Submitted by No_Victory_1611 t3_123z8t2 in explainlikeimfive
According to the equations, it's 90°, but why particularly 90° why not parallel or some other number?
Comments
ArkyBeagle t1_jdxq6fx wrote
> The true answer is that they aren't two different things but two expressions of one thing: electromagnetism.
Whether we call it electricity or magnetism is almost an artifact of how we measure it. Although the needle on an old-school analog voltmeter is a magnetic device...
I always liked the cover to Richard Lyon's "Understanding Digital Signal Processing". It's not specifically about E&M but the picture just lights the idea up for me:
PerturbedHamster t1_jdy1ifc wrote
They aren't, unless you're talking about an electromagnetic wave in vacuum. For the case of a wave, the magnetic field comes from the changing electric field, and the electric field comes from the changing magnetic field. Maxwell's equations tell us then that the curl of E looks like the changing magnetic field, and the curl of B looks like the changing electric field. To (over)simplify the math, the curl of a thing is perpendicular to the thing, so that's why the magnetic and electric fields are perpendicular in a wave.
breckenridgeback t1_jdygypz wrote
> To (over)simplify the math, the curl of a thing is perpendicular to the thing
That is not true.
For example, if F is the vector field sin(x) i + 3 k, we have:
- curl(F) = cos(x) k
- F dot curl(F) = 3cos(x) != 0.
Nonzero dot product -> not perpendicular.
breckenridgeback t1_jdyhxt6 wrote
You can do electromagnetism with fields other than the electric and magnetic fields and get the same result. In fact, if you're a moving observer, electric fields will start to generate magnetic fields and vice-versa.
In reality, electric and magnetic fields are underlying manifestations of the same (coordinate-independent) underlying "thing". This thing, electromagnetism as a unified object, is more properly described by the four-potential, of which the electric and magnetic fields are parts. We call the part that doesn't care whether you're moving "electric" and the part that does "magnetic". But that is only a choice of coordinates, in the same way that you can do your linear algebra with <1,1> and <1,2> as basis vectors rather than <1,0> and <0,1> and everything will work out fine.
It turns out that you can, in a sense, decompose any (non-changing) vector field this way into an "electric-like" field and a "magnetic-like field", in the sense that these fields share some of the important mathematical properties of the electric and magnetic fields respectively.
breckenridgeback t1_jdyi5xf wrote
> That is one of the questions where you say, "that is just how it is.".
It's not so much "how it is" as that it's a specific choice of coordinates. The electric field is simply the part that, in a particular choice of coordinates, does not depend on motion. Changes in coordinates to a moving observer will "mix" the electric field into the magnetic and vice-versa.
PerturbedHamster t1_jdz002w wrote
I know it's not true in general, that's why I said it's an oversimplification. Given we're explaining vector calculus to a five year old, though, I thought it would be OK. What is true, though, is that if a vector field only has a single component then the curl does have to be perpendicular to the field. That's what's going on with linearly polarized light, and why I didn't feel too bad about oversimplifying.
Coldfriction t1_jdx2d8f wrote
That is one of the questions where you say, "that is just how it is.".
The true answer is that they aren't two different things but two expressions of one thing: electromagnetism. There is truly only one single force present, but if you look at it from one side it looks like electrical forces and fields and from the other side it looks like magnetic forces and fields. The sides are always perpendicular because you have to be perpendicularly looking to only see one aspect of the electromagnetic force and not the other. You can in fact look at it from a skewed angle and see both.
So I don't have a better answer than that for an ELI5 answer. The electric field is like looking at the electromagnetic force from the front and the magnetic force is like looking at it from the side. If you can see some of the front you aren't looking straight at the side and if you can see some of the side you aren't looking straight at the front. In our dimensional space the perspectives have to be perfectly perpendicular to only see one aspect at a time.