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I understand that exciting electrons, basically freely moving electrons cause electromagnetic waves. The faster they accelerate the higher the frequency of the waves.

If this is indeed the case, then why aren't we bombarded by an infinite number of high frequency, low frequency and all kinds of radiation every second?

Relative to us, everything can be accelerating at a very high speed in a short interval of time. I don't understand this acceleration creating different waves, to be honest.

Like for a millisecond, the acceleration is always infinite as the time difference reaches zero, so shouldn't we have an infinite number of infinite energy waves everywhere?

Now to magnetism, why don't I see electromangetic waves when I move a magnet and try to measure the waves created by it? It also is supposed to create electromangetic waves due to changing magnetic field from space a to space b right?

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    \$\begingroup\$ you are being bombarded with radiation all the time. \$\endgroup\$
    – dandavis
    Commented Jun 21 at 21:55
  • \$\begingroup\$ @dandavis then why is it not infinite :) and the second part does not make sense, since acceleration is dependent on time difference, how do we know from which point to which point is acceleration considered by nature? \$\endgroup\$ Commented Jun 21 at 21:59
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    \$\begingroup\$ read into "inertial frames of reference", and other relativity-based concepts. \$\endgroup\$
    – dandavis
    Commented Jun 21 at 22:02
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    \$\begingroup\$ Is the inverse square law being overlooked by this question? \$\endgroup\$
    – Sotto Voce
    Commented Jun 21 at 22:08
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    \$\begingroup\$ @VishwaMithraTatta You may want to read about the ultraviolet catastrophe. It was numerically solved, eventually, by Max Planck in 1900. But wasn't explained until Einstein, about 5 years later. (Not dissimilar to Kepler's ellipses numerically solving orbital problems, but as Kepler wrote himself "a smaller pile of dung to replace a bigger one", which remained unexplained until Newton.) \$\endgroup\$ Commented Jun 21 at 23:05

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  1. We are bombarded by EM radiation from many sources. Here, from https://swling.com/blog/2016/06/steve-points-out-the-itu-r-recommendations-on-radio-noise/, is radio noise from various sources.

enter image description here

At higher frequencies there's thermal radiation from pretty much everything. Still higher is light, lots of that around. Even higher, there are gamma rays from radioactivity (everything is radioactive if you look at it with enough sensitivity).

  1. Magnetic loop antennas are a thing. The trick is that they make a field that changes a lot quicker than you can move a magnet, so they radiate more efficiently.
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You could indeed make an EM radiator by moving a magnet -- spinning it cross-axis, say.

The problem is, for the speed to be fast enough to have reasonable (or even detectable?) emissions, no known material can withstand such mechanical stress. I guess, in a very informal sense, mechanical waves are much slower, and "lower impedance", than free electromagnetic waves are: the drag due to air friction, or the stress due to centripetal force, is considerably more important than the drag due to "electromagnetic friction" in air. (Note that mechanical stress can be seen as equivalent to electric breakdown; that a spinning magnet can spin only so fast before exploding, can be seen as analogous to a capacitor handling so much voltage before sparking through. So, it's to say that, you can "spin" a capacitor much faster, electrically, than you can a mechanical part: a small capacitor can oscillate billions of times per second, a mechanical part of comparable size merely hundreds of thousands.)

We can consider the case in non-air materials, though. A metal is a conductor, which can also be seen as a frequency-dependent lossy permeability and/or permittivity. Or, for an optical analogy, a very high (and lossy) index of refraction. In particular, the index can be extremely high: thousands, say. Magnetic fields moving through such materials, necessarily develop a drag force, and a substantial one at that, compared to typical field strengths. We can view this as fields propagating through a medium, dense enough that it gives perceptible influence -- whether we express that influence as a radiation pressure, or in simpler and more classical terms as fields and forces. (Though I'm not sure that radiation pressure, exactly, is an appropriate term to use from this perspective.)

In other words: spinning a magnet in vacuum doesn't do very much, but spinning a magnet in an EM medium with the equivalent "viscosity" of heavy grease, generates significant drag force.

And so indeed, we have machines that use this effect. Low-loss permeable materials are used for reluctance motors; lossy conductors are used for induction motors and EM brakes (indeed, an induction motor magnetized with DC is a powerful brake). This includes the magnet case: a synchronous motor has a spinning magnet surrounded by a permeable core, with windings around the core; the permeability of the core, and the effect of the windings, can be considered a bulk medium of high viscosity (albeit one dependent on what we've wired to the thing!). If we simply short the terminals, the winding resistance acts to brake the magnet: we thus have a drag force, and our spinning magnet is doing work "radiating" electromagnetically.

Of course, we do not get propagating waves out of motors, at a distance -- the ratio of coupling, from waves within dense media such as these, to the outside world, is very small indeed. If the index of refraction is thousands, then waves will be largely confined by total internal reflection. (Not that an optical argument is really meaningful for wavelengths as long as used in motors anyway, but to the extent that the effect remains equivalent even for fractional wavelengths.)

There are still "things" we can get "spinning" fast enough to compare electromagnetically; but they are so small -- basically molecular -- that quantum effects become relevant. Thus we can have rotational modes of polar molecules ranging from GHz to infrared, and vibrational and extensional modes ranging from long IR to UV. But, where a motor spins faster when driven by higher frequencies (or the magnet emits, likewise), quantum mechanics dictates the ways in which molecules move; a rotational mode might be defined by a ladder operator, which has a constant energy change between steps (and thus constant frequency for the photons that couple with it), and so we get a variable amplitude (amount of energy present in the mode) but not a variable frequency. But this, too, is an approximation: there are also quantum systems where the energy increment varies, dependent on total energy, and which does look very much like a spinning particle, the frequency increasing with energy.

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    \$\begingroup\$ There were Alexanderson alternators which directly generated lowish-frequency RF waves - in wires, not in air - by rotating thousands of magnets past a mismatched number of wire coils at high speed (something like 500 wave cycles per revolution, 200 revolutions per second). They still didn't manage to spin magnets 100,000 times per second, and they still used electricity-based antennas, but they used something sort of similar. \$\endgroup\$ Commented Jun 22 at 19:22

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