geoana.em.static.MagneticPoleWholeSpace.magnetic_flux_density

MagneticPoleWholeSpace.magnetic_flux_density(xyz, coordinates='cartesian')

Compute the magnetic flux density produced by the static magnetic pole.

This method computes the magnetic flux density produced by the static magnetic pole at the set of gridded xyz locations provided. Where \(\mu\) is the magnetic permeability of the wholespace, \(m\) is the moment amplitude, \(\mathbf{r_0}\) the pole’s location and \(\mathbf{r}\) is the location at which we want to evaluate the magnetic flux density \(\mathbf{B}\):

\[\mathbf{B}(\mathbf{r}) = \frac{\mu m}{4\pi} \frac{\Delta \mathbf{r}}{| \Delta \mathbf{r}|^3}\]

where

\[\mathbf{\Delta r} = \mathbf{r} - \mathbf{r_0}\]

For reference, see equation Griffiths (1999).

Parameters:

xyz(n, 3) numpy.ndarray xyz

gridded xyz locations at which we calculate the magnetic flux density

coordinates: str {‘cartesian’, ‘cylindrical’}

coordinate system that the location (xyz) are provided. The solution is also returned in this coordinate system. Default: “cartesian”

Returns:

(n, 3) numpy.ndarray

The magnetic flux density at each observation location in the coordinate system specified in units T.