# Measuring Magnetic Field Intensity (H) and Magnetic Flux Density (B).

## Main Question or Discussion Point

Now here is a real world practical application.

Australia Post has a warning for shipping magnetic material in the post. Section D2.9.2 states...
Any material that, when packed, has a magnetic flux density of 0.159 A/m or more at a distance of 2.1 meters from any point on the surface on the package (is deemed a dangerous good).

They call it magnetic flux density but use A/m units, are they getting A/m confused with Tesla or am I confused? Under their definition, how would you measure 0.159 A/m because I don’t think a magnetometer will do the job.

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marcusl
Gold Member
B is magnetic induction, aka magnetic flux density, and is measured (in SI units) in Tesla. It describes induction in a material. H is magnetic field (sometimes called magnetic intensity) in a vacuum, and is measured in A/m. So the Post got the labels confused, as you note. However it is easy to relate them. By definition,

$$\vec{B}=\mu_0\vec{H}+\vec{M}$$

Since M is zero in the air, you can use a magnetometer that measures either B or H and then convert to the desired unit.

As a note, it is regrettable that the SI system (invented by engineers) uses different units for B and H. In the old Gaussian (cgs) system they have the same dimensions, making intuitive sense.

sophiecentaur
Gold Member
I guess you could call their bluff and ask them for the measurement system they would use.

ps no one should mock engineers!!! They can make life too hard for you.

As a note, it is regrettable that the SI system (invented by engineers) uses different units for B and H. In the old Gaussian (cgs) system they have the same dimensions, making intuitive sense.
Was the SI system really invented by engineers? I can't confirm or deny this, but it seems surprising. The SI sytem has a long history of evolution which has included mathematicians, scientists and engineers. I think it is generally viewed as a useful system of units when doing experimental work, which of course would include engineering. From theory points of view, other systems of units are sometimes preferred. There are pros and cons to each system depending on what one is doing.

Personally, I don't find it regrettable that SI units are used for EM. This system is very intuitive and convenient when doing experimental and design work. But then again, I'm an electrical engineer, so your comment is not out of line.

Of course, your opinion is as valid as mine or anyone else's, but I can't help but want to quote an interesting comment by Richard Fitzpatick from his PHY387K course notes which are available online in PDF form. This just helps offer the OP alternative points of view. I actually was surprised to see this choice from a physics professor, and would have expected these exact words from an electrical engineering professor only. But, there it is.

In 1960 physicists throughout the world adopted the so-called S.I. system of units, whose standard measures of length, mass, time, and electric charge are the meter, kilogram, second, and coloumb, respectively. Nowadays, the S.I. system is used almost exclusively in most areas of physics. In fact, only one area of physics has proved at all resistant to the adoption of S.I. units, and that, unfortunately, is electromagnetism, where the previous system of units, the so-called Gaussian system, simply refuses to die out. Admittedly, this is mostly an Anglo-Saxon phenomenon; the Gaussian system is most prevalent in the U.S., followed by Britain (although, the Gaussian system is rapidly dying out in Britain under the benign influence of the European Community). One major exception to this rule is astrophysics, where the Gaussian system remains widely used throughout the world. Incidentally, the standard units of length, mass, time, and electric charge in the Gaussian system are the centimeter, gram, second, and statcoloumb, respectively.

You might wonder why anybody would wish to adopt a different set units in electromagnetism to that used in most other branches of physics. The answer is that in the Gaussian system the laws of electromagnetism look a lot "prettier" than in the S.I. system. There are no $$\epsilon_0$$'s and $$\mu_0$$'s in any of the formulae. In fact, in the Gaussian system the only normalizing constant appearing in Maxwell's equations is c, the velocity of light. However, there is a severe price to pay for the aesthetic advantages of the Gaussian system. The standard measures of potential difference and electric current in the S.I. system are the volt and the ampere, respectively. I presume that you all have a fairly good idea how large a voltage 1 volt is, and how large a current 1 ampere is. The standard measures of potential difference and electric current in the Gaussian system are the statvolt and the statampere, respectively. I wonder how many of you have even the slightest idea how large a voltage 1 statvolt is, or how large a current 1 statampere is? Nobody, I bet! Let me tell you: 1 statvolt is 300 volts, and 1 statampere is 1/3 X 10^-9 amperes. Clearly, these are not particularly convenient units!

In order to decide which system of units we should employ in this course, we essentially have to answer a single question. What is more important to us: that our equations should look pretty, or that the our fundamental units should be sensible? I think that sensible units are of vital importance, especially if we are going to make quantitative calculations (we are!), whereas the prettiness or otherwise of our equations is of marginal concern. For this reason, I intend to use the S.I. system throughout this course.
Another interesting thing is that Jackson's latest edition of EM fields book now uses both systems. I actually would have preferred that he not transition to the SI system because I always viewed his book as a work of art, and somehow the beauty is marred by the switch, in my eyesight. At that level of study, the cgs system is perfectly fine, and perhaps even preferred from many points of view. Also, unit conversions will be quite trivial by the time someone is using that text.

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The originator of the SI units was Prof. Giovanni Giorgi who proposed the metre, kilogram, second, and ampere as the four fundamental units (since increased to 7). In particular, he originated the 'rationalised' concept of dealing with the pi (constant) in such a way that the pi appeared in 'circular' things and was absent from 'straight' things.

For a little more see here: http://en.wikipedia.org/wiki/Giovanni_Giorgi

I don't mind non-SI units, but I have a heavily dislike of traditional electromagnetic cgs units--normalizing out the factors of $4\pi$ and shifting them to the sources of EM fields is massively backwards. Leave them in the Green's functions for the differential equations and just set $\epsilon_0 = \mu_0 = 1$.

Sorry - this is a thread hijack - but from where do you get the symbols for pi, epsilon sub zero, etc. and how do you insert them in a post?

Thanks.

marcusl
Gold Member
The quotation in post #4 misses a key advantage of cgs units for electromagnetism--that E and M are actually relativistic manifestations of the same electric force, seen in different frames. Since relativity unites electricity and magnetism and shows that they are one, it is logical that they should be measured in the same units, not different ones as in SI.

As I recall, though, the cgs units for electrostatic quantities are not the same as the units for electromagnetic quantities.

marcusl
Gold Member
It is true that there are several flavors of units based on centimeters/grams/seconds. The esu/emu systems you refer to were used, for instance, in the first edition of Smythe's book Static and Dynamic Electricity. I was thinking of the Gaussian system used by Jackson (2nd edition) and Schwartz (Principles of Electrodynamics), where E and B have the same underlying units. Even the emu system, however, has the advantage that B and H are identical in a vacuum (compare this to SI units where B in a vacuum is approximately 1e8 times larger than H).

You are of course correct.

After a couple of hours reflecting on this I came to this understanding.

The widespread use of SI units in general, and in electrical engineering in particular (electrical engineers being amongst the first to embrace SI units) lies in the observation that B = kH (where k is some constant, possibly unity) is only true in materials for which the B-H relationship is linear. Since all practical electrical magnetic materials are highly non-linear - usually by careful design - the simple relationship fails and it becomes less confusing to think of B as the magnetic induction and distinguish from H, the magnetic field.

Interestingly, though, the current trend is towards operating power conversion circuitry at ever increasing frequencies (100kHz to 10MHz), permitting the use of low inductance components and sometimes air cores for chokes and transformers.

B is magnetic induction, aka magnetic flux density, and is measured (in SI units) in Tesla. It describes induction in a material. H is magnetic field (sometimes called magnetic intensity) in a vacuum, and is measured in A/m. So the Post got the labels confused, as you note. However it is easy to relate them. By definition,

$$\vec{B}=\mu_0\vec{H}+\vec{M}$$

Since M is zero in the air, you can use a magnetometer that measures either B or H and then convert to the desired unit.

As a note, it is regrettable that the SI system (invented by engineers) uses different units for B and H. In the old Gaussian (cgs) system they have the same dimensions, making intuitive sense.
Why should B & H have the same units? What's intuitive about that? The SI system does make sense because A/m and V*sec/m2 are relevant. The SI system is very good. The cgs units, however, do have a useful property. In non-ferrous media, B=H, meaning that they are 1 and the same entity. This does make sense. But w/ ferrous media, the differing units make sense regarding energy storage and loss.

Claude

marcusl