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Thread: propagation of EM waves

  1. #1 propagation of EM waves 
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    I am having a bit of trouble understanding why the electric and magnetic fields of an electromagnetic field are in phase (maximum e- field corresponding to maximum mag field, as in attached pic) instead of out of phase. There are two reasons it seems to me that there should be 0 mag field at e- field max and vice versa:
    1. When looking at textbook diagrams of an antenna (see attachment), (Where a voltage is applied to move positive charge to the upper part, then voltage reversing direction, and positive charges moving to the lower part), I have to think that the electric field would be highest when the top part has filled with positive charge and the bottom part has filled with negative charge. At this point it would seem that the magnetic field would be 0, because there is no current. The current would be at a maximum, and therefore the field at a max, I am thinking, when the charge (and e- field) are lowest (when neither top nor bottom have any charge).
    2. When I look at Maxwell's equations, I see that a CHANGING e- field should create a magnetic field, and a CHANGING magnetic field should create an e- field. But when the e- field is at a max, its rate of change is 0, so it makes sense that there would be 0 magnetic field created. The electric field is changing the fastest when its value is 0, so it would make sense to me that the created mag field would be HIGHEST when the e- field is 0. The same argument could apply to the e- field created by a changing magnetic field.

    So can anyone convince me that it makes sense for the e- and mag fields to be in phase? I can't seem to convince myself.
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  3. #2  
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    Quote Originally Posted by mhuntress View Post
    I am having a bit of trouble understanding why the electric and magnetic fields of an electromagnetic field are in phase (maximum e- field corresponding to maximum mag field, as in attached pic) instead of out of phase. There are two reasons it seems to me that there should be 0 mag field at e- field max and vice versa:
    1. When looking at textbook diagrams of an antenna (see attachment), (Where a voltage is applied to move positive charge to the upper part, then voltage reversing direction, and positive charges moving to the lower part), I have to think that the electric field would be highest when the top part has filled with positive charge and the bottom part has filled with negative charge. At this point it would seem that the magnetic field would be 0, because there is no current. The current would be at a maximum, and therefore the field at a max, I am thinking, when the charge (and e- field) are lowest (when neither top nor bottom have any charge).
    2. When I look at Maxwell's equations, I see that a CHANGING e- field should create a magnetic field, and a CHANGING magnetic field should create an e- field. But when the e- field is at a max, its rate of change is 0, so it makes sense that there would be 0 magnetic field created. The electric field is changing the fastest when its value is 0, so it would make sense to me that the created mag field would be HIGHEST when the e- field is 0. The same argument could apply to the e- field created by a changing magnetic field.

    So can anyone convince me that it makes sense for the e- and mag fields to be in phase? I can't seem to convince myself.
    The reason that they are in phase is dictated by the fact that the equations of propagation are identical:



    so, the solutions have an identical form.


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    The thing is, in your reasoning you'd have to continue to the infinite sum. The changing E field, induces a changing B field, which induces a changing E field (added to the original one) which induces a changing B field (added to the previous one) etc. Etc. etc. In this case the equations to the summations well and the result is given by the maxwell equations as xyzt gives you.

    Since there is no charge, that is what happens.
    In the information age ignorance is a choice.
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