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Solving Differential Equations Involving Vector Fields

  1. Apr 23, 2009 #1
    Given the curl and divergence of a vector field, how would one solve for that vector field?

    In the particular case I would like to solve, divergence is zero at all coordinates.
    Last edited: Apr 23, 2009
  2. jcsd
  3. Apr 23, 2009 #2


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    The problem you describe comes up in electromagnetism. The case of zero divergence would be modeled by finding the static magnetic field induced by a steady state electric current density J(x). The curl of the B field is proportional to the current density.

    Look up the Biot-Savart's Law which gives the B field as an integral involving the current.
  4. Apr 24, 2009 #3
    The application here is maxwell's equations. However, my use of point particles precludes the Biot-Savart Law (as the current density is constantly changing)
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