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Fourier Transform of Potential

  1. Jan 29, 2013 #1
    1. The problem statement, all variables and given/known data
    I have been given the following:

    A(r', ω) = μ/4∏*∫ J(r', ω)*exp(-j*k*R)/R dV'

    And am being asked to find the inverse FT of A(r', ω)

    2. Relevant equations
    Given that k = ω/c and R = |r - r'|

    3. The attempt at a solution
    I know what the inverse FT transform is, but what I am confused with is how to carry out this integration; I know that there will be two integrals, one from the equation I listed above, and the other from the inverse FT, but what do I do with the R variable? It is just a scalar, so it can be moved outside of the integrals, correct?

    When I solved it, I obtained an exponential out front, and it looked like a simple phase-shift FT transform pair. What I obtained was:

    (μ/8∏^2) * exp(j*(t - R/c) *J(r, t)/R

    Thank you for your help.
     
  2. jcsd
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