choclo.dipole.magnetic_u#

choclo.dipole.magnetic_u(easting_p, northing_p, upward_p, easting_q, northing_q, upward_q, magnetic_moment_east, magnetic_moment_north, magnetic_moment_up)[source]#

Upward component of the magnetic field due to a dipole.

Returns the upward component of the magnetic field by a single dipole on a single computation point

Parameters:

easting_p, northing_p, upward_pfloat

Easting, northing and upward coordinates of the observation point in meters.

easting_q, northing_q, upward_qfloat

Easting, northing and upward coordinates of the dipole in meters.

magnetic_moment_east, magnetic_moment_north, magnetic_moment_upfloat

The east, north and upward component of the magnetic moment vector of the dipole. Must be in $A{m}^2$.

Returns:

b_ufloat

Upward component of the magnetic field generated by the dipole on the observation point in $\text{T}$.

Notes

Returns the upward component $B_z(\mathbf{p})$ of the magnetic field $\mathbf{B}$ on the observation point $\mathbf{p}=(x_p,y_p,z_p)$ generated by a single dipole located in $\mathbf{q}=(x_q,y_q,z_q)$ and magnetic moment $\mathbf{m}=(m_x,m_y,m_z)$.

$$B_z(\mathbf{p})=\frac{{\mu }_0}{4\pi }[\frac{3(\mathbf{m}\cdot \mathbf{r})z}{\Vert r{\Vert }^5}-\frac{m_z}{\Vert r{\Vert }^3}]$$

where $\mathbf{r}=\mathbf{p}-\mathbf{q}$, $\Vert \cdot \Vert$ refer to the $L_2$ norm and ${\mu }_0$ is the vacuum magnetic permeability.