Doesn't the whole concept of describing arbitrary waveforms as a sum of sinusoids fall apart when you consider nonlinear systems? The reason you can do all these convenient acrobatics of angular frequencies etc is because sinusoids are the solution to the *linear* wave equation. The moment...
This has probably popped into every cycling engineer's head at some point (inckuduin mine). The problem is that most energy is lost during riding by friction and wind resistance, none of which can be recouped. Because any device will add weight to the bike, thus requiring additional energy by...
Unless I am mistaken, a completely uniform field, impossible as it is to create, would exert no force.
You can derive the resulting field easily, since you can just add the magnetic field of each coil (Superposition Principle). They would just counteract each other, probably resulting in...
Given the frequency with which the question comes up, I think we should be a bit more discerning in our answer. Earnshaw's theorem is not as restrictive as most people assume. For example, you can very easily levitate a block of Bismuth in a static magnetic field because it is diamagnetic.
@davenn, have you tried looking up Bloch walls? It's the rather common term for the walls between magnetic domains.
@Sveral, are you entirely certain that the Bloch wall is that continuous? From my experiments in my EE studies back in the day, magnetic domains were pretty haphazard and all over...
That seems a rather elaborate setup, of first setting up a contracting force (the angle of the mirrors), then creating a way to overcome that force (through charge), only to then try to measure an entirely different force.
But presuming your setup now, I think one major difficulty will be, how...
I am suggesting an "engineering approximation" here, where you try to confine the errors to an arbitrarily small region of space.
It's the same as with the Gibbs phenomenon when approximating a signal with sine waves. You will never get rid of the overshoot because it is a mathematical...
That depends on the definition of "close". True, of course you will never have a non-zero divergence, but if the incoming field lines are bundled very close together and then fan out radially, you are very close to emulating non-zero divergence.
That said, I would think that in a limited space you should be able to approximate any field distribution arbitrarily closely, with enough surrounding magnets.
I mean, mathematically I guess it also makes sense that you can't reduce it. If you can describe it as a four-dimensional tensor, that sort of implies that it can not be reduced to lower dimensions, correct? Or could you actually have "redundancy" in a tensor?
Awesome answers, thanks everybody. I somewhat suspected that if one was able to reduce EM to either just E or B, this would have been pointed out more in literature, but the wording in the Wikipedia page seemed suggestive.
This Wikipedia article
https://en.m.wikipedia.org/wiki/Relativistic_electromagnetism
seems (to me) imply that there is always a frame of reference in which a magnetic field can be rather viewed as an electric field modified by relativistic considerations. Is that always true? That is...
It's just an outcome of mathematics. The difference of two sine waves that are phased 120 degrees apart will be another sine wave with 1/sqrt(2) the height of the original ones.
Also, another cool aspect, when you use two phase wires for a circuit instead of one phase wire against ground, the subtraction of the sine waves comes out that you get another sine wave of 1/sqr(2) the amplitude. E.g. in Europe a household receives 360V 3-phase, but from there you can get...
There was another thread just yesterday that veered off massively, so I think it's worth pointing out that "electromagnetic" isn't just a convenient moniker to refer to the magnetic and electric field together, but rather that they are really are one combined, inseparable entity. That is, the...
I think it's an excellent visualization. Usually people go for the "water flowing through narrowing pipes" analogy, but yours is closer to physical reality.
Mythbusters has an episode on that topic, where they try to deflect a bullet with a magnet. The best they manage is by lining up a rail of super strong permanent magnets and then shoot the bullet a millimeter above the rail along it. The deflection they get is still tiny and it grazes the last...
Not only that, but Ohm's Law and the Kirchhoff Laws are simplified solutions of Maxwell's equations, so anytime you use those, you actually use Maxwell.
At this point in time the question is rather, what electrical device didn't have Maxwell applied during it's design? Antennas, RF interference etc etc are designed and vetted with those equations.
Maybe a good Einstein quote adds something here:
„An Freiheit des Menschen im philosophischen Sinne glaube ich keineswegs. Jeder handelt nicht nur unter äußerem Zwang, sondern auch gemäß innerer Notwendigkeit. Schopenhauers Spruch: „Ein Mensch kann zwar tun, was er will, aber nicht wollen, was...
When it comes to these things, you can't look at it from a classical, static point of view. This is quantum mechanics, where particles aren't exactly in one spot but rather exist in a cloud of probability, and they also often have a large kinetic energy...
They are only in the same spot for an infinitesimal small amount of time, since they are flying away from each other. Look into how particle accelerators work, that's really the same principle.
Also, IIRC you can't create an electron and a proton on their own. I believe the latter would have to...
While particles can indeed be created out of energy, the total sum of charge however is conserved, just like energy:
https://en.m.wikipedia.org/wiki/Charge_conservation
So, you can't just create an electron from energy, there *has* to be a positive charged particle created at the same time to...
The problem is that you created an unphysical scenario (if I understand it correctly, your wording is very confusing). Charges don't just appear magically in place, they need to be transported in from somewhere else. That is, your scenario directly violates the conservation of energy, but your...