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If I wave around a bar magnet, the magnetic field in the space around it changes. Is this enough to go through the whole speed of light derivation implying that the motion creates an electromagnetic wave? If so how do I determine the wavelength and direction of the resulting wave?

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    $\begingroup$ Yes, waving a magnet around does create an electromagnetic wave. Can you wave some $10^{15}$ times a second? If you can, it will start to glow. :-) $\endgroup$ – CuriousOne Jan 14 '16 at 2:43
  • $\begingroup$ I'm going to have to try that sometime. I assume the same thing would happen for charged objects? And how do we figure out the wavelength and direction? $\endgroup$ – Faraz Masroor Jan 14 '16 at 2:44
  • $\begingroup$ Same for charged objects. You can calculate the resulting radiation with the Green's function for Maxwell's equations, which requires solving a four dimensional integral. This can be done experimentally, by the way. One can wiggle relativistic electrons in a special magnet called an undulator or wiggler (not quite the same thing, but similar) and the result can be light all the way into the x-ray spectrum. There are quite a number of these synchrotron light sources in the world: en.wikipedia.org/wiki/List_of_synchrotron_radiation_facilities. $\endgroup$ – CuriousOne Jan 14 '16 at 2:52
  • $\begingroup$ Since the magnetic field will not weaken during your movement, it will be not responsible for the EM radiation. But a magnet is made from electrons and nucleus. This particles will radiate under any acceleration. $\endgroup$ – HolgerFiedler Jan 14 '16 at 8:25
  • $\begingroup$ It could be not exclude that under the influence of heavy accelerations you heat up the magnet and destroy the magnetic arrangements in the material. $\endgroup$ – HolgerFiedler Jan 14 '16 at 8:28
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The proton is a very small magnet (both in size, and in magnetic field strength). Inside a 3 Tesla MRI machine, it will resonate (spin) at 128 MHz, and at that frequency it produces a radio wave which can be picked up and used to make images of the human anatomy. Well- usually you spin a bunch of protons coherently and measure the sum signal.

Problem is - as you scale up your magnet, it gets harder to spin it fast... So for a macroscopic magnet, you will emit only very low frequency E/M waves.

You asked "How do I determine the wavelength and direction?". The wavelength follows directly from the frequency, since all EM waves travel at $c$. So rotating a magnet at frequency $f$ implies a wavelength $\lambda = \frac{c}{f}$.

The direction is a little bit trickier - but if you are rotating your dipole about a particular axis, the radiation will follow a 3D "donut like" pattern, with no emission along the axis of rotation, and the strongest emission in a circularly symmetrical pattern in the plane perpendicular to the axis. See for example this presentation for calculations of a rotating (electrical) dipole - a lot of the math is similar in shape (although different in the details).

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  • $\begingroup$ Protons are not what are giving magnets their magnetization, it's the electrons. One can "wiggle" electrons very nicely at x-ray frequencies, so to speak. $\endgroup$ – CuriousOne Jan 14 '16 at 16:57
  • $\begingroup$ @CuriousOne - yes, but a proton is the smallest "magnet" I could think of. $\endgroup$ – Floris Jan 14 '16 at 19:06
  • $\begingroup$ True. Good question, too... does quark spin-spin coupling make a significant impact? What's the magnetic moment of quarks, anyway? $\endgroup$ – CuriousOne Jan 14 '16 at 19:11
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Technically, yes. The changes in magnetic and electrical fields will propagate outwards at the speed of light. The wavelength is determined by the frequency, so it would depend on how fast you were spinning the magnet. You would have to spin the magnet very, very fast to produce anything other than extremely low frequency radio waves. Even a 10khz signal would need the magnet to spin at 10,000 rps (rotations per second) which is 600,000 rpm. I don't know of any material that wouldn't rip itself apart at that speed.

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  • $\begingroup$ The described process happens with any body as well as with a magnet. The only thing that could happens is, that you destroy the magnetic orientations of the involved particles. $\endgroup$ – HolgerFiedler Jan 14 '16 at 8:32
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You will get a continuous spectrum of electromagnetic waves, rather than a single wavelength. If you give the magnet a periodic motion with a frequency f, the radiation will have components at all multiples of f.

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