1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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;
    r=(50m)ez



    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

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar
    Homework Helper
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Signal from dipole detcted at loop in free space
Loading...