[alancalverd]

Is a rotating magnet really emitting energy in free space? It certainly induces a current in a conductor, but there's no conductor, and even if there is, there is no braking effect if the circuit is open.

[alancalverd]

 frequency of 159 MHz.    That's the top end of the radio frequencies, maybe early microwave.

No big deal - it's between the VHF (civilian) and UHF (military) aircraft  comms bands.

[paul cotter]

Indeed, one can go to many tens of gigahertz and the same phenomena occur as at 1mhz, the chief difference is the reduction in length of the radiator and the use of waveguides rather than coax cable.

[paul cotter]

Necromancy?, BC. I always thought necromancy was the divination of future events by dissecting a dead creature and examining it's entrails. This method has not as yet been ascertained to be effective!

[hamdani yusuf]

The question is the same, what is the photon energy radiated by the rotating magnet?

Small.
3000 RPM is 50Hz so the photon energy is 50 times Planck's constant.

That's high school maths. Why have you reopened a long-dead thread to ask about it?

Have your read my first post here carefully?

The reason E = hv is that h is joule second and v is cycles divided by seconds. Since cycles have no dimension you can simply cancel out the unit of seconds in the numerator and denominator leaving the dimension of the answer as joules. Note that cancelling a unit has no effect on the values in the equation. This is what we use dimensional analysis for. I have explained this in words rather than just using maths since that is how you requested answers.

The unit for h is actually Joule second per cycle. Reduced Planck's constant, called ħ (h bar) has a unit of Joule second per radian. They have the same dimension, but different in numerical value.
Using ħ can reduce the number of symbols used in equations of quantum mechanics, where we need to write down 2π if h were used instead.

I posted it because I think the statement in bold above needs clarification. Just because a unit has no dimension, it doesn't mean that it can just be ignored. You will get different value if you use different units, such as radian, degree, grad, brad, etc.
https://en.wikipedia.org/wiki/Angle#Units

[alancalverd]

I posted it because I think the statement in bold above needs clarification. Just because a unit has no dimension, it doesn't mean that it can just be ignored. You will get different value if you use different units, such as radian, degree, grad, brad, etc.

Jeffrey didn't cancel "cycles" but "seconds", because [E] = ML²T^-2 and [ν]= T^-1 so [h] = ML²T^-1.

[X] means "dimensions of X "

Conventionally, the frequency of radiation is always stated in Hz, to avoid the confusion you have made for yourself.

[Eternal Student]

Hi.

Is a rotating magnet really emitting energy in free space?   It certainly induces a current in a conductor, ......

    Inducing current in a conductor is a separate issue.  It creates e-m waves in the region of space around itself, these will propogate.  There is no reason it would stop emitting e-m radiation in free space.

      In astronomy, pulsars are thought to emit some radiation due to rotation of magnetic dipoles which is just called "magnetic dipole radiation".   (They can also emit other energetic particles, the magnetic dipole radiation is just one component of what they emit).
    See section 6.1.4   of this online article for more discussion and forumulae to describe the amount of power radiated as dipole radiation.     https://www.cv.nrao.edu/~sransom/web/Ch6.html    - that's part of the 'National Radio Astronomy Observatory' website and should be safe and reliable enough.
    That article also assumes this emitted energy does come from the rotational kinetic energy of the neutron star (read "neutron star" as "the big magnet"):
    Magnetic dipole radiation extracts rotational kinetic energy from the neutron star and causes the pulsar period to increase with time.

    To paraphrase all of this:   A rotating dipole in free space really does seem to emit e-m radiation,  furthermore this loss of energy may cause the rotating magnet to slow down and stop spinning over time.  By Newtonian mechanics, some torque would seem to operate on the rotating object.

So the original question is not without some practical or experimental relevance.

In open space, this rotating magnet is emitting radiation and thus losing energy.    Where is that energy coming from?  If the rotating magnet reduces its (rotational) k.e.  - where is the torque coming from that makes that happen?

    It's not a question I can easily answer and I would like to get some opinions on it.   There are a few solutions already existing in some Q&A websites like Quora but their quality.... is... variable.

It might be something better put into a separate thread rather than side-tracking this one too much.

Best Wishes.

[Eternal Student]

Hi.

Thanks also for the information about how high up the e-m spectrum you can go with an AC signal in an antenna.
    We don't seem to use AC signal generators and an antenna to generate microwaves (we seem to use magnetrons in Microwave ovens etc.).   If I've understood what you ( @alancalverd and @paul cotter  ) have said,  then we could generate microwaves with an AC signal generator and an antenna if we wanted to and the emission remains fairly sharply peaked at the desired microwave frequency instead of being a broader spectrum.
    The next question in the back of my mind would be,   why don't we just use that in a microwave oven?   I'll guess a magnetron offers some cost advantage.

Best Wishes.

[paul cotter]

A magnetron is a cheap and powerful source of microwaves where frequency accuracy and stability are not of great concern. One could do the same with an oscillator+amplifier at much greater cost and complexity. A microwave oven operates ~3ghz. Cellphones are devices that use microwave frequencies, my old phone uses 0.9-1.8ghz and I think current(4g and 5g) models use much higher frequencies. My satellite gogglebox signal arrives from the satellite at ~10ghz. So electronic generation at these high frequencies is commonplace.

[alancalverd]

By Newtonian mechanics, some torque would seem to operate on the rotating object.

This simply does not make sense. Consider a magnet rotating in an infinite vacuum. Where does its angular momentum go?  Newtonian mechanics says it is conserved!

[Eternal Student]

Hi.

Consider a magnet rotating in an infinite vacuum. Where does its angular momentum go?  Newtonian mechanics says it is conserved!

    That is indeed an interesting problem to resolve.    Just to be clear, I didn't make up the original situation and the questions that follow from it.

    Starting from the beginning, a rotating magnetic dipole  (or electric dipole) should generate e-m radiation.   That's probably the first thing to check.   Assuming this does happen, as indeed it does seem reasonable to do, we are left with a set of problems to resolve.
     If the rotating magnet doesn't slow down, it keeps radiating some energy at a constant rate for ever.   Where is that coming from?  Does the magnet lose some mass until eventually it would be all gone?

     In partial answer to your ( @alancalverd )  question, or at least as something you should consider,  we have the following:
    Photons are considered to be spin 1 particles in the standard model.  As such, under a treatment of the situation with Quantum Electro Dynamics (QED) or compatible form of QFT, they can carry an intrinsic angular momentum.   So there is a precedent for us to imagine that light may carry angular momentum.

    In Classical electrodynamics it's harder to identify an angular momentum in light but not impossible.   I'm told that as early as 1909,  Poynting suggested that circularly polarized light has an angular momentum volume density associated with it.
    It is not too difficult to imagine that circularly polarised light (where the orientation of of the E and B fields is rotating) can carry momentum and it now seems common to associate this classical representation of what is happening in terms of E and B fields with the Spin Angular Momentum (SAM) of photons exhibited in quantum theories like QED.
    Wikipedia has an entire page discussing the various ways in which light can carry angular momentum:
https://en.wikipedia.org/wiki/Angular_momentum_of_light     which inlcudes SAM and OAM.
Spin Angular Momentum of light is also discussed here,   https://en.wikipedia.org/wiki/Spin_angular_momentum_of_light

    Anyway, what I'm saying is that the angular momentum lost by a rotating magnet may be found in the e-m radiation that was emitted by it.

Best Wishes.

P.S.   I'm getting very worried about side-tracking this thread.   A moderator should feel free to move it.  @hamdani yusuf  should feel free to ask us to stop.

[paul cotter]

Indeed ES, electromagnetic fields do have momentum. I have glanced over the relevant maths for a rigorous derivation and it is quite complex- don't ask me to show this, it is beyond my abilities. This is not Hamdani's thread, he resurrected an old thread from "timey" and then we hijacked it!

[alancalverd]

Starting from the beginning, a rotating magnetic dipole  (or electric dipole) should generate e-m radiation. 

I think not. You need to accelerate a charge to generate a photon. So it is entirely possible that a spinning neutron star could excite radiation from any gas cloud, plasma or passing ion, but a magnet in an infinite vacuum won't. 

[Eternal Student]

Hi.

You need to accelerate a charge to generate a photon.

    It is a way but do really think it's the only way to generate e-m radiation?
    Atoms generate e-m radiation when an electron changes orbit, we don't model this with electrons moving in well defined circular orbits and having a brief period of acceleration (and indeed we can't because they would always be emitting radiation if we did).    EM radiation is emitted for reasons that are not explained by a charge having been accelerated.
    A positron and an electron can annihilate and produce a gamma ray (well, a pair of them) and no acceleration of a charge was involved.
    Maxwells equations do a fair job of describing electromagnetic radiation.   There are terms linking ∇ x E to the time rate of change of B.     If the B field is changing at a place then the E field must also change at that place.   If a magnetic dipole with lengh L between the poles is rotating, then you can be fairly certain the B field at points in space along its path of rotation will be changing with time.  An oscillating B field should generate e-m waves appearing at some distance from it under the same conditions that an oscillating E field should.

    I'm sure you ( @alancalverd ) have said all of these things to other people in the past.

    I don't have a copy of Griffth's  Introduction to Electrodynamics to hand at the moment but apparently the section around equation 9.53 fully derives the e-m radiation that must arise in the far field from an oscillating magnetic dipole.   This is a standard textbook and as an engineer you probably have a copy on the shelf.   A rotating magnetic dipole isn't covered there but can be considered as two oscillating dipoles,  one along the x-axis and one on the y-axis,  oscillating with the same frequency but π/2  out of phase.   Sometimes this is called a crossed oscillating quadrupole. There are a few places on the internet that may provide a complete derivation for the e-m radition arising from a rotating magnetic dipole.   LaTex isn't working so I'm not going try it here.

     In all honesty,  I think it's fairly well established that a rotating magnet in free space will produce e-m radiation. However, if you can find fault with this result then I'm only too pleased to hear about it.   If a rotating magnet doesn't produce e-m radiation, that'll be great - it would make most the remaining problems that arise from it go away.

Best Wishes.

[paul cotter]

I also am fairly sure a rotating magnet would radiate em. It would have to rotate at quite a high speed to generate easily detectable radiation. I have been trying for several hours to mentally model the maths involved but I have failed so far. We normally look at charge acceleration to produce em as it is the most convenient method but one has to remember that the magnetic field is simply the electric field as seen from a different frame of reference.

[hamdani yusuf]

I posted it because I think the statement in bold above needs clarification. Just because a unit has no dimension, it doesn't mean that it can just be ignored. You will get different value if you use different units, such as radian, degree, grad, brad, etc.

Jeffrey didn't cancel "cycles" but "seconds", because [E] = ML²T^-2 and [ν]= T^-1 so [h] = ML²T^-1.

[X] means "dimensions of X "

Conventionally, the frequency of radiation is always stated in Hz, to avoid the confusion you have made for yourself.

He didn't cancel cycle, but ignored it as if it wasn't there. You can't say always if there are exceptions.
Why can't someone state frequency in other units, such as kHz, THz, rpm, etc?

Frequency (symbol f), most often measured in hertz (symbol: Hz), is the number of occurrences of a repeating event per unit of time.[1] It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency (symbol ω, with SI unit radian per second) by a factor of 2π. The period (symbol T) is the interval of time between events, so the period is the reciprocal of the frequency: f = 1/T.
https://en.wikipedia.org/wiki/Frequency

[Bored chemist]

Necromancy?, BC. I always thought necromancy was the divination of future events by dissecting a dead creature and examining it's entrails. This method has not as yet been ascertained to be effective!

And someone tried to divine the future from the entrails of a long-dead thread.
It's not clear why.

[Bored chemist]

He's not talking about a betatron.

He's talking about the angular speed of an electron. What else would you call a device that makes electrons orbit at a constant 10⁹radians per second?

You seem to have invented a requirement for an orbit.
Pushing electrons to and fro in an antenna is cyclical (Particularly if the antenna is resonant.)

Possible answers to your question would include
https://en.wikipedia.org/wiki/Halo_antenna
and
https://en.wikipedia.org/wiki/Cavity_magnetron

[Bored chemist]

I also am fairly sure a rotating magnet would radiate em. It would have to rotate at quite a high speed to generate easily detectable radiation. I have been trying for several hours to mentally model the maths involved but I have failed so far. We normally look at charge acceleration to produce em as it is the most convenient method but one has to remember that the magnetic field is simply the electric field as seen from a different frame of reference.

I never could do the maths, but I don't care.

I can get a toy magnet and put it on the turntable of a record player.

I can put a compass near it.
And I can watch the compass needle move.
If I'm lucky it will even rotate in synchrony with the turntable.

The force acting on the needle is electromagnetic.

The carrier of the EM force is the photon.
So, in this case, I know that a rotating magnet emits EM radiation. That force is periodic and thus there must be a component of the EM radiation with the same period.So it must have photons with energies corresponding to the frequency of rotation of the record player.


Re. "but a magnet in an infinite vacuum won't. "
If the magnet falls over in a non-existent forest with no observers, does it matter?

I contend that it will still emit EM radiation.
Imagine that we somehow have a magnet in an infinite empty universe.
We set it spinning (We know it is spinning, because an ant who happens to be standing on it notices the centrifugal effect).

After a while, and at some distance from the magnet, we magically call a compass needle into being.

Does the needle have to "wait" for EM radiation from the magnet to reach it, or is that changing field already there?

I can't see how it would so I think the magnet must have been emitting EM radiation all along.

But... if there's EM radiation, then there are photons.
And, if there are photons, the universe isn't empty.
So the solution may be that you can't have a rotating magnet in an empty universe.

All seems a bit esoteric..
But let's ignore nearly the whole of the universe and consider some hydrogen atoms.
Some of them have the magnetic dipoles of the electron and the proton aligned parallel, and in others it's antiparallel.
And if one happens to flip from the first state to the second, it emits a photon of about 21 cm wavelength.

That photon crosses space and is picked up many years later by a detector here on earth.

But we have only been constructing such detectors for about 100 years.
So, for a source more than 100 light years away, the detector had not been built when the photon was emitted.

I think that's close enough to " we magically call a compass needle into being." for the analogy to work.

An electron- with a magnetic diploe moment- was flipped and sent out EM radiation. It did so in a universe in which the detector did not exist.
You may say that, without the proton of the hydrogen atom, the energy of the photon would be undefined. Which is a fair point
But, at that point, I think you need to be able to do Laplace transforms and, as I said, I can't do the maths.

[paul cotter]

I have looked up the derivation of the wave equation via the Laplacian of the E or H field in phasor form and it is completely symmetric: a time variation in either produces an em wave.