Delta functions in spherical coordinates and how to avoid losing them: Fields of point charges and dipoles

In calculations involving the divergence, curl, or Laplacian operators in spherical polar coordinates, the radial delta function contributions are sometimes inadvertently lost. This loss can be avoided by the judicious introduction of a step function. We apply this trick to confirm some subtle details about the fields of point electric and magnetic dipoles. (C) 2003 American Association of Physics Teachers.