choclo.dipole.magnetic_field

choclo.dipole.magnetic_field(easting_p, northing_p, upward_p, easting_q, northing_q, upward_q, magnetic_moment_east, magnetic_moment_north, magnetic_moment_up)

Magnetic field due to a dipole.

Returns the three components of the magnetic field due to a single dipole a single computation point.

Note

Use this function when all the three component of the magnetic field are needed. Running this function is faster than computing each component separately. Use one of magnetic_e, magnetic_n, magnetic_u if you need only one of them.

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_e, b_n, b_ufloat

Easting, northing and upward components of the magnetic field generated by the dipole at the observation point in \(\text{T}\).

Notes

The magnetic field vector \(\mathbf{B}\) at the observation point \(\mathbf{p} = (x_p, y_p, z_p)\) generated by a single dipole located at \(\mathbf{q} = (x_q, y_q, z_q)\) and magnetic moment \(\mathbf{m}=(m_x, m_y, m_z)\) is

\[\mathbf{B}(\mathbf{p}) = \frac{\mu_0}{4\pi} \left[ \frac{ 3 (\mathbf{m} \cdot \mathbf{r})\ \mathbf{r} }{ \lVert r \rVert^5 } - \frac{ \mathbf{m} }{ \lVert r \rVert^3 } \right]\]

in which \(\mathbf{r} = \mathbf{p} - \mathbf{q}\), \(\lVert \cdot \rVert\) refers to the \(L_2\) norm, and \(\mu_0\) is the vacuum magnetic permeability.

References

• [Blakely1995]