# What is the difference between B and H?

Discussion in 'Physics' started by amilton542, May 17, 2014.

1. ### amilton542 Thread Starter Active Member

Nov 13, 2010
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64
Hi,

What's the difference between flux density B and magnetic field intensity H?

Both of the two confuse me, they seem to be used interchangeably.

2. ### studiot AAC Fanatic!

Nov 9, 2007
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Are you familiar with Coulomb's (inverse square) Law of electric charge?

The difference is basically the same as the difference between the E and D vectors in electricity.

3. ### amilton542 Thread Starter Active Member

Nov 13, 2010
491
64
Could you elaborate.

I know Coulomb's law, but is that not for electric fields?

4. ### nsaspook AAC Fanatic!

Aug 27, 2009
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In vacuum B and H are equivalent but H&D are used as a tools to simply field calculations with matter (macroscopic theory).
http://en.wikipedia.org/wiki/Effective_magnetic_field#Definition

There is only one electromagnetic field (E⃗ and B⃗ ) but much of the historical names and definitions were from a time when fields were seen as separate entities or waves traveled in ethers so it's confusing at times.
http://en.wikipedia.org/wiki/Electromagnetic_fields#Dynamics_of_the_electromagnetic_field
http://en.wikipedia.org/wiki/History_of_Maxwell's_equations#On_Physical_Lines_of_Force

Last edited: May 18, 2014
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5. ### studiot AAC Fanatic!

Nov 9, 2007
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It is helpful that you know Coulomb's law.
It is also helpful to understand that this is all classical physics. Quantum Theory, Particle Physics and/or Relativity are not needed.

So let us start back with Newton and his law of gravitation.

$F = s\frac{{{M_{{1_2}}}{M_2}}}{{{r^2}}}$

This states that for two masses there is a force between them proportional to each mass and inversely proportional to the square of the distance between them. s is the constant of proportionality to make this an equation.

After it became possible to measure this force, it was noticed that for certain objects there was an additional force in action over and above that given by the gravity equation.

This was found to follow the same form (Coulombs law)

$F = t\frac{{{Q_{{1_2}}}{Q_2}}}{{{r^2}}}$

Well physicists are lazy customers and like to recycle equations rather than introduce new ones.
So when magnetism was being investigated another additional force was proposed and the relationship experimentally verified by Michell in 1750.

$F = u\frac{{{P_{{1_2}}}{P_2}}}{{{r^2}}}$

A quantity known as the pole strength was introduced.

Do you notice any similarity?

Note I have only used some of the standard symbols for clarity of comparison.
Note also that all these three are experimental results. Observations on the physical world.

Now from Newton's time it was noted that in each case there were two actors in the play and that these actors were able to exert their influence over a distance.
This observation was puzzled over then, and still is to this day.
The above observation are on tangible quantities. Within limits, we can measure out a specific mass, charge, or magnet of a given pole strength.
But that does not explain how it happens.

Enter the field theories, which run something like this:

Take one of the objects and propose that it generates a 'Field' of influence around it, affects the second object.
We cannot directly see or touch this field but if we assume it is there we can do some useful mathematics with that assumption.

So we define an electric field of the first charge

$E = \frac{{{Q_1}}}{{4\pi \varepsilon {r^2}}}$

Similarly we define the magnetic field due to the first pole

$H = \frac{{{P_1}}}{{4\pi \mu {r^2}}}$

We can now calculate the work involved in bringing in a second charge or pole against these fields. This is the same (apart from sign) as the potential energy stored in that field by doing this.

$W = \int { - Edr = \int - } \frac{{{Q_1}}}{{4\pi \varepsilon r}}$

and

$W = \int { - Hdr = \int - } \frac{{{P_1}}}{{4\pi \mu r}}$

But this still does not tell us what these fields look like.

To see this we introduce further quantities, called electric flux and magnetic flux respectively. We imagine these as lines of 'flow' similar to those in a flowing fluid, hence the term flux. This is not really a good analogy but one often offered because the mathematics is similar and the physicists are up to their old recycling trick.

Now we have two quantities associated with these fluxes.

There is the flux density, which varies from point to point, and the total flux which passes through a given area or volume.

Again the formulae are similar (why wouldn't they be?)

The electric flux density is

$D = \varepsilon E$

and the magnetic flux density is

$B = \mu H$

Whilst the total fluxes are:

$\Psi = \int {Eds}$
or
$\Psi = \int {Edv}$

and

$\Phi = \int {Hds}$
or
$\Phi = \int {Hdv}$

So {E and D}, {H and B} are not quite the same.

Both pairs are vectors that differ by a scalar constant so are aligned in the same direction.

Note the flux density interpretation (D, B) makes the maths of relating the field to the charge or pole strength easier using Gauss' Law.
Note also that whilst we have directly observed charge we have not observed the corresponding magnetic monopoles.
Both descriptions are models that ease the calculation of some desired property of the physical reality, but neither are complete.

Finally we return to your initial question, the difference between B and H which are both vectors describing a magnetic field, differing by a scalar constant.

I offer this analogy in terms of fluid flow. Momentum and velocity are two vectors describing the flux or flow regime, pointing in the same direction and one is a scalar multiple of the other since momentum is mass times velocity.

Does this help?

Last edited: May 18, 2014
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6. ### amilton542 Thread Starter Active Member

Nov 13, 2010
491
64
I'll return when I have more questions.

Thanks.

7. ### dudenheimer New Member

May 18, 2014
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0
H is magnetic field intensity. Currents of different magnitude will produce stronger or weaker magnetic fields around them. Magnets on the fridge or elsewhere have magnetic fields of different strength.

B is magnetic flux density. Flux density changes from material to material. B is equal to said material's magnetic permeability times magnetic field intensity.

B = μH

Many metals and dieletrics have permeability equal to permeability of free space (4pi x 10^-7). However, ferromagnetic materials such as iron can have μ thousands of times higher, which basically means that the magnetic field's effects will extend farther into the material before weakening. All the Fe atoms have special properties that allow their magnetic dipoles to essentially line up and create a chain reaction which allows the magnetic field to "permeate" through the material much more freely and uninhibited than it would in air.

But back to the original question B is just H in a specific material. For a magnetic field (H) of constant strength, magnetic flux density (B) is 2000-5000 times larger for the field in iron than it is for the same magnetic field in air

8. ### studiot AAC Fanatic!

Nov 9, 2007
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It is an interesting view, but not quite, any more than momentum is just velocity for a specific fluid.

B and H have different physical dimensions (units), therefore they represent physically different (vector) fields. I was trying to avoid vector calculus in my answer but what is the relation between curl(B) and curl(H) ?

Are you suggesting that they should be identical in vacuo?

9. ### dudenheimer New Member

May 18, 2014
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sure they're both vectors but by and large their directions will be identical, what matters is the difference in magnitude. Yes, magnetic field intensity is represented by (A/m) while magnetic flux density is measured in Teslas (Wb/m^2)

I am stating the fact that the relation between the magnitudes of vectors representing magnetic field intensity and magnetic flux density (H & B, respectively) are related by a constant called magnetic permeability and denoted by μ.

In vacuum the same equation holds, B = μH, where the μ-value specific to vacuum is 4pi x 10^-7 (H/m). μ can change for materials at different temperatures as well. Its all tabulated. The equation I've stated is proven. Permeability values for different materials have all been tabulated. There's no need to talk about vector calculus unless you're just trying to sound slick with the curl, divergence, dot & cross products, and all the associated jibber jabber.

10. ### studiot AAC Fanatic!

Nov 9, 2007
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This is just rubbish.

You cannot compare their magnitudes any more than you can compare 6 Newtons with 60 Newton-metres.

The constitutive relation B = μH, and others, only holds for homogeneous, isotropic media.

I said I was trying to avoid vector mechanics in this thread, and why.

If you genuinely understand the vector mechanics then why not help Iam58 in this thread, where he is trying to develop an expression for the magnetic field of a travelling electromagnetic wave in a medium with a particular unusual μ and other properties, instead of mocking it?

Last edited: May 20, 2014
11. ### dudenheimer New Member

May 18, 2014
3
0
actually I was completely wrong in my above comments. I said it backwards. Truth is the flux densities are independent of medium while the actual field strengths depend on the medium. The equations are correct but the permeability factor acts to cancel itself in the original magnetic field (H) equation.

12. ### BR-549 Well-Known Member

Sep 22, 2013
1,922
351
Dudenheimer nail it.
Electric fields are open. They have poles. Magnetic fields are closed and have no poles. They have rotation. All magnetic fields come from fundamental particles. And they have no poles. But they have circulating charge.....from where magnetism is born with rotation. And actually electric fields have no poles. There is only one kind of charge. Charge always moves. If the charge twist to the left.....it emits a negative charge. To the right....positive charge. It'a all direction.