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Radiation from Oscillating Dipole

  1. Jan 18, 2016 #1
    1. The problem statement, all variables and given/known data

    Dipole.png

    2. Relevant equations


    Given in the question.

    3. The attempt at a solution

    For part a I obtained an expression for the the dipole moment:

    ##P(t)= P_0 cos(wt)##

    And therefore, for part b, I obtained the expressions

    ##\frac{dP}{dt} = -wP_0 sin(wt)## and ##\frac{d^2P}{dt^2} = -w^2P_0 cos(wt)##.

    Now when I make use of Eq. 1.39 to obtain ##E_\theta## for part c), I substitute in the above expression for ##\frac{d^2P}{dt^2}##, but end up with the cos term being ##cos(wt)## from ##\frac{d^2P}{dt^2}## as opposed to ##cos(kr-wt)## which is required. Not sure where I'm going wrong.
     
  2. jcsd
  3. Jan 18, 2016 #2

    TSny

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    In Eq. 1.39, the square brackets in the numerators denote a condition on the time at which you evaluate the quantities inside the brackets. Check your notes or text for details.
     
  4. Jan 18, 2016 #3
    Ah I believe that the derivatives must be evaluated at the retarded time, is that correct?
     
  5. Jan 18, 2016 #4

    TSny

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    Yes.
     
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