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Earlier today I asked about the differences and connections between electric fields and magnetic fields explained to me intuitively, and I was given the answer "It's complicated and you need to study on your own", with a link to a wikipedia page on tensors (I hardly understood any of it) and a video of Richard Feynman being a condescending jackass. This is not enough of a response for me.

I want to clear up, first of all, that when I ask for an intuitive explanation, I do not mean "explain it with a clever analogy", which is always what physicists assume I mean. An example of an intuitive explanation of an electric field is the following:

"Some particles have an electric charge, either + or -. When there are 2 particles with the same charge, they repel each other. Opposite charges attract. However, since there are lots of charged particles in the world, any one charge is effected by multiple other charges at once. Because of this, we use a model called an electric field, which describes the net force a charge will experience at any point in space due to the electric charges of particles in its surroundings. We can also describe a single particle or group of particles as having an electric field. This electric field is the effect that the particle or group of particles has on other charges in its surroundings."

See? No rubber band analogies, but also no equations with variables and symbols you don't learn about in an intro to physics course. And whenever a vocab word is introduced (like electric field), it is defined, instead of me providing a link to a wikipedia article that uses such cryptic lingo that I would need a bachelor's degree in physics in order to follow in the first place.

Yes, I am bitter.

And I understand that there are questions that can't be easily answered like this. I understand I may need to due research on my own. But where the hell do I start? I've been linked to Wikipedia a couple of times, and that just made things more confusing. And I don't have any intentions of shelling out the money to get a second degree just so I can get an answer.

What do I do? Where do I go to understand it? Are there any sites for this? Any books?

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  • $\begingroup$ Sorry, but some things are just deep! You asked for "the origin of magnetism". That's a tall order, because while we can derive magnetism, there simply is no route to that derivation without equations and prerequisites. Sure, we could insert an introduction to special relativity before the beginning of the existing answers, and insert an introduction to calculus before the beginning of that answer -- but then we'd have an extremely clunky, ten page answer that's neither fun to read or write. $\endgroup$ – knzhou Nov 14 '16 at 4:40
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    $\begingroup$ There are a few things we can do. We can tell you how we know magnetism exists, but not explain its origin. We can explain its origin with a lot of pictures -- but most of the explanation would be a lie. We could give a really sketchy outline of the true explanation, but it would be unsatisfying, because you'd see the huge holes. $\endgroup$ – knzhou Nov 14 '16 at 4:42
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    $\begingroup$ But we simply can't make something hard into something easy, in a truthful and concise way. Physics is cumulative. You can't just pick it up from two minutes reading text. (I mean, think about the analogous situation with math. Imagine a middle schooler asking you what the Laplace transform is "without equations".) $\endgroup$ – knzhou Nov 14 '16 at 4:43
  • $\begingroup$ If you want some intuition, I wrote an answer today about how the magnetic field is to the electric field, as rotation is to linear acceleration. But it's a very sketchy explanation. $\endgroup$ – knzhou Nov 14 '16 at 4:44
  • $\begingroup$ Sometimes when learning a new thing you need to understand it as just that - a new concept. e.g. An electric field is a thing that exerts a force on a charged particle. It's defined by what it does, accept it and move on. There are no secrets being hidden from you there. $\endgroup$ – mattfitzgerald Nov 14 '16 at 5:56
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Understanding a topic depends very much on the framework that you allow yourself to start with.

If you just want to understand why electromagnetism is in place, there is not really much to understand: it exists experimentally in the universe but it does not come from any other a priori principle. One could as well imagine the existence of a universe with completely different interactions in place: unfortunately it is just not what we live in.

If you then ask what particles in the universe are responsible for generating and feeling the electromagnetism then the answer is that there exist charges and currents that are capable to do so: it is also another experimental fact that there exist two different type of charges, whereas only one type of current (no magnetic monopoles). Here you can perform different types of experiments and figure out how it empirically works, what attracts what (repells, respectively), accepting that is a matter of fact that such forces are present.

If, then, you want to have a description that allows you to make predictions then you would have to invent a more or less complicated framework that goes around doing numerical calculations; also, you need to define how precise you want your predictions to be, because according to the level of precision you can use different techniques. The framework that people use nowadays to describe electromagnetism is classical field theory on fibre bundles (that pretty much reduces to tensor calculus, as you mentioned already): it matches pretty well the empirical observations and predicts the future events quite closely; we could not come up with anything simpler (if you know of a way, you are welcome). However, if you look at things closely you might realise that some phenomena cannot be really described by the classical tensor fields: the world is quantised and you will need to invent quantum mechanics (actually quantum field theory) to describe it. We have done so and it is a mess of more or less complicated mathematical objects, but it works quite well (actually it works marvelously well) and we content ourselves with that description. While doing the "quantum things" you realise that there are some quantities (described for some reasons by this or that mathematical quantitiy) that appear to explaing everything, if put in the right place; an example above all is the existence of particles with spin: it is there (we do not know why) but it is useful to justify some experimental results. In this case we believe that electromagnetism has "a lot to do with spin", but we could not have guessed it if we had not put ourselves into the "quantum state of things".

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There is no easy way to understand physics without mathematics, because physics as we know it is based on our ability to fit mathematical functions to the behavior of observations. We keep these models if they can predict future behaviors for new experiments and observations, and if not, change them.

These mathematical models introduce concepts like the electric field you are describing , but the interaction between these concepts in mathematical functions cannot be described with words. That is why for popularization analogies are used. ( just as analogue computers can solve problems).

If it were possible to understand electromagnetism without its mathematics the ancients would have discovered it, instead of "earth,fire, water , air" . It was the use of calculus by Newton that created physics as we know it, and new concepts, like gravitation

Electromagnetism is a confluence of electric and magnetic fields, that may be described by handwaving. People had described electricity and magnetism for centuries. The were also described for decades mathematically as individual electric and magnetic fields but it was Maxwell's equations that tied different observational laws into a mathematical model: see the left collumn here. Electromagnetism came out of this elegant mathematical formulation.

And I understand that there are questions that can't be easily answered like this. I understand I may need to due research on my own. But where the hell do I start? I've been linked to Wikipedia a couple of times, and that just made things more confusing. And I don't have any intentions of shelling out the money to get a second degree just so I can get an answer.

To really understand physics you have to put elbow grease in understanding the mathematics modeling it, or be satisfied with analogue examples in popularized articles.

What do I do? Where do I go to understand it? Are there any sites for this? Any books

Those of us who are physicists started like this, because we wanted intenseley to understand what the highschool courses sketched. There is no shortcut to this, as there is no shortcut to becoming an olympic level runner. It depends how much you are "burning" to know. There are courses on the net , the MIT courses for example, if your really want to , you could follow at no cost.

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The facts

Charged particles have both an electric field and a magnetic dipole moment (MDM). This holds for electrons and protons as well as for positrons and anti-neutrons. The magnetic field is called a moment because it is not uniformly distributed around the particle.

For stationary particles and not varying fields it is known that an external electric field does not influence the direction of the MDM and an external magnetic field does not attract nor repeal the electric field of the charge.

Beside the fact that a charged particle is the source of both fields there is an other phenomenon, connecting both field. A moving - nonparallel - to an external magnetic field charge will be deflected (Lorentz force). In details this are three penomena because the variation of magnetic field or movement or acceleration/deflection are all processes of induction (generator, electric device, inductive coil).

The last not least phenomenon, important for the understanding of the electromagnetism, is the emission of EM radiation during acceleration of charged particles. Moving particles in an external field not only are moving in circles, the are moving in a spiral path and coming to rest after some time. The external magnetic field in sum does not take nor give energy to the moving charge (Lorent force works with permanent magnets as well as with electromagnets) and the slow down of th particle happens due to the radiation of photons from the particle.

For the full picture it has to be realised that the rise of the kinetic energy of charged particles is always a process of applying electromagnetic radiation to the particle or to have the charged particle in an electric field.

Electromagnetism

There is a science that investigate magnetic, electric and electromagnetic phenomenons. If I understood right, what you want to know about is what is the EM phenomenon. From Maxwell, Planck and Einstein it was introduced step by step that

  • light as well as radiation in a greater range of wavelengths is composed from an electric field component and a magnetic field component (measurable in antenna radiation)
  • EM radiation will be emitted in portions (only with this assumption it was possible to give the right equation for the Blackbody radiation)
  • this portions are called quanta and later photons.

Remarks

Until now electric field, magnetic field and EM radiation are subjects of statistical interpretations. The fields are continuous and seem not to by quantised other their extend and the extend is infinite. This limits the further understanding of how EM radiation occurs in detail and a theory about the quantisation of electric fields, magnetic fields and EM radiation 100 years after Einstein is overdue. When the description of this fields and there actions will be easier understandable.

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  • $\begingroup$ "and a theory about the quantisation of electric fields, magnetic fields and EM radiation 100 years after Einstein is overdue." Seriously? I thought this has been done. What's wrong with what we have? $\endgroup$ – flippiefanus Nov 14 '16 at 15:19
  • $\begingroup$ @flippiefanus Are photons composed particles is a paper that maybe is not necessary but unthought until now. Want to say me why this is impossible? More deep see about One-dimensional structures of space at the same site. $\endgroup$ – HolgerFiedler Nov 14 '16 at 15:43

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