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 \(A m^2\).
- easting_p
- Returns:
- b_u
float
Upward component of the magnetic field generated by the dipole on the observation point in \(\text{T}\).
- b_u
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.