# magnetic and electric fields

#### PG1995

Joined Apr 15, 2011
816
Hi

There is almost one-to-one correspondence between magnetic and electric fields. It is not very surprising in view of the fact that one cannot exist without the other, they are like twins. Please note that I don't need very rigorous approach towards these concepts because I have just started learning all this stuff. Thanks.

The term magnetic field can refer to two closely related fields: B and H. B is also called magnetic flux density or magnetic induction. Likewise, H is often called magnetic field intensity. But, in my view, calling them H-field and B-field is a rather good choice.The distinction between the two is important. This page could be quite helpful for this. Summarily, H is the field actually generated by electric current while B is enhanced magnetic field due to response of some other material. In other words, H could be said as 'causative field' and B as 'responsive field'. For example, if a solenoid has an iron core, it's magnetic field is increased manifolds.

Both vector fields are related: B=μH, where μ is called permeability or magnetic constant of a material. As it is obvious from the relation that both fields point in the same direction. The magnetic constant of free space or vacuum is 4π × 10−7 H/m. It means that free space will increase the H field by 4π × 10−7 factor.

Q1: Is there any material which does not affect the H field and leave it as it is. In such a case, μ would be unity. Metglas has μ=1.25. For superconductors μ=0.

A similar relation also exists for electric field, D=εE, where ε is permittivity of the medium. For free space ε0 = 8.85 × 10−12 F/m. Here one thing should be keep in mind that permittivity is is the measure of the resistance that is encountered when forming an electric field in a medium. Therefore, higher the permittivity, the higher the resistance. In layman terms, D is charge density on a surface (charge could be negative or positive), and this charge density gives rise to electric field E. D is very similar to H in that in case of the H the product "nxI" determines the strength of H (H=nI, where "n" is number of turns per unit length and "I" is current) while in case of D quantity of charge per unit area determines its strength. More charge density means strong electric field. So, it can be said D is 'causative field' and 'E' is responsive field.

Q2: This question is quite similar to Q1. Is there any material which neither resist electric field not enhance it? Even free space has some resistivity to offer to the electric field.

Thank you for the help.

The following link(s) could be useful to someone like me:
1: http://www.ie.itcr.ac.cr/acotoc/Maestria_en_Computacion/Sistemas_de_Comunicacion_II/Material/Biblio2/chapt03.pdf
2: http://www.antenna-theory.com/definitions/electricfluxdensity.php

Regards
PG

#### crutschow

Joined Mar 14, 2008
24,706
Certainly you can have a magnetic field without an electric (external) field such as from a bar magnet.
And you can have a electric field without a magnetic field, such as from a charged dielectric.
So your generality about a one-to-one correspondence between the two is not always true.

Most dielectrics have little effect on a magnetic field.

What do you mean "Even free space has some resistivity to offer to the electric field"?

#### steveb

Joined Jul 3, 2008
2,436
I can try to give some guidance here, on a point by point basis.

One of your references (Chap 3) is excellent and you should use this and read all points very carefully. All of the critical information is in there. In the other thread I mentioned I would try to track down a good reference on your questions, but no need because this one is very good.

The other reference is not very useful for you right now. You see there a hint about anisotropic media, and the main point here is that permeability and permittivity can in general be 2nd rank tensors, which would be represented by a 3x3 matrix. It's good to know this now, but it is still too early for you to worry about it too much.

The term magnetic field can refer to two closely related fields: B and H. B is also called magnetic flux density or magnetic induction. Likewise, H is often called magnetic field intensity. But, in my view, calling them H-field and B-field is a rather good choice.The distinction between the two is important.
Seems good to me.

Summarily, H is the field actually generated by electric current while B is enhanced magnetic field due to response of some other material. In other words, H could be said as 'causative field' and B as 'responsive field'. For example, if a solenoid has an iron core, it's magnetic field is increased manifolds.
This seems not quite right to me. First, one can say that charges and currents are the sources that generate fields, and the fields have relationships between each other. I would say that B is the more fundamental field in the sense that Maxwell's equations in free space are written in terms of B and E, and there is no need to define H and D. Also, force is used to define B and E, which makes them more logical choices for the basic fields. Then H and D are useful when other material properties are considered.

You can consider D to be a response to E, although more generally, D can be a response to both E and B. Also H can be considered a response to E and B as well, though usually it is a response to B only, and E does not matter too much in most cases.

Both vector fields are related: B=μH, where μ is called permeability or magnetic constant of a material. As it is obvious from the relation that both fields point in the same direction. The magnetic constant of free space or vacuum is 4π × 10−7 H/m. It means that free space will increase the H field by 4π × 10−7 factor.
In free space there is no problem here. In the more general case of matter, H and B do not necessarily have to be in the same direction (see anisotropic materials).

Q1: Is there any material which does not affect the H field and leave it as it is. In such a case, μ would be unity. Metglas has μ=1.25. For superconductors μ=0.
There are many material that have very small magnetic interactions with μ nearly that of free space. You can google a table of values for various media.

A similar relation also exists for electric field, D=εE, where ε is permittivity of the medium. For free space ε0 = 8.85 × 10−12 F/m. Here one thing should be keep in mind that permittivity is is the measure of the resistance that is encountered when forming an electric field in a medium. Therefore, higher the permittivity, the higher the resistance. In layman terms, D is charge density on a surface (charge could be negative or positive), and this charge density gives rise to electric field E. D is very similar to H in that in case of the H the product "nxI" determines the strength of H (H=nI, where "n" is number of turns per unit length and "I" is current) while in case of D quantity of charge per unit area determines its strength. More charge density means strong electric field. So, it can be said D is 'causative field' and 'E' is responsive field.
I'm not crazy about this description, but it will probably suffice for now. The big blunder here is that D is not charge density at the surface. There is some similarity, but D is a vector and charge is a scalar.

Q2: This question is quite similar to Q1. Is there any material which neither resist electric field not enhance it? Even free space has some resistivity to offer to the electric field.
Again I'm not crazy about this description. I don't like to think of free space having resistivity to fields. Free space has electric field in response to charge. If a material is there, then additional net effective fields are set up due to the material responding to the field.

The only thing that comes to mind is that conductors have different properties, and a super conductor would have the most different effect. The electric field will be small in a conductor, at least in the static case. I wouldn't say that the material does not resist/enhance, because the material will allow charges to flow until the net field from the new charge distribution cancels out the originating field.

#### WBahn

Joined Mar 31, 2012
25,545
A book that I would highly recommend -- in fact, it is (in my opinion) by far the best written textbook, in any field, I have ever come across -- is Electromagnetic Fields by Roald K. Wangsness. One of the things I really liked about the book was that each equation presented includes solid hints/references to prior results. For instance, he might say something like, "Combining the results of 12-3 and 12-4, in light of 10-6 and drawing upon 3-5, 4-9, and 6-2, we arrive at 12-5." By referencing all of the equations needed to make the next transition, he provides you with references to the material from which those equations sprang, if you need to review, and also doesn't leave you hanging in the wind because you don't recall some obscure relationship from the prior semester. This last point was particularly valuable for me because my Intermediate E&M course used Naffey (sp?), which I not-so-lovingly refer to as the black book from Hell. So I had to spend a lot of time learning the prior material and the backward references were wonderful for that. Also, the first chapter is an outstanding review of vector calculus.

#### PG1995

Joined Apr 15, 2011
816
Certainly you can have a magnetic field without an electric (external) field such as from a bar magnet.
And you can have a electric field without a magnetic field, such as from a charged dielectric.
So your generality about a one-to-one correspondence between the two is not always true.

Most dielectrics have little effect on a magnetic field.

What do you mean "Even free space has some resistivity to offer to the electric field"?
Thank you, Carl.

Perhaps, I was simply oversimplifying things. Thanks for pointing this out.

I was wrong where I said even free space has some resistivity to offer to electric field. If a change is placed in free place then the electric field originating from this charge or induce in free space is proportional to the charge and constant of this proportionality is ε_0. I hope I have it right this time.

Regards
PG

#### PG1995

Joined Apr 15, 2011
816
A book that I would highly recommend -- in fact, it is (in my opinion) by far the best written textbook, in any field, I have ever come across -- is Electromagnetic Fields by Roald K. Wangsness. One of the things I really liked about the book was that each equation presented includes solid hints/references to prior results. For instance, he might say something like, "Combining the results of 12-3 and 12-4, in light of 10-6 and drawing upon 3-5, 4-9, and 6-2, we arrive at 12-5." By referencing all of the equations needed to make the next transition, he provides you with references to the material from which those equations sprang, if you need to review, and also doesn't leave you hanging in the wind because you don't recall some obscure relationship from the prior semester. This last point was particularly valuable for me because my Intermediate E&M course used Naffey (sp?), which I not-so-lovingly refer to as the black book from Hell. So I had to spend a lot of time learning the prior material and the backward references were wonderful for that. Also, the first chapter is an outstanding review of vector calculus.
Thank you, WBahn, for taking time to recommend this book and reviewing it. I have looked it up. It looks little advanced for me at this stage. Perhaps, I can use it in future. Anyway, I have included it in my list of useful books.

Regards
PG

#### PG1995

Joined Apr 15, 2011
816
My special thanks to you for taking time to provide me guidance on a point by point basis. I understand that my understanding of these concepts is naive and there are quite a few loopholes.

steveb said:
This seems not quite right to me. First, one can say that charges and currents are the sources that generate fields, and the fields have relationships between each other. I would say that B is the more fundamental field in the sense that Maxwell's equations in free space are written in terms of B and E, and there is no need to define H and D. Also, force is used to define B and E, which makes them more logical choices for the basic fields. Then H and D are useful when other material properties are considered.

You can consider D to be a response to E, although more generally, D can be a response to both E and B. Also H can be considered a response to E and B as well, though usually it is a response to B only, and E does not matter too much in most cases.
A static charge(s) is source of electric field and a moving charge(s), also called electric current, is responsible for magnetic field. Correct?

You are right in saying that E and B are more logical choices because force is used to define them and force has more intuitive and natural 'feel' for understanding as compared to D and H which don't involve the concept of force. But in my view, E and B are given quantitative treatment using D and H. Let me elaborate on this a bit. There can be no E without D because charge is what gives rise to electric field, therefore by establishing relationship between E and D, it can be found out what 'quantity' of E would be produced by a certain quantity of 'D'. The same argument goes for B and H where there can be no B without H where H=ni.

steveb said:
In free space there is no problem here. In the more general case of matter, H and B do not necessarily have to be in the same direction (see anisotropic materials).
OK. But B=μH, where B and H are both vector quantities and vector quantities cannot be equated unless they are vectors pointing in the same direction. This is what led me to say that B and H point in the same direction. If they don't always point in the same direction then I would argue that the relation B=μH isn't always true.

steveb said:
There are many material that have very small magnetic interactions with μ nearly that of free space. You can google a table of values for various media.
I was wrong about Q1 where I said, "Is there any material which does not affect the H field and leave it as it is?". Suppose you have a solenoid in free space. It's H-field is given by H=ni, where "n" is number of turns per unit length and "i" is direct current flowing through the turns. We also have a straight wire carrying direct current adjacent to the solenoid. The wire would experience force due to magnetic field of the solenoid. By changing either "n" or "i" you can affect the strength of B field and consequently force experienced by the wire. Though my understanding could be really crude, I think calling the quantity "H=ni" an H-field is just a fancy label for it. In my view, the quantity H just tells us how much effort is being put into establishing the B field. Actually in my Q1, I was saying that when we could have μ=1. Now I think that depends on how we define B- and H-fields. For instance, in Newton's 2nd law we have: F=kma, where "k" is constant of proportionality. In SI system, 1 newton is defined as the force which gives rise mas of 1 kg an acceleration of 1 m/s^2. Therefore, k=1.

steveb said:
I'm not crazy about this description, but it will probably suffice for now. The big blunder here is that D is not charge density at the surface. There is some similarity, but D is a vector and charge is a scalar.
Yes, you are right that D is a vector quantity. But I would say (as I said in the other thread) that there is quite a similarity between the two, isn't there? Assume for the sake of argument that charge density is also a vector quantity directed in the same direction as D, would you still say D and charge density are different quantities?

steveb said:
Again I'm not crazy about this description. I don't like to think of free space having resistivity to fields. Free space has electric field in response to charge. If a material is there, then additional net effective fields are set up due to the material responding to the field.
It really helped me where it says, "Free space has electric field in response to charge.". I agree. And as I said above in another post that I was wrong where I said even free space has some resistivity to offer to electric field. If a charge is placed in free place then the electric field originating from this charge or induced in free space is proportional to the charge and constant of this proportionality is ε_0.

Best wishes
PG

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#### steveb

Joined Jul 3, 2008
2,436
A static charge(s) is source of electric field and a moving charge(s), also called electric current, is responsible for magnetic field. Correct?
That is basically correct. Complications come about when we talk about frames of reference and dynamic cases. However, for a basic description and particularly for static cases, this suffices.

Just to highlight the problem with making general statements like this. Consider an antenna that uses current flow as the source to generate the fields. Here an electromagnetic wave (which has both E and B fields) is generated by a current only.

You are right in saying that E and B are more logical choices because force is used to define them and force has more intuitive and natural 'feel' for understanding as compared to D and H which don't involve the concept of force. But in my view, E and B are given quantitative treatment using D and H. Let me elaborate on this a bit. There can be no E without D because charge is what gives rise to electric field, therefore by establishing relationship between E and D, it can be found out what 'quantity' of E would be produced by a certain quantity of 'D'. The same argument goes for B and H where there can be no B without H where H=ni.
I think you make a valid point. In the final view of EM theory, E,D,B and H are all important fields, and saying one is more fundamental than another is probably a matter of viewpoint. It is often possible to build a logically consistent theoretical framework using different foundations.

OK. But B=μH, where B and H are both vector quantities and vector quantities cannot be equated unless they are vectors pointing in the same direction. This is what led me to say that B and H point in the same direction. If they don't always point in the same direction then I would argue that the relation B=μH isn't always true.
This relation is true if we consider that μ is a second rank tensor in the more general case of anisotropic media. A second rank tensor can be respresented as a 3x3 matrix. Remember that μ=μoμr in general and if μr is a 3x3 matrix, then the direction of B can be different than the direction of H.

Yes, you are right that D is a vector quantity. But I would say (as I said in the other thread) that there is quite a similarity between the two, isn't there? Assume for the sake of argument that charge density is also a vector quantity directed in the same direction as D, would you still say D and charge density are different quantities?
I would say that there is a similarity to some extent, but personally, I wouldn't try to think of "charge as a vector quantity directed same as D". I made some comments in the other thread about this. I would say that if you just want to have a mental picture to help you, and if you don't try to do anything mathematical with this concept, then it isn't harmful to hold on to your viewpoint for a while.