choclo.prism.magnetic_uu#
- choclo.prism.magnetic_uu(easting, northing, upward, prism_west, prism_east, prism_south, prism_north, prism_bottom, prism_top, magnetization_east, magnetization_north, magnetization_up)[source]#
Upward derivative of the upward component of the magnetic field.
Returns the upward derivative of the upward component of the magnetic field due to a single rectangular prism on a single computation point.
- Parameters:
- easting
float Easting coordinate of the observation point. Must be in meters.
- northing
float Northing coordinate of the observation point. Must be in meters.
- upward
float Upward coordinate of the observation point. Must be in meters.
- prism_west
float The West boundary of the prism. Must be in meters.
- prism_east
float The East boundary of the prism. Must be in meters.
- prism_south
float The South boundary of the prism. Must be in meters.
- prism_north
float The North boundary of the prism. Must be in meters.
- prism_bottom
float The bottom boundary of the prism. Must be in meters.
- prism_top
float The top boundary of the prism. Must be in meters.
- magnetization_east
float The East component of the magnetization vector of the prism. Must be in \(A m^{-1}\).
- magnetization_north
float The North component of the magnetization vector of the prism. Must be in \(A m^{-1}\).
- magnetization_up
float The upward component of the magnetization vector of the prism. Must be in \(A m^{-1}\).
- easting
- Returns:
- b_uu
float Upward derivative of the upward component of the magnetic field generated by the prism on the observation point in \(\text{T}\). Return
numpy.nanif the observation point falls in a singular point: prism vertices, prism edges or interior points.
- b_uu
See also
Notes
Computes the upward derivative of the upward component of the magnetic field \(\mathbf{B}(\mathbf{p})\) generated by a rectangular prism \(R\) with a magnetization vector \(M\) on the observation point \(\mathbf{p}\) as follows:
\[B_{zz}(\mathbf{p}) = \frac{\mu_0}{4\pi} \left( M_x u_{xzz} + M_y u_{yzz} + M_z u_{zzz} \right)\]Where \(u_{ijk}\) are:
\[u_{ijk} = \frac{\partial^3}{\partial i \partial j \partial k} \int\limits_R \frac{1}{\lVert \mathbf{p} - \mathbf{q} \rVert} dv\]with \(i,j,k \in \{x, y, z\}\).
References