How does changing flux produce a field.

[Yuqing]

I have some trouble understanding how changing flux produces a field. For example, I know that a changing magnetic field will induce an electric field because the flux of the magnetic field is changing. But how does this change in flux create the electric field. I just can't picture it.

Is it a purely derived phenomenon worked out from mathematics and empirical observations or is there a certain level of intuition behind it?

 

[Born2bwire]

In classical electromagnetics, Maxwell's equations are pretty much first principles. There isn't any theory that you can use to derive them outside of experimental data. How do you explain a changing magnetic field inducing an electric field?

 

[Yuqing]

So is it simply an effect that was mathematically derived?

Is there perhaps some analogy or example that can help explain this phenomenon?

 

[diazona]

It was observed experimentally (and then you can write equations to describe the observations, of course). Now that you mention it, though, it is slightly counterintuitive - I can't think of a good analogy of something more directly observable.

 

[Yuqing]

Am I right in saying that the phenomenon of changing flux inducing a field is just an axiom? Do we fundamentally understand why it occurs?

 

[jtbell]

Moving into quantum mechanics, we can say that Maxwell's Equations are the way they are because the universe has local U(1) gauge symmetry.

Of course, this begs the question, "why does the universe have local U(1) gauge symmetry?"

The bottom line is, we always come to a point where we just have to shrug and say, "that's the way things are," at least until someone finds a deeper explanation.

 

[ExactlySolved]

Do we fundamentally understand why it occurs?

Yes, all the dynamical properties of the electromagnetic field can be derived from coulomb's law + special relativity. This is not how magnetic fields were discovered historically, of course.

The fun part is that in quantum mechanics you don't even need coulombs law, just the relativistic equation of motion for a free particle together withthe principle of locality is sufficient to derive the existence of a field with the properties of E&M.

"why does the universe have local U(1) gauge symmetry?"

Quantum states are only detemined up to a phase, which corresonds to a global U(1) invariance, while the principle of locality promotes it to a local U(1) invariance. This is not how local gauge symmetry was discovered historically, of course.