Why magnets attract and repel each other?

I have been studying physics recently, electromagnetism in particular. At some point, I realized that I did not understand why magnets attract each other. We have four fundamental forces: electromagnetic, weak, strong, and gravitation. Obviously electromagnetic force is responsible for repulsion and attraction of magnets. But how exactly does it work?

Attraction and repulsion between electric charges is simple enough for me and does not need further explanation (as for now, at least). But a force between magnets seems so weird and complicated... and if electric force and magnetic force are not the same then we have five fundamental forces, not four. So there must be a way to explain magnetic force using electric force.

I was looking on the Internet for the explanation and I could not find anything that would satisfy me. In one video on YouTube, Richard Feynman refuses to answer the question why magnets attract each other by saying that this is something he simply cannot explain to a layman. There is also a video by some weird dude which explains it in a way that at the first glance seems totally wrong. Finally, I found a video by MinutePhysics in which they say that “if you want to know why [particles] are tiny magnets you may as well ask why are particles charged in the first place (…) no one knows.” Although they explain internal structure of magnets, they do not address the question why magnets attract or repel, depending on how we would place them relative to each other. Explaining a big magnet boils down to saying that it consists of many tiny magnets. Alright. But why tiny magnets attract or repel each other? Why the force between them is the way it is?

One piece of the puzzle is the analysis of a magnetic force created by a current in a wire. The source of this force is due to electric force and relativity. There is a plenty of videos on the Internet explaining that. So we understand why current generates magnetic field and we know how its field lines look like.

Second piece of the puzzle are the field lines generated by a magnet. They are of course different to field lines generated by a wire. But after some creative thinking, it is possible to figure out that if we make a loop out of the wire, the resulting shape of field lines will be exactly the same as with the permanent magnet. In hindsight, it seems easy.

So the permanent magnet is like a loop of current. If you put two loops with the currents running in the same direction on top of each other, they will attract as two straight wires with the currents running in the same direction will attract. This is why south of one magnet is attracted to the north of the other magnet. However, if you put two loops with the currents running in the opposite directions on top of each other, they will repel because two wires with the current running in the opposite directions repel. This is why magnets repel when you try to connect them through their south poles or north poles.

A permanent magnet is made of many little aligned loops of current. A small part of magnetic field is due to aligned electron orbitals. Much bigger part is due to aligned spins of electrons. So you may think about an electron as a little loop of wire, although this is probably not perfectly accurate, as seemingly there is no definite path on which the charge circulates inside the electron.

I went to a nearby university to confirm with a local physics professor that modelling a magnet with a loop of wire is a good idea. It got confirmed. So I made a YouTube video about it, to fill the apparent niche. See below.

Finally, there are a number of further questions that remain unanswered to me, but which I hope I will solve, as I dive deeper into the subject (some of them will surely turn out silly):

• It is so easy to explain (with no math!) why an electron moving along the wire with a current is attracted or repelled by the wire. But why an electron moving perpendicular to the wire has a force acting on it?
• Given the electron’s charge, what is the implied diameter of or the current in the “loop inside the electron?” Does the answer make sense when compared to classical estimates of electron’s diameter?
• Are electron spins actually aligned as magnet is created or do they merely have to point in any direction with positive component in the direction of magnetic moment of the entire magnet? Experimentally, will a resulting magnetic field be closer to a sum of perfectly aligned electron magnetic fields or closer to a sum of fields randomly distributed as long as they are not pointing in the wrong direction?
• Suppose electric force is caused by particles emitted by a charged particle which move with the speed of light and change momentum of another charged particle whenever they “hit” one. We can experimentally verify this hypothesis. Presence of charges “weakens” the field if the particles get “absorbed.” Something aka electron absorbing a photon. We can shield ourselves from electromagnetic radiation. But can we shield ourselves from an electric field? And I am not talking about building a Faraday’s cage. I am talking about reducing electric field by placing any charges (even neutralized by opposite charges nearby) between me and the source of the field in question. Were there any experiments that verified this reduction does not happen, so the hypothesis about emitted particles was proven wrong? I need to know it, so that I can accept superposition principle, move on, and eventually sleep safe and sound.

May the (magnetic) force be with you!