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

1. Nov 22, 2010

### magnetics

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.

2. Nov 24, 2010

### marcusl

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.

3. Nov 24, 2010

### sophiecentaur

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.

4. Nov 24, 2010

### stevenb

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.

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.

Last edited: Nov 24, 2010
5. Jun 26, 2012

### crwilliams

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

6. Jun 26, 2012

### Muphrid

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 $\epsilon_0 = \mu_0 = 1$.

7. Jun 27, 2012

### crwilliams

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.

8. Jul 1, 2012

### marcusl

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.

9. Jul 2, 2012

### crwilliams

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

10. Jul 2, 2012

### marcusl

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).

11. Jul 2, 2012

### crwilliams

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.

12. Feb 13, 2014

### cabraham

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

13. Feb 18, 2014

### marcusl

Electricity and magnetism are related through special relativity--in fact, the magnetic force is exactly the Coulomb electric force as seen in a moving reference frame. Since E and M are the same at a fundamental level, it is intuitive to measure them with the same units. The widespread, indeed universal, use of SI units for electrical quantities makes this impractical to the point that Gaussian units have been abandoned--but the latter are relativitistically consistent and logical whereas the former are not.