A general problem with magnetism

In summary, the magnetic field can be categorized into two forms: one due to charges in motion (both free and bound) and the other due to changing electric fields (as in electromagnetic waves). However, these two forms are identical in terms of vector calculus, making it difficult to distinguish between them without knowledge of the current densities and electric fields in the region. Attempts to divide the magnetic field into different forms may be meaningless. There is also a theoretical concept of magnetic monopoles, but their existence is still debated and their role in the quantization of electric charge has been proposed by P.A.M. Dirac.
  • #1
Tanja
43
0
I'm completely confused because of a previous post on Newtons second law and magnetism! Can someone help me to find a connecting or a superior explanation for the magnetic field as it appears in its the 2 forms?

1.) In some solid due to spin alignment.
2a.) In a cirque current flow.
2b.) In electromagnetic waves and as a special potential for the Maxwell's equations.

And what would happen to the solution of Maxwell's equation if div B wouldn't be zero, claiming that there are magnetic monopols? And what if the flux of the magnetic field over any closed surface S wouldn't be zero?

Thanks
 
Physics news on Phys.org
  • #2
Try to answer one clear specific question at a time.
Your confusion could be resolved by reading a good textbook at the
advanced UG or graduate level.
 
  • #3
Tanja said:
I'm completely confused because of a previous post on Newtons second law and magnetism! Can someone help me to find a connecting or a superior explanation for the magnetic field as it appears in its the 2 forms?

1.) In some solid due to spin alignment.
2a.) In a cirque current flow.
2b.) In electromagnetic waves and as a special potential for the Maxwell's equations.


I would argue on this division of the magnetic field, because "spin alignment" *is* a "cirque current flow" on the atomic scale (roughly speaking)

A more natural division is:

magnetic fields due to charges in motion, both free and bound, specified by the maxwell equation:

[tex]
\nabla\times\mathtbf{\vec B}=\mu_0\mathtbf{\vec J}
[/tex]

And magnetic fields due to changing electric fields, as in electromagnetic waves, specified by the maxwell equation

[tex]
\nabla\times\mathtbf{\vec B}=\mu_0\epsilon_0\frac{\partial\mathtbf{\vec E}}{\partial t}
[/tex]

But since both these fields still have [tex]\nabla\cdot\mathtbf{\vec B}=0[/tex] one cannot distinguish one from the other simply by measuring the curl and the divergence and having no knowledge of the current densities and electric fields, so the division of the magnetic field is meaningless alltogether.

Tanja said:
And what would happen to the solution of Maxwell's equation if div B wouldn't be zero, claiming that there are magnetic monopols? And what if the flux of the magnetic field over any closed surface S wouldn't be zero?

Well first of the one is a conseqence of the other, that is:

[tex]
\nabla\cdot\mathtbf{\vec B}=0\,\Leftrightarrow\,\oint_\mathcal{S}{\vec B}\cdot d\mathbf{\vec a}=0
[/tex]

(To verify, apply the divergence theorem). If the magnetic flux through a closed surface was non-zero, there would have to be somewhere within where magnetic field lines begun or ended: a magnetic monopole. A full treatment of maxwell equations, including magnetic monopoles has been made, but it is rather crumblesome, but does imply an even greater symmetry between electric and magnetic fields.

In the context of relativity, magnetic monopoles are quite meaningless, as here, a magnetic field is just an electric field from another point of view and vice versa, so electric charge alone can account for both types of fields. In quantum mechanics however, scientists beg for them to exist. P. A. M. Dirac proposed on a theoretical argument that the existence of magnetic charge, just a single one, anywhere in the universe, would account for the quantizitaion of electric charge.
 
  • #4
Troels said:
I would argue on this division of the magnetic field, because "spin alignment" *is* a "cirque current flow" on the atomic scale (roughly speaking)

Even in a hydrogen atom the electron doesn't rotate in a circuit around the nuclei. The most likely place to be is a sphere and there would be no definite direction of the magnetic field. As you probably know, in other atoms it's much more compleceted and I don't think that there is a case where the average electron movements can be compared to a cirque current flow. The only example I could imagine is are excitons, but they don't exist in solids with magnetic properties.

I don't understand what you mean in the middle part.

Thanks a lot for the hint on Dirac and on the full treatment of maxwell equations, including monopoles. I'll try to find more information there.
 
  • #5
Tanja said:
Even in a hydrogen atom the electron doesn't rotate in a circuit around the nuclei

I am aware of that. I didn't set out to give a complete quantum mechanical treatment of magnetization (we are, after all in the forum "classical physics"), which I tired to emphazise with the remark "roughly speaking". but the essential point remains: quantum mechs or not, magnetic fields are still due to the motion of electric charges OR alternating electric fields (or a combination thereof). And the two have completely identical properties as far as vector calculus is concerned, which means that you cannot tell what the source of a particular magnetic field is, unless you happen to have knowlegde of electric fields and current densities in the region.

Tanja said:
Can someone help me to find a connecting or a superior explanation for the magnetic field as it appears in its the 2 forms?

The morale is: It is rather pointless to attempt to make a distinction between "different forms" of magnetic fields, because you won't be able to tell them apart anyway. They may have different sources, true, but a measurement of the magnetic field alone cannot tell which.
 
Last edited:

What is magnetism?

Magnetism is a fundamental force of nature that results from the movement of electric charges. It is the force that causes certain materials, such as iron, to attract or repel each other.

What is a general problem with magnetism?

A general problem with magnetism is that it can weaken over time, causing magnets to lose their strength and become less effective.

What causes magnets to weaken?

There are a few factors that can cause magnets to weaken, such as exposure to high temperatures, physical damage, and demagnetizing fields created by other magnets or electrical currents.

Can magnets lose their magnetism completely?

Yes, magnets can lose their magnetism completely if they are exposed to extreme temperatures or strong demagnetizing fields. However, this is a gradual process and can take a long time to happen.

Can magnets be re-magnetized?

Yes, magnets can be re-magnetized by exposing them to a strong magnetic field again. This process is commonly used to restore the strength of weak magnets.

Similar threads

  • Electromagnetism
Replies
5
Views
151
Replies
2
Views
787
  • Electromagnetism
Replies
7
Views
948
Replies
32
Views
3K
Replies
9
Views
1K
Replies
10
Views
2K
Replies
7
Views
1K
Replies
27
Views
3K
  • Introductory Physics Homework Help
Replies
11
Views
1K
Replies
11
Views
2K
Back
Top