# Magnetism lingo: Applied H? or Applied B?

When discussing magnetism or magnetic systems, Do you apply an H-field? or apply a B-field?

I suppose this is in the general situation where you apply a magnetic field to a material.

In relation to B-H loop showing hysteresis, I notice that the "x-axis", typically dependent variable, is H and "y-axis", typically independent variable, is B... does this mean that you apply H and observe B?

If you apply an H-field, why do http://www.magnet.fsu.edu/mediacenter/factsheets/records.html" say the "record magnetic field produced is 100 Tesla" where Tesla is the unit for B?

So if i say i have an "external magnetic field" is it in units of Tesla? or Ampere/meter?
So if i say i have an "applied magnetic field" is it in units of Tesla? or Ampere/meter?

in other words, do you apply Teslas or A/m's?

Last edited by a moderator:

Related Classical Physics News on Phys.org
Chickens & eggs. Neither one can exist w/o the other. At this point in scientific understanding, nobody can show that either one comes first. H & B are said to be "mutually inclusive".

However, we can, & do, drive magnetic components w/ either a voltage source or a current source. An inductor is often excited with a dc bias in the form of a current source (or a voltage source plus a resistance, which is the equivalent). Here, H is fixed, & B is determined by the H value & core material. H is independent, B is dependent.

Often, traasformers are driven from a voltage source. In this case the voltage source value forces a fixed value of B. Then H is determined by the core properties. Here, B is independent, H is dependent.

It can work either way.

Claude

Last edited:
Chickens & eggs. Neither one can exist w/o the other. At this point in scientific understanding, nobody can show that either one comes first. H & B are said to be "mutually inclusive".
This is actually misleading or even wrong.

At the risk of getting off topic:
B is the fundamental magnetic field quantity. It is the only magnetic field that appears in the http://www.google.com/url?url=http:...NoTeGjD4zksQOCt_mmBA&ved=0CCMQygQwAA&cad=rja". H is a derived field; it arises as a form of convenience when dealing with the magnetization of materials.

However, we can, & do, drive magnetic components w/ either a voltage source or a current source. An inductor is often excited with a dc bias in the form of a current source (or a voltage source plus a resistance, which is the equivalent). Here, H is fixed, & B is determined by the H value & core material. H is independent, B is dependent.

Often, traasformers are driven from a voltage source. In this case the voltage source value forces a fixed value of B. Then H is determined by the core properties. Here, B is independent, H is dependent.

Last edited by a moderator:
Getting back to the OP....

When discussing magnetism or magnetic systems, Do you apply an H-field? or apply a B-field?
In general, you usually apply H. The reason comes from the equation
curl H = Jfree.
In words, (the curl) of H is directly related to "free" (e.g. applied) currents. This is in direct contrast to B, which is related to both free and "bound" currents. Free currents are the ones that you measure with an Ammeter on your circuit board. Bound currents include currents occurring in atomic and molecular scales. So it turns out that it is difficult to calculate B, but relatively easy to calculate H. The ease of calculation allows you to easily relate the specific quantity with something you can easily control in the lab; in this case, relating H to an applied current.

Griffith's gives a nice analogy to E and D. He says that the reason we tend to like E better is because we can directly relate it to voltages, which is something we can easily measure in the lab. D, however, is difficult to work with because it is related to free charge. How often in the lab, do you directly place a certain amount of charge on something? Unless that's your specific research, I'm willing to bet that the answer is not very often.

In relation to B-H loop showing hysteresis, I notice that the "x-axis", typically dependent variable, is H and "y-axis", typically independent variable, is B... does this mean that you apply H and observe B?

If you apply an H-field, why do http://www.magnet.fsu.edu/mediacenter/factsheets/records.html" say the "record magnetic field produced is 100 Tesla" where Tesla is the unit for B?
Again, H is directly controlled by the current you induce in your electromagnet/solenoid/whatever; thus it is the independent variable. B, however, is measured (somehow) within the material that is being magnetized. Remember, in simple media, H and B are proportional via the permeability. In that case, a B-H plot would simply be a straight line. Well, when you have a hysteresis loop, you are working with a non-linear medium; thus it's "weird" shape. You get that shape because B and H are no longer proportional.

Another way of thinking of the hysteresis loop is by replacing B with M (magnetization). The plot would be similar, just with different numbers. With a hysteresis loop, you are essentially looking at how varying H will change the magnetization of a given material. That magnetization is conveyed to you by B.

So if i say i have an "external magnetic field" is it in units of Tesla? or Ampere/meter?
So if i say i have an "applied magnetic field" is it in units of Tesla? or Ampere/meter
This is probably more of a toe-mae-toe, toe-mah-toe thing. I once had a professor say that to avoid confusion you should just say either "B" or "H" instead of "magnetic field" if you're trying to be quantitative.

Last edited by a moderator:
This is actually misleading or even wrong.

At the risk of getting off topic:
B is the fundamental magnetic field quantity. It is the only magnetic field that appears in the http://www.google.com/url?url=http:...NoTeGjD4zksQOCt_mmBA&ved=0CCMQygQwAA&cad=rja". H is a derived field; it arises as a form of convenience when dealing with the magnetization of materials.

However, we can, & do, drive magnetic components w/ either a voltage source or a current source. An inductor is often excited with a dc bias in the form of a current source (or a voltage source plus a resistance, which is the equivalent). Here, H is fixed, & B is determined by the H value & core material. H is independent, B is dependent.

You cite "Wikipedia" as a reference that B is more basic than H. Even high school students studying at the AP level are informed that Wiki alone is not a credible reference. Students who rely solely on Wiki, w/o corroberation, are given an F grade.

Second, notice the equation from Maxwell "curl H = J + dD/dt." In Wiki, it is expressed as "curl B = mu*J +..." Any Maxwell equation can be expressed using H or B, E or D. It's just a matter of making use of the fact that D = epsilon*E, & B = mu*H.

For Ampere's Law, the most basic form is "curl H = J + dD/dt", where J is conduction current, & dD/dt is displacement current. Hence the relation between conduction current & mag field is most basic in J & H. In other words, for a given J in a conductor, there is a specific value of H. This H value is totally independent of medium. The B value however, depends on the medium since B = mu*H. Thus for a current density J, H is determined solely by J, but B is determined by J as well as Mu, the permeability of the medium.

The fact that you have to be told this demonstrates that you don't know enough to be rebuking others. The fact that H is independent of medium, while B is dependent, is spelled out in any good fields text. Have you had e/m fields at the engr or phy level?

I'm not attacking your intelligence. I just can't understand how you can even imagine that all the uni e/m texts are wrong, & that you have knowledge the science community lacks. I worked in inductive component design for several years, & since then have branched out into general EE, but still do mag work.

The fact that B& H are mutual & neither is more basic has been reaffirmed by science, relativity, Maxwell, EE community, magnetic material producers, etc. These are the experts. You, OTOH, take an excerpt from Wiki, the crackpot center of the world, give it your own narrow interpretation based on your preconceived preferences, & run with it.

Wiki is not only unreliable. But they didn't even say what you claim they said.

Regarding your last question, here it is. Faraday's Law, FL herein, says that V = -N*d(phi/dt). The flux is "phi", & the flux density, flux/area = weber/m^2 or tesla, is "B". So, A*B = phi, where A = area.

Thus V = -N*A*dB/dt. If the primary of an xfmr is connected across a good constant voltage source, CVS herein, then V, the voltage is forced to be constant. Since N the turns number, & A the area, are fixed, & V is fixed, then dB/dt is determined solely by V, the voltage value of the CVS. Since V is usually a sine function, dB/dt will be a cosine, multiplied by radian frequency.

Thus the magnitude of B is determined by voltage V & frequency omega, as well as A & N. H, however, is determined by the mu of the core material. A high mu material, is subjected to the same V & B as a low mu material. The higher mu core incurs a lower H value than the low mu core, & hence lower magnetizing current.

Depending on how a magnetic device is excited, H could be independent of the material, w/ B dependent on mu, or vice-versa. As I said, based on decades of experience & study, they are inclusive. Neither is fundamentally more basic, they co-exist in unison, neither being the cause nor the effect. We can, however, drive magnetic devices in different manners. We can force H to be constant w/ B dependent, or the other way around. Just as a forced H & given mu determines B, a forced B & given mu can determine H.

It works both ways. Did I make it clear. I'll gladly elaborate if you wish.

Claude

Last edited by a moderator:
You cite "Wikipedia" as a reference that B is more basic than H. Even high school students studying at the AP level are informed that Wiki alone is not a credible reference. Students who rely solely on Wiki, w/o corroberation, are given an F grade.
I gave the Wikipedia link so that people can easily see what is meant by the "microscopic" Maxwell equations, as opposed to the "macroscopic" Maxwell equations. I prefer to do this because I have neither the time nor the inclination to Latex several different vector equations. The fact that you use this as your primary point of rebuke, as well as your other non-essential comments, shows your immaturity in having a scientific debate.

If you want real references, then start with Griffiths, Jackson, Stratton, and Landau/Lifgarbagez (Vol 8.). I present nothing new to the table, just my way specific way of explaining things.

Second, notice the equation from Maxwell "curl H = J + dD/dt." In Wiki, it is expressed as "curl B = mu*J +..." Any Maxwell equation can be expressed using H or B, E or D. It's just a matter of making use of the fact that D = epsilon*E, & B = mu*H.
Again, the microscopic Maxwell equations do not contain D and H; only the macroscopic ones do.

I'm not attacking your intelligence. I just can't understand how you can even imagine that all the uni e/m texts are wrong, & that you have knowledge the science community lacks. I worked in inductive component design for several years, & since then have branched out into general EE, but still do mag work.
Again, look at the texts I've referenced above, or pretty much any other one for that matter. Your views are the ones in direct contradiction. Truthfully, I questions whether you actually believe what you say or if you just get off on leading others astray with fallacies.

cabraham said:
Often, traasformers are driven from a voltage source. In this case the voltage source value forces a fixed value of B. Then H is determined by the core properties. Here, B is independent, H is dependent.
Thus V = -N*A*dB/dt. If the primary of an xfmr is connected across a good constant voltage source, CVS herein, then V, the voltage is forced to be constant. Since N the turns number, & A the area, are fixed, & V is fixed, then dB/dt is determined solely by V, the voltage value of the CVS. Since V is usually a sine function, dB/dt will be a cosine, multiplied by radian frequency.
You are misinterpreting the equation you have cited. In that equation, V is induced by the dB/dt term. It does not work vice-versa. Your rational implies that dB/dt can be induced by V. This, however, is absurd.

Suppose for a moment that you are correct. Then by applying a constant V, it follows that dB/dt must also be constant. This would give rise to a magnetic field that becomes strong and stronger and would approach infinity. Therefore, you cannot be correct.

-----

Quite frankly, I've said what I have to say. It is up to further readers to use their brains to determine who is correct. Unless you have any legitimate points of discussion, I will let you have the last word if you wish because I fear that, like your magnetic field, this debate can go on forever.

I gave the Wikipedia link so that people can easily see what is meant by the "microscopic" Maxwell equations, as opposed to the "macroscopic" Maxwell equations. I prefer to do this because I have neither the time nor the inclination to Latex several different vector equations. The fact that you use this as your primary point of rebuke, as well as your other non-essential comments, shows your immaturity in having a scientific debate.
As I said, E or D, B or H, they are related via mu or epsilon. No fields text I've ever seen ever said which is more basic. However, you state that B is basic, w/ H derived via H = B/mu. I replied that sometimes that is the case. Take 3 inductors connected in series, driven from a constant dc current source.

The 1st inductor is air cored, the 2nd has a low mu ferrite core, mu = 100, the 3rd has a high mu nickel-iron core, mu = 1e5. All 3 are driven w/ the same current, hence all 3 have the same H value. Regardless of the medium used as core material, H1=H2=H3, period, that's what it is.

But the B values are all different. B1 = mu0*H, B2 = 100*mu0*H, & B3 = 1e5*mu0*H. Here the B value is medium dependent, derived from H & the specific mu value of the core material. Further, the stored energy varies as W = B*H/2. H is the same for all 3, but the high mu core has the largest B hence the largest energy.

Now, let us connect 3 transformers in parallel. A common ac voltage source excites all 3 of them. From Faraday's Law:

Bpk = V/(4.44*f*A*N).

Look it up anywhere, Griffith's, or whoever. Any energy conversion book will affirm. All 3 xfmrs have the same B value approx. Xfmr1 is air cored, xfmr2 has low mu ferrite core, & xfmr3 has high mu nickel iron core. The H values now vary, unlike the 1st example.

The lowest mu, the air core unit, has the highest H value, followed by low mu, then high mu. The energy per unit cycle is greatest for the air core unit, since B is constant but H is highest for lowest mu.

These 2 examples illustrate how either H or B can be the fixed quantity, w/ the other derived from the fixed one, plus factoring in the mu value. One quantity is independent of medium, the other is dependent.

If you want real references, then start with Griffiths, Jackson, Stratton, and Landau/Lifgarbagez (Vol 8.). I present nothing new to the table, just my way specific way of explaining things.

Again, the microscopic Maxwell equations do not contain D and H; only the macroscopic ones do.

Again, look at the texts I've referenced above, or pretty much any other one for that matter. Your views are the ones in direct contradiction. Truthfully, I questions whether you actually believe what you say or if you just get off on leading others astray with fallacies.

You are misinterpreting the equation you have cited. In that equation, V is induced by the dB/dt term. It does not work vice-versa. Your rational implies that dB/dt can be induced by V. This, however, is absurd.Suppose for a moment that you are correct. Then by applying a constant V, it follows that dB/dt must also be constant. This would give rise to a magnetic field that becomes strong and stronger and would approach infinity. Therefore, you cannot be correct.

-----

Quite frankly, I've said what I have to say. It is up to further readers to use their brains to determine who is correct. Unless you have any legitimate points of discussion, I will let you have the last word if you wish because I fear that, like your magnetic field, this debate can go on forever.
How can V be induced by dB/dt, when V has already been defined as the primary value of the CVS driving the xfmr? Just as dB/dt can induce V, so can V induces dB/dt. When a xfmr primary is connected to a low impedance CVS, the flux density B is dictated by V, f, A, & N. Forcing the primary to operate at a constant amplitude & frequency ac voltage will result in an ac core flux density B of fixed amplitude & frequency. B is determined by V, f, A, & N. The mu of the core material does not influence B except in the 2nd order.

As far as a constant V resulting in a runaway B tending towards infinity, that would be the case if V were dc. I stipulated an ac voltage. The integral of a trig function is another trig function divided by radian frequency. A constant frequency constant amplitude voltage source on the primary was stipulated. B is sinusoidal in that case.

I am not leading anyone astry, I just never saw any ref text that stated what you claim. B & H are mutual. Either can be independent of medium, the other becomes derived. I have yet more examples if anyone wishes to continue. Nothing personal, I assure you. If I came across as insulting, I apologize & assure you it wasn't intentional. BR.

Claude

Last edited: