabs.com/

\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote in
message news:racu90$svq$1@dont-email.me...
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?


--
Click to expand...
 
Tim Williams wrote:
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.
Click to expand...

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.
 
Tim Williams wrote:
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.
Click to expand...

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.
 
Tim Williams wrote:
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.
Click to expand...

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.
 
\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote in
message news:raf445$1vt$1@dont-email.me...
> Where do you measure l_e?

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.

> What is V_s?

V.s is the product of volts and time, flux (webers). (Notice I consistently
used underscore to denote subscript.)

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.
Click to expand...

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
Website: https://www.seventransistorlabs.com/
 
\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote in
message news:raf445$1vt$1@dont-email.me...
> Where do you measure l_e?

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.

> What is V_s?

V.s is the product of volts and time, flux (webers). (Notice I consistently
used underscore to denote subscript.)

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.
Click to expand...

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
Website: https://www.seventransistorlabs.com/
 
\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote in
message news:raf445$1vt$1@dont-email.me...
> Where do you measure l_e?

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.

> What is V_s?

V.s is the product of volts and time, flux (webers). (Notice I consistently
used underscore to denote subscript.)

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.
Click to expand...

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
Website: https://www.seventransistorlabs.com/
 
\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote
in news:racu90$svq$1@dont-email.me:

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?
Click to expand...

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

<https://www.youtube.com/watch?v=bwreHReBH2A>
 
\"Tom Del Rosso\" <fizzbintuesday@that-google-mail-domain.com> wrote
in news:racu90$svq$1@dont-email.me:

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?
Click to expand...

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

<https://www.youtube.com/watch?v=bwreHReBH2A>
 
Tim Williams wrote:

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...
Click to expand...

And for the same reason you read it from the datasheet of the core, not
measure. One can also resort to FEM sims, but I believe it is pretty
rare outside of academia.

Best regards, Piotr
 
Tim Williams wrote:

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...
Click to expand...

And for the same reason you read it from the datasheet of the core, not
measure. One can also resort to FEM sims, but I believe it is pretty
rare outside of academia.

Best regards, Piotr
 
\"Piotr Wyderski\" <peter.pan@neverland.mil> wrote in message
news:rapefq$1p6jh$1@portraits.wsisiz.edu.pl...
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...

And for the same reason you read it from the datasheet of the core, not
measure. One can also resort to FEM sims, but I believe it is pretty rare
outside of academia.
Click to expand...

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
Website: https://www.seventransistorlabs.com/
 
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