choclo.dipole.magnetic_u

choclo.dipole.magnetic_u(easting_p, northing_p, upward_p, easting_q, northing_q, upward_q, magnetic_moment)

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 (float) – Easting coordinate of the observation point in meters.

• northing_p (float) – Northing coordinate of the observation point in meters.

• upward_p (float) – Upward coordinate of the observation point in meters.

• easting_q (float) – Easting coordinate of the dipole in meters.

• northing_q (float) – Northing coordinate of the dipole in meters.

• upward_q (float) – Upward coordinate of the dipole in meters.

• magnetic_moment (1d-array) – Magnetic moment of the dipole. It should have three components in the following order: mag_moment_easting, mag_moment_northing, mag_moment_upward. Should be in \(A m^2\).

Returns

b_u (float) – 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 \(\mathbf{m}=(m_x, m_y, m_z)\).

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

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