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I EM waves in a rotating frame

  1. Jul 3, 2017 #1
    Hello there,

    I have a question (two very similar questions) about the time and phase delay between rotating objects. I want to describe two extreme cases here: I would appreciate any helps.

    Case 1
    Imagine two observers (people with telescopes maybe) in space that are standing thousands of kilometers apart and directly facing each other in free space.

    At time t0 they are standing still. At t1 they start rotating about the axis between them (their centers of bodies) with let's say 360 degrees/second in the same directions. And after a time delay, at t2 , the "news that the other observer had started rotating" arrives to each observer.

    What would an observer see after t1 and t2 ?

    My guess is that;
    during from t1 to t2, an observer would see him/herself rotating relative to the other one. In other words, s/he would see the other one starting to rotate in the opposite direction.

    But at t2, the other observer would seem to have stopped rotating relative this one. However, s/he would look standing tilted with an angle of maybe like 10-20 degrees.

    Case 2

    Same as in the Case 1 but let's replace the observers with huge horseshoe magnets, poles directly facing each other, looking like this:
    < .................................... >

    (pulling or pushing orientation doesn't matter). Let's say at t0, they were pushing each other with F0.

    Between t1 and t2, would the force start decreasing?

    After t2, would they reach a stable force F2 which is smaller than F0? (Due to them "seeing" each other tilted with an angle)

    I know the examples here are too extreme to be realistic but in order to render any other factors uneffective, I needed to exaggerate. Thank you for your time.
  2. jcsd
  3. Jul 6, 2017 #2


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    For Case 2, for the very long distances you specify, we must assume that the static magnetic field is negligible. However, an accelerating magnet can radiate an EM wave, so the second magnet will respond to an EM wave radiated by the first. But the radiated field depends on acceleration, not on velocity, so at t2 the second magnet will receive a sudden kick as a consequence of the start of movement of the first magnet.
  4. Jul 8, 2017 #3
    Is it easy deriving general equations for the magnitude, etc of such EM wave?
  5. Jul 9, 2017 #4


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    For an accelerating electric charge, there is the Lamour Equation (Wiki) which gives the radiated power, but I have never seen the equivalent equation for an accelerating magnet. There is always that niggling doubt in my mind about radiation by a magnet! After all, a magnet consists of moving charges anyway.
  6. Jul 9, 2017 #5
    Oh, ok. Thanks.
  7. Jul 14, 2017 #6
    If they saw each other through a telescope before they started rotating, they will see nothing after they started due to aberration of light, I am afraid to say. Aberration of light changes apparent position of illuminated object. I think they must tilt telescopes forward at corresponding to their velocity angle so as a ray of light could pass through the telescope. At least, they can find this angle by trial and error.
    Related article: R C Jennison. Ray path in a rotating system 1963 Nature No 4895 p. 739
    Last edited: Jul 14, 2017
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