Magnetic fields

[Sriman Dutta]

We have two notions of the magnetic field. One is the B field, commonly called the magnetic flux density and the other one is the H field, also called the magnetic field strength. However, I want to know the difference between them. Most equations involving magnetic field uses B. However what is the use of H is still not clear to me. I have seen some relations between them in Wikipedia. However I couldn't understand that well.

So please show how they are different and in what way the H field is useful.

[Bender]

https://en.m.wikipedia.org/wiki/Ampère%27s_circuital_law

 

H is useful for calculating the flux density in magnetic circuits with different magnetic materials.

 

I find it especially useful when working with permanent magnets.

http://www.electronics-tutorials.ws/electromagnetism/magnetic-hysteresis.html

 

When using Hopkinson's law for magnetic circuits, B is the "current density" and H is related to the voltage.

Edited April 16, 2017 by Bender

[studiot]

Have you studied electric fields?

 

The relationship between B and H is very similar to the relationship between E and D.

 

In many situations one is a constant times the other but in non-isotropic media they may point in different directions (they are all vectors).

 

If you let me know whether you understand about E and D I will explain further.

[Sriman Dutta]

I know about the E field. But the concept of D field is new to me. To speak the truth I haven't seen it before.

 

But I know about the E field well enough.

It can be described as the force exerted on a test charge when it passes through the sphere of influence of another electrically charged body( considering the charge on the test particle negligible).

[math]E=\frac{F}{q}[/math]

Another popular notion is that E is the electric flux density. It is the derivative of the electric flux with respect to the surface through which the flux is considered.

[math]E=\frac{d\phi_E}{dS}[/math]

By Gauss' Law, we have yet another relation:

[math]\int_S E.dS = \frac{Q}{\epsilon_0}[/math]

Edited April 18, 2017 by Sriman Dutta

[studiot]

OK thank you for that information.

 

The teaching of electricity and magnetism nearly always runs along the following path these days.

 

A force on a suitable body is noted and an electric/magnetic effect deduced to account for it.

This effect is defined in terms of the force produced and the position in space and is a vector quantity.

 

The work done as the body moves around is calculated and related to the position to define a potential field.

 

Sometimes a second vector quantity is defined as a vector derived from the first one.

Either E and B can be defined first, with D and H as the derived vectors or the other way round (which is the older method).

 

But often the significance of the second vector is not presented, hence your question.

 

So consider this statement in the light of the following.

 

You need two vectors to have a dot (scalar) product and energy is a scalar.

 

Starting with a mechanical example we have

 

Stored Mechanical Energy per unit volume = 1/2 stress x strain

 

Stored Electrical Energy per unit volume = 1/2 E x D

 

Stored Magnetic Energy per unit volume = 1/2 B x H

 

edit (note these are all dot products not cross products)

 

Are you beginning to see a pattern ?

 

There are differences in the nature of stress, E and B but scalar multiplied by another suitable vector they yield the energy stored in the system.

 

There are actually many more examples that could be listed and they all spring from a common root in continuum mechanics.

 

How are we doing?

Edited April 19, 2017 by studiot

[Sriman Dutta]

So electrical energy stored per unit volume is 0.5*E*D. But both units should be of N/C ( though I don't know the exact unit of D).

Moreover I knew that the formula to find the electrical potential energy is

[math] Energy= k\frac{Qq}{r}[/math]

[studiot]

So electrical energy stored per unit volume is 0.5*E*D. But both units should be of N/C ( though I don't know the exact unit of D).

Moreover I knew that the formula to find the electrical potential energy is

[math] Energy= k\frac{Qq}{r}[/math]

 

I am a little unsure from this reply where you want to go from her or even if you want to carry on the discussion?

 

Can you not find out what the units of E and D and the k you mention in your version of Coulomb's law?

[Sriman Dutta]

Well, I am not sure about the formula.

[KipIngram]

Sriman: you could think of H and B as roughly analogous to voltage and current in a resistive circuit. Don't read too much into the analogy, but just as V and I are proportional for a given resistor, H and B are proportional for a given material. But voltage obeys Kirchoff's Voltage Law - its integral around a closed path is zero -, whereas current obeys Kirchhoff's Current Law - the sum of currents entering or leaving any point in a circuit is zero.

 

For H and B, you have similar behavior. The integral of B over any closed surface is zero (no magnetic monopoles, divergence of B is zero), whereas the integral of H around a closed path is equal to the ampere-turns encircled by the path (curl of H = J).

 

In a medium of constant permeability both sets of relations would hold for both B and H, with appropriate proportionality factors. But that's the "physics difference" between them. H is something that satisfies a line integral / curl related law; B is something that satisfies a surface integral / divergence related law.

 

Hope this helps!

[Sriman Dutta]

Oh....that's great. I get to see it. Thanks very much. :-)