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!

Fourier Tranform of electric dipole charge density

  1. Jul 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Hi,

    This is supposed to be simple, so I guess I miss something..
    We have charge q at x1=d*cos (w*t), y=0, z=0. and charge -q at
    x2=-d*cos (w*t), y=0, z=0. I need to do fourier transform to the charge density.

    2. Relevant equations
    The fourier transform is : [itex]\rho_{\omega} = \int \rho (r,t)e^{i\omega t} dt [/itex]


    3. The attempt at a solution
    I first try only for the first charge. We have [itex]\rho (r,t) = \delta(x-d\cdot cos (\omega t))\cdot\delta(y)\cdot\delta(z) [/itex]
    But I don't know how to do the intergral :
    [itex]\rho_{\omega} = \int \delta(x-d\cdot cos (\omega t))\cdot\delta(y)\cdot\delta(z)e^{i\omega t} dt [/itex]
    Any ideas? Do I really need to do this integral?
     
  2. jcsd
  3. Jul 5, 2011 #2

    Mute

    User Avatar
    Homework Helper

    Generally, if you have an integral over a delta function of another function, you can use the relation

    [tex]\delta(f(t)) = \sum_{j}\frac{\delta(t-t^\ast_j)}{|f'(t^\ast_j)|},[/tex]
    where the [itex]t^\ast_j[/itex] are the solutions of [itex]f(t^\ast) = 0 [/itex]. Note that this relation doesn't work if the derivative is zero at a solution.
     
  4. Jul 6, 2011 #3
    Hi,

    Thanks for your answer.
    Actually the question is to find the potential of this charges far from the origin,so I guess I should transform the dipole moment vector only..
    Using the identity for the delta function I get weird things like exp(arccos (x/d))...
    It is just interesting if the transform of the charge density could be useful.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fourier Tranform of electric dipole charge density
Loading...