# 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 (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_east (float) – The East component of the magnetic moment vector of the dipole. Must be in $$A m^2$$.

• magnetic_moment_north (float) – The North component of the magnetic moment vector of the dipole. Must be in $$A m^2$$.

• magnetic_moment_up (float) – The upward component of the magnetic moment vector of the dipole. Must 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.