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 fields 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_pfloat

Easting coordinate of the observation point in meters.

northing_pfloat

Northing coordinate of the observation point in meters.

upward_pfloat

Upward coordinate of the observation point in meters.

easting_qfloat

Easting coordinate of the dipole in meters.

northing_qfloat

Northing coordinate of the dipole in meters.

upward_qfloat

Upward coordinate of the dipole in meters.

magnetic_moment_eastfloat

The East component of the magnetic moment vector of the dipole. Must be in \(A m^2\).

magnetic_moment_northfloat

The North component of the magnetic moment vector of the dipole. Must be in \(A m^2\).

magnetic_moment_upfloat

The upward component of the magnetic moment vector of the dipole. Must be in \(A m^2\).

Returns:

b_efloat

Easting component of the magnetic field generated by the dipole on the observation point in \(\text{T}\).

b_nfloat

Northing component of the magnetic field generated by the dipole on the observation point in \(\text{T}\).

b_ufloat

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

Notes

Returns the three components 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 \(\mathbf{m}=(m_x, m_y, m_z)\).

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

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