How does the electromagnetic force unify electric and magnetic forces?

[Michio Cuckoo]

This may at first seem like a very stupid question, but I can't seem to get to the root of magnetism.

As we all know, all charges exert electric forces on each other, and point charges obey the inverse-square law.


I know how a moving charge generates a magnetic field according to Ampere's law.

But how is the magnetic field actually generated? Why should a magnetic field be generated in this form?

Also, how do you show that both electric and magnetic forces are both aspects of the same force?.
Is relativity the only way to explain it?

 

[Drakkith]

This may interest you: http://en.wikipedia.org/wiki/History_of_electromagnetic_theory

 

[Michio Cuckoo]

Nah, wikipedia doesn't explain things very clearly

 

[Muphrid]

This is like asking why a charge should generate an electric field or how it does that. There is no mechanism here. Charges and currents generate electric and magnetic fields. This is simply what they do, the same way masses generate gravitational fields.

Relativity is the only way to show that E and B form a single field (F). What you see is that for any current (stationary charges are currents in the time direction), the field F is a directed plane defined at every point in space. The two directions that span that plane are the direction of the current creating it and the direction between the observer and the current. This is the meaning of the Faraday tensor F, and it's something I feel is often lost because people seldom have a geometric understanding of indexed tensors.

In the end, EM theory (in vacuum) just boils down to a simple differential equation:

\nabla F = -\mu_0 j

And everything else follows from that. It couldn't be simpler: derivative of a field has a source.

 

[Michio Cuckoo]

What? It can't be that simple. What about evidence for magnetic monopoles?

 

[marcusl]

This may at first seem like a very stupid question, but I can't seem to get to the root of magnetism.

As we all know, all charges exert electric forces on each other, and point charges obey the inverse-square law.I know how a moving charge generates a magnetic field according to Ampere's law.

But how is the magnetic field actually generated? Why should a magnetic field be generated in this form?

Also, how do you show that both electric and magnetic forces are both aspects of the same force?.
Is relativity the only way to explain it?

1. Yes, in the classical view the only way to explain magnetism is through relativity. The magnetic force is the manifestation of the usual Coulomb electric force as transformed from a moving frame to the rest frame. This unity of electricity and magnetism is one of the deep beauties of classical physics.

I know of three undergrad textbooks that explain this material. The first two are excellent, both written by Nobel laureates who provide deep insights into their topics:
1. Purcell, Electricity and Magnetism (I think...), vol 2 of Berkeley Physics series
2. Schwartz, Principles of Electrodynamics (Dover). He treats both parallel and perpendicular motion.
The third is Griffith's E&M text. I have no personal experience with it, but it is used widely in universities throughout the US.

Max Born, another Nobelist, wrote a book in 1920, called Einstein's Theory of Relativity, for a more general audience. The 1962 Dover edition contains a brief description of E&M unity using only high school algebra.

2. There is currently no evidence for the existence of magnetic monopoles.

 

[Drakkith]

What? It can't be that simple. What about evidence for magnetic monopoles?

There is currently no evidence for them to my knowledge.

 

[kmarinas86]

This may at first seem like a very stupid question, but I can't seem to get to the root of magnetism.

As we all know, all charges exert electric forces on each other, and point charges obey the inverse-square law.I know how a moving charge generates a magnetic field according to Ampere's law.

But how is the magnetic field actually generated? Why should a magnetic field be generated in this form?

Also, how do you show that both electric and magnetic forces are both aspects of the same force?.
Is relativity the only way to explain it?

Currents and the magnetic fields such currents generate exist at right angles to one another.

There might be a mechanical reason for this, similar to how torque applied to a spinning flywheel causes precessional rotation at right angles to the applied torque (rotational force).

Subatomic particles such as electrons behave as though they were rotating. They have intrinsic angular momentum. They will precess under field stress just as a top on a table does. At some point, it "resonates" with the field.

http://en.wikipedia.org/wiki/Magnetic_resonance
http://en.wikipedia.org/wiki/Nuclear_magnetic_resonance
http://en.wikipedia.org/wiki/Cyclotron_resonance
http://en.wikipedia.org/wiki/Ion_cyclotron_resonance
http://en.wikipedia.org/wiki/Electron_cyclotron_resonance
http://en.wikipedia.org/wiki/Electron_nuclear_double_resonance
http://en.wikipedia.org/wiki/Electron_paramagnetic_resonance
http://en.wikipedia.org/wiki/Ferromagnetic_resonance
http://en.wikipedia.org/wiki/Gyromagnetic_ratio
http://en.wikipedia.org/wiki/Gyroradius
etc.

Right now, the world doesn't know the reason why magnetism behaves the way it does. Nevertheless, it wouldn't be a bad idea to imagine magnetic fields as being a "gears and sprockets" kind of mechanism.

 

[Muphrid]

The world of EM becomes a lot clearer when you abandon the idea of electric and magnetic fields being vectors--they're really not, and when you forget that you ever thought they were, the picture of how electricity and magnetism are related becomes a lot clearer.

Instead, the magnetic field is an oriented plane at every point in space. This may be momentarily confusing, but remember you already think of a vector field as a little oriented line segment (an arrow) at every point in space.

In this picture, then, the "real" magnetic field is the plane perpendicular to the "usual" vector magnetic field that we typically talk about. Instead of magnetic field lines going in circles around the current generating them, we have magnetic field sheets. If you have a short wire of current, each magnetic field sheet goes along the length of the wire and extends radially outward.

Similarly, the electric field isn't a vector either. It, too, consists of little planes in every point of spacetime. I say spacetime because the currents that generate electric fields go in the time direction. Exactly like the magnetic field, the electric field sheets are spanned by the radial direction and the direction of the current--it's just in this case, the direction of current is in the time direction.

This is why magnetic monopoles don't exist: the magnetic field for a spatial current and the electric field for a timelike current are actually the same! They're both sheets that contain the current itself and extend radially outward.

 

[kmarinas86]

The world of EM becomes a lot clearer when you abandon the idea of electric and magnetic fields being vectors--they're really not, and when you forget that you ever thought they were, the picture of how electricity and magnetism are related becomes a lot clearer.

How clear is Quantum Electrodynamics to you?

 

[marcusl]

Michio Cuckoo, I suggest you be careful with post #8, which contains a muddle of information that is somewhere between unhelpful and wrong, and post #9, which makes no sense to me at all.

 

[Muphrid]

I know nothing of QED and won't pretend to; I didn't mean to imply that that my comments pertained to anything other than classical theory.

Nevertheless, if QED still uses the Faraday tensor F_{\mu \nu} in, for example, a Lagrangian, then the picture of what the Faraday tensor is and how it describes electromagnetic fields is still relevant. The Faraday tensor describes planes at every point in space exactly as I described it--it is a bivector field.

 

[kmarinas86]

Michio Cuckoo, I suggest you be careful with post #8, which contains a muddle of information that is somewhere between unhelpful and wrong, and post #9, which makes no sense to me at all.

Now that I think about it, the questioning style itself might be unhelpful.

I mean, wouldn't it be better to ask how do we measure magnetism as opposed to trying to explain it as something emergent?

It seems like people such as myself are attracted to these sorts of "why" questions that are somehow stated as a "how" question. "How does something work?" is more of a why question than questions like "What does it do?" or "What happens if I put that next to this?" or "How big is this response to an applied field?"

In fact, if you like, it might actually be a good idea to add some rules to this forum stating some guidelines about what kind of questions will lead to more constructive answers. All kinds of "why questions" that don't likely lead to very constructive answers should be pinned to the top at the forum. That is my suggestion. I think it could save some time in the long run.

 

[Drakkith]

Now that I think about it, the questioning style itself might be unhelpful.

I mean, wouldn't it be better to ask how do we measure magnetism as opposed to trying to explain it as something emergent?

I don't believe so. If I asked you why time dilation occurs you would explain that different reference frames can measure time and space differently and that time dilation is only an "emergent" property of viewing frames that aren't at rest relative to your own. Magnetism is not different in my opinion.

In fact, if you like, it might actually be a good idea to add some rules to this forum stating some guidelines about what kind of questions will lead to more constructive answers. All kinds of "why questions" that don't likely lead to very constructive answers should be pinned to the top at the forum. That is my suggestion. I think it could save some time in the long run.

I would guess that 99+% of posters do NOT read the forum rules before posting. Those that do have a good chance of staying on to be long term members and will probably understand this at some point anyways if they don't already.

 

[alexvine]

Say a small magnet is brought near a paper clip. When the distance between the two is sufficiently small, the paper clip will be pulled to the magnet.

What I want to know is: What is going on in the space between the magnet and the paper clip while this is happening.

 

[kmarinas86]

Say a small magnet is brought near a paper clip. When the distance between the two is sufficiently small, the paper clip will be pulled to the magnet.

What I want to know is: What is going on in the space between the magnet and the paper clip while this is happening.

The present level of our world's science does not have an answer to that question. Sorry about that.

I wouldn't be surprised though to find out that some intelligent life in the universe has it figured out. Science on Earth is in a mere infant stage at this time.

You should try to ask again in perhaps 10 years or more, when our scientists figure out what magnetic field fluxes are made of.

 

[jnorman]

inre: "The present level of our world's science does not have an answer to that question."

that should have been the first and only reponse to the OP's question. you can list equations all day long, but they do not substitute as an answer to the question, "what is a field, and how does it work?" we simply do not know.

 

[Relay]

This is an excellent question. From observation we know how it works and have many equations to model this with. But I think you are more interested in knowing why magnetism works. As far as I know, nobody knows the answer to that.
The best explanation so far is given by Feynman; see link

 

[Drakkith]

inre: "The present level of our world's science does not have an answer to that question."

that should have been the first and only reponse to the OP's question. you can list equations all day long, but they do not substitute as an answer to the question, "what is a field, and how does it work?" we simply do not know.

A field is something we have created and defined to help us describe and understand the behavior of interacting particles. We know exactly how a field works because we created it. Now, whether our fields accurately predict the behavior of particles is an ongoing process. Currently they do very very well in nearly every circumstance.

 

[Khashishi]

I like Muphrid's explanation #9 a lot. Let me see if I can explain it a little. In one picture of relativity, nothing is at "rest" because everything is moving forward in time, which is treated as a coordinate much like space. Something moving in space is actually moving in some direction in space-time. An acceleration is a (hyperbolic) rotation in space-time.

In Newtonian physics, the physics of a system does not depend on what angle you look at the system in. If you rotate the system, calculate the equations of motion, and rotate them back, it shouldn't change the results. The same is true for shifting the overall velocity of the system and shifting it back. This is called Galilean invariance and predates Einstein, but relativity is needed to make this compatible with the idea of a constant speed of light. In relativity, the shift is velocity is actually a hyperbolic rotation, which unifies the Galilean invariance into a rotation invariance.

The trajectory of charged bodies can't change if you rotate the system and rotate it back! Consider a wire containing equal amounts of positive and negative charges, with a net current. For simplicity, imagine the positive charges are at rest and the negative charges are moving along the wire in one direction. What is the force on another charge outside the wire? Well, if we don't know how to calculate the magnetic force directly from the current, we can transform into another frame where the current is zero (where the positive charges and negative charges are moving with opposite velocity). Because of length contraction, the positive charges are closer together and the negative charges are farther apart, so there's a net positive charge. This charge exerts a force on the external charge, which causes it to move. Which means in the original frame with a current, there needs to be a force which causes the external charge to move. But there is no electric force, because the charge in the wire is zero. This is called the magnetic force.

But we can see that the magnetic force is just the same thing as the electric force in a moving frame of reference, so we call it the electromagnetic force.