Solving Differential Equations Involving Vector Fields

1. Apr 23, 2009

Savant13

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. Apr 23, 2009

jambaugh

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.

3. Apr 24, 2009

Savant13

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)