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Energy distrubution in a magnetic field

  1. Apr 6, 2012 #1
    Hello, I was just thinking about an inductor and how inductors store energy in a magnetic field around them. I then had a thought about Light speed, lol. If a inductor creates a magnetic field which then starts to move outward at light speed, then is all the energy with that field displaced through out it varying with distance, so the closer to the inductor, the more energy and then less and less the farther out. Now lets say that inductor which is say 1 ft long and 1 ft wide is on for enough time so that the field moving at light speed reaches the moon at obviously Greatly diminished strength.
    Now If a magnetic field can not move faster then Light speed (299,792 Km/s ) then what would happen if you set up that inductor which created the field to a circuit where the inductors fall time was on the order of 83 picoseconds or about 1 inch, the distance light would travel in 83 picoseconds. So the question is Would the inductor even be capable of returning the energy in the magnetic field back to the circuit before it turned off since the energy is displaced throughout the field varying with distance.


    You know what maybe a simpler question, lol. how is the energy in a magnetic field displaced throughout it? Like is 90% of the energy located within a area of 1 inch around the inductor?
     
  2. jcsd
  3. Apr 7, 2012 #2

    mfb

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    You cannot discharge your 1foot-inductor in a time equivalent to some inches - the time is just too short to reach the full length.

    But to answer another question you asked: Most of the energy is stored in a region comparable to the size of your inductor. If your discharge needs some nanoseconds, you can get most of the energy back.

    At higher frequencys, the antenna is smaller too (if you operate it at its resonance, which is a good idea), so you scale your whole system down.
     
  4. Apr 7, 2012 #3
    I have one other question about this. If the inductor shuts down faster than the time it takes the field to collapse and the magnetic field (EM field) that had not reached the inductor in time just becomes an EM wave (radiation) that continues to propagate outward, then how does this work with a Electromagnet (Inductor) used to generate a force on some other coil? I mean if most of the energy in the magnetic field was propagated away as radiation because it could not collapse in time to return the energy to the coil, then how would another coil experience that force from the other coils magnetic field when it is now just radiation?

    I have never seen a electromagnet experience a force from an antenna generating radio-waves unless it is close enough in which case it is the interaction of the magnetic fields not the EM wave interacting with the other Electromagnets magnetic field. From what I can gather, if two electromagnets are close together, say 1 ft, one of them will keep increasing it frequency to and past the point where the magnetic field can not possibly collapse back in time before the coil switch's off. At this point the magnetic field is more or less propagated away as a EM wave, so from this I would assume that the other coil that is not changing will keep experiencing less and less force because more and more of the other Electromagnets magnetic field is somehow propagated away as a EM wave instead of just a Magnetic field.

    Do you see where I am having a problem with this? My biggest issue is how can a magnetic field which is so inherently different from say a radio-wave but is still considered to also be a EM wave. From what I know, a EM wave is a self propagating wave that does not need any other source other then it's creation, it also doesn't need to come back to it's source and once it is created it will not disappear once it's source is shut off. A magnetic field is created by a changing electric field and ALWAYS come's back to it's source, it is also possible to create enormous amounts of force between two magnetic fields unlike a EM wave witch for the most part won't create much force at all ( if it is a laser then you could get quite a bit).
     
  5. Apr 8, 2012 #4

    mfb

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    Usual dimensions of transformators are centimeters to meters, and usual frequencies are Hz to MHz, which translates to 300 000 kilometers to 300 meters. Therefore, the electromagnetic field has enough time to be (roughly) in an equilibrium with the current flows at all time.


    This would be an extremely tiny force.

    Why?

    That is right.

    Well, that is... a bit more tricky.


    For example, you can calculate the electromagnetic field around an antenna where charges are oscillating between both ends of it. The equations are a bit ugly, but the result is that you have two different types of fields:
    1) The near field, which falls off quickly with distance (1/r^2 and quicker I think) - here, you have energy flow between antenna and near field in both directions.
    2) The far field, which falls off with 1/r, where the direction of energy flow is only away from the antenna. If you look at energy density, not field strength, it falls off with the square of the amplitude and therefore with 1/r^2, which is the result you would expect for outgoing radiation.

    For other types of current and charge distributions, you get the same two components, they just look a bit different in their geometry.
    If you operate the antenna much below its resonance frequency, the near field component has a much larger volume, and you can recover much more energy.
     
  6. Apr 8, 2012 #5
    sorry i think i might have messed up one bit here

    You replied saying why, I assume it is because I made it sound like that is just what happens when two Electromagnetic are close together. What I meant was if the source powering the Electromagnet kept increasing it's frequency then the force generated between the two should at some point diminish to a much lower value then before because more and more of the magnetic field is turned into radiation because less and less of the magnetic field can collapse back in time.
     
  7. Apr 9, 2012 #6

    mfb

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    You'll get serious problems to increase the frequency up to that level, or the amplitude in the transformer drops a lot (as it is way too slow to react).
     
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