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I am currently learning university-level electromagnetism and have a problem arranging that with pre-existing school-knowledge. Unfortunately, the books I looked into so far simply introduce the electric and magnetic fields without any regard to how it is taught in high school...

I find the subject quite confusing and would be thankful for some clarifications on the matter:

  1. We are taught that the electromagnetic force is one fundamental force -> what and why is this split between electic and magnetic forces?
  2. The electric field acts on charged particles (+ or -), -> the magnetic field acts on dipoles? Do I need to categorically split materials into electric ones and magnetic ones?
  3. From a book: "All static magnetic fields are produced by moving electric charge." -> then how do I understand ordinary magents that are not connected to any power source?
  4. The force of a magnetic field on a charged particle (I assume something like an electron) is dependent on the speed of said particle. -> Then what is the force between two non-moving magnets?, and on what exactly is it acting?
Qmechanic
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Adam
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3 Answers3

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Be patient; you'll see that everything you learn will be consistent with what you know, and you'll be able to understand electromagnetism better!

  1. Electric fields can turn into magnetic fields (and vice versa) when you change reference frames. When working in a single reference frame, it's useful to distinguish between electric and magnetic fields (and forces), but they're really two sides of the same coin.
  2. The force on a charged particle is called the Lorentz force. Both electric fields and magnetic fields exert forces on charged particles. Electric charge (and dipoles) differ from magnetic dipoles. Notably, magnetic charge has not been observed to exist, though if it did, Maxwell's equations would be symmetric between the electric and magnetic fields.
  3. Ordinary magnets are assemblages of magnetic dipoles. In the Amperian model, these can be modelled as little current loops (and hence moving electric charge). The little current loops circulate forever, not requiring an external power source.
  4. The force between two magnets results from the force on a magnetic dipole in an external magnetic field with a gradient. The same thing happens between two electric dipoles!
DanDan0101
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    Your part 1 is pedagogically going to cause students to think that you can convert a pure magnetic field into a pure electric field, when in fact, and I think you know, Lorentz invariant quantities enforce that this transformation is impossible. – naturallyInconsistent Oct 24 '23 at 15:03
  • @naturallyInconsistent What do you think is a clearer way to phrase it? That's a good point and I want to make an edit. – DanDan0101 Oct 24 '23 at 21:10
  • @naturallyInconsistent I didn't understand your point... If a moving charge interacts with a magnetic field, if you move to the rest-frame of this charge, because now the charge isn't moving, it can only interact with and electric field, so a magnetic field has become an electric field by this transformation, no? – Nadav Har'El Oct 24 '23 at 22:04
  • @DanDan0101 I have an answer below, you know? I addressed that. – naturallyInconsistent Oct 25 '23 at 01:04
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    @NadavHar'El Not at all. If you study the Faraday tensor formulation, you will learn that while the energy $\propto(E^2+B^2)$ is going to be Lorentz transformed between frames, there are Lorentz invariants $E^2-B^2$ and $E\cdot B$; this means that there is no transformation you can do that converts a pure magnetic field into a pure electric field, and vice versa, and their behaviour is simply different. – naturallyInconsistent Oct 25 '23 at 01:07
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  1. We are taught that the electromagnetic force is one fundamental force -> what and why is this split between electic and magnetic forces?

We found out that electric and magnetic fields can be converted partially into each other and thus cannot be studied completely separately from each other, but rather must be merged into one coherent understanding. However, at the same time, we can mathematically prove that a pure electric field will never be able to be converted into a pure magnetic field, and vice versa, and so it is necessary to have both, not just one of them. They simply differ in their behaviour, both in Maxwell's equations, and in the Abraham-Lorentz force law.

  1. The electric field acts on charged particles (+ or -), -> the magnetic field acts on dipoles? Do I need to categorically split materials into electric ones and magnetic ones?

From here onwards you need to know an important fact:

Every magnetic dipole is mathematically equivalent to a tiny Ampère-ian loop of wire with a current flowing through it, both in how it sets up a magnetic field that way, and in how it would be affected by externally applied magnetic fields. This means that you can mathematically replace all magnetic stuff to just talking about electric charges.

The electric field acts on charges, and magnetic field acts on moving charges, both governed by the Abraham-Lorentz force law. Then you can derive how magnetic field acts on magnets, since a magnet would just be equivalent to many loops of wire with current in them.

  1. From a book: "All static magnetic fields are produced by moving electric charge." -> then how do I understand ordinary [magnets] that are not connected to any power source?

Actually, these are often mostly about the spins of the electrons or ions inside the magnetic materials, and thus should not be considered as actually having currents moving at all. However, as mentioned above, even this spin is to be mathematically converted into loops of wire, and it is in that form that we might pretend that this statement is true.

  1. The force of a magnetic field on a charged particle (I assume something like an electron) is dependent on the speed of said particle. -> Then what is the force between two non-moving magnets?, and on what exactly is it acting?

The loop of wire with current in it would have a certain magnetic moment. The coupling of the magnetic moment to the magnetic field brings about a certain energy term, and that is just the same as an electric dipole v.s. an electric field. If you look up the Wiki page for the many terms above, in particular the magnetic moment, you will find out how we deal with things.

However, again, this is a simplification, albeit one that trades a tremendous amount of vector integral calculus into a much simpler thing to deal with, basically opening up the analysis that would otherwise be too much for a beginner. You could, however, learn to integrate the forces two loops of wire with current flowing through them would exert on each other, if you really so wish; even though this is but a mathematical exercise of very little practical physical insight and physical utility.

naturallyInconsistent
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Your question has a huge scope, and I can't do it justice in a short reply, but I'll try:

You can think of the electromagnetic field as generating two different forces: The electrostatic force (Coulomb force) which you studied in school, where the electric field acts on charged particles, e.g., electrons, whereas the Lorentz force the magnetic field acts on moving charged particles and is proportional (and orthogonal!) to their velocity. In Einstein's special relativity, these two effects are basically the same - in a frame moving with a charged particle, the magnetic field transforms into an electric field which affects the now-still charged particle.

You asked about magnets. Magnetism is caused by electrons around atoms and spinning in themselves, so is indeed caused by moving charges. Because a piece of material has a huge number of electrons, their magnetic field can cancel each other or enforce each other - under certain conditions all the magnetic fields are aligned in the same direction, don't cancel each other, and the material becomes a macroscopic "magnet".

Nadav Har'El
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    Under standard physics, spin is an intrinsic property and not due to movement of charges; that we pretend the magnetic moment is equivalent to a tiny current loop is just mathematical fiction that works too well to discard. – naturallyInconsistent Oct 24 '23 at 15:01
  • I agree that this was an over-simplification. However, a magnetic moment due to real, orbital, circular motion also exists so this idea of charges rotating around inside a material that appears to be sitting still is not entirely fictional. Whether or not electrons are really "spinning" around their axis is a good question (if they are point particles, they can't!), but as you said the mathematics certainly behaves as if they do. – Nadav Har'El Oct 24 '23 at 17:02
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    @naturallyInconsistent Total angular momentum is conserved, but spin is not, spin is interconvertible with macroscopic rotation; the fact that an electron cannot have zero spin is an independent constraint. To me this means spin really is a form of rotation, and "but nothing is really spinning!" is either wrong or moot. – zwol Oct 24 '23 at 18:34
  • @zwol, P.SE is about standard physics. I'm myself in favour of an extended wavefunction spinning, but that is not standard physics. – naturallyInconsistent Oct 25 '23 at 01:04
  • @naturallyInconsistent IMHO this is the territory of interpretations -- there's no experiment we can do that will probe whether an electron "is really spinning", although I'll point out that it has been demonstrated that you can apply a torque to a macroscopic object by shining polarized light on it -- so I'll just leave it by saying that I think "but nothing is really spinning!" is pedagogically counterproductive, making students think that spin doesn't transfer angular momentum. – zwol Oct 25 '23 at 13:13