 Magnetic dipole inclination versus latitude

For a centred magnetic dipole moment pointing toward geographic south, the field at northern latitude $\lambda$ has northward component $B_N=B_{\mathrm{eq}}\cos \lambda$ and downward component $B_D=2B_{\mathrm{eq}}\sin \lambda$. These follow by resolving the magnetic dipole field into local radial and meridional directions. The downward inclination is therefore $\tan \iota =B_D/B_N=2\tan \lambda$, while the magnitude is $B_{\mathrm{eq}}\sqrt{1+3{\sin }^2\lambda }$. This ideal aligned-dipole model has no eastward component and does not capture actual geographic departures of the geomagnetic field.