Electric Potential and Field of a Dipole
Mathematica 9 can not only compute in different coordinate systems but also transform between them. In this example, Mathematica computes an electric field from a potential in spherical coordinates, then transfroms to Cartesian coordinates to create a visualization.
Compute the electric field of a dipole from its potential and verify that it is a vacuum solution by computing the divergence:
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Compute the equivalent fields in Cartesian coordinates for p=1 and visualize the equipotential surfaces and lines of force:
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