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Homework Help: Signal from dipole detcted at loop in free space

  1. Sep 7, 2012 #1
    1. The problem statement, all variables and given/known data
    A Hertzian dipole at origin generates a signal in empty space which is detected at a wire loop with position vector;

    2. Relevant equations
    Signal is detected by changing magnetic field;
    B(t)=B0 sin(2∏ft)ex
    Show it is consistent with the Maxwell's solution to a plane wave
    B=iB0 exp[i(kz-wt)]ex

    3. The attempt at a solution
    Hmmm! I'm not getting far enough manipulating Maxwell's equations to provide an answer. Could someone give a little help, please?
  2. jcsd
  3. Sep 9, 2012 #2

    rude man

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    A few hints only; you need to grab the bull by the horns yourself:

    1. what is really meant by B=iB0 exp[i(kz-wt)]ex?

    2. know the complex Euler relation betw. exponent and sine/cos?

    3. Keep in mind that, at the receiving antenna, time is defined as t = 0, which is delayed from that of the transmitting antenna, so there will be a phase lag between transmitter and receiver.

    This is mostly math.
  4. Sep 10, 2012 #3
    Thank you.
    1. I think that B=iB0 exp[i(kz-wt)]ex is the propogation of the signal/wave in the x direction

    2. Euler relation betw. exponent and sine/cos
    e^ix = cos x + i sin x (circular wave [e^ix] split into 2 planes . . . . . .

    3. I realise I may be doing things the wrong way, but doing things by yourself when you have no time & tired is sooo hard to follow the right path . . . .
    I'm trying.
  5. Sep 10, 2012 #4

    rude man

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    How can a signal be imaginary?
    No circulraly polarized wave here. This hint means little until you figure out hint #1.

    I understand, but we are strictly prohibited from doing more than giving you hints and telling you if your approach is correct or not.
  6. Sep 11, 2012 #5
    . . . . . "what is really meant by B=iB0 exp[i(kz-wt)]ex?"

    This is a solution to the wave equation - a combination of sin(kz-wt) & cos(kz-wt).

    "The electric field of a sinusoidal plane wave that travels in the direction of the
    propagation vector k and is polarized transverse to that direction" . . . . is represented by this equation.

    However, for this I have the general solution
    E(r; t) = E0 sin (k.r - wt).
    This is similar to the equation I have stated at the beginning, however I'm not sure where the "i" in front of Bo comes from.

    I really do appreciate the hints. I'm not moaning, honest!
    Last edited: Sep 11, 2012
  7. Sep 11, 2012 #6

    rude man

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    No offense taken, mate! :-)

    But you didn't answer my question: how can an electric wave be imaginary? If you answer that question correctly you will see why the "i" is needed ahead of the expression for the transmitted wave.
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