choclo.dipole.magnetic_n

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

Northing component of the magnetic field due to a dipole

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

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_nfloat

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

Notes

Returns the northing component \(B_y(\mathbf{p})\) 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 \(\mathbf{m}=(m_x, m_y, m_z)\).

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

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