How the angle between the magnetic axis of earth and the geographic axis of earth can be calculated?
[Physics] about angle between magnetic axis and geographical axis of earth
earthgeomagnetism
Related Solutions
The north-seeking pole always points toward magnetic north, assuming it is only feeling Earth's magnetic field. A magnet has no idea (so to speak) which direction is geographic north.
Any source that tells you that a magnet points geographically north is only as correct as the statement that geographic north and magnetic north are the same direction.
Start with some definitions :
Angle of Dip $\delta$ is the angle in the vertical plane aligned with magnetic north (the magnetic meridian) between the local magnetic field and the horizontal.
Angle of Declination $\theta$ is the angle between the magnetic and geographic meridians, or the angle in the horizontal plane between magnetic north and true north.
Source : TutorVista
In the magnetic meridian the vertical and horizontal components of the magnetic field are $B_v=B\sin\delta$ and $B_h=B\cos\delta$. The projection of the horizontal component $B_h$ onto the geographic meridian is $B_g=B_h\cos\theta$.
The plane perpendicular to the geographic meridian makes angle $180^{\circ}-(90^{\circ}+\theta)=90^{\circ}-\theta$ with the magnetic meridian. The projection of $B_h$ onto this plane is $B_p=B_h\cos(90^{\circ}-\theta)=B_h\sin\theta$.
The apparent angles of dip in the geographic meridian and the plane perpendicular to it are given by $$\tan\delta_1=\frac{B_v}{B_g}$$ $$\tan\delta_2=\frac{B_h}{B_p}$$ Therefore $$\frac{\tan\delta_1}{\tan\delta_2}=\frac{B_p}{B_g}=\frac{B_h\sin\theta}{B_h\cos\theta}=\tan\theta$$ $$\theta=\tan^{-1}(\frac{\tan\delta_1}{\tan\delta_2})$$
Best Answer
The magnetic axis of the Earth is defined as the axis of the closest fitting magnetic dipole to Earth's magnetic field.
The magnetic field of the Earth is not exactly a dipole, it is even asymmetric between the Northern hemisphere and the southern hemisphere: the North magnetic pole is located at 86.27°N and the South magnetic pole at 64.26°S. Moreover, they move over time.
However, Earth's magnetic field can be approximated to the first order by a dipole. (You can get a higher order expansion by adding higher orders: a quadrupole, an octupole... This is what the IGRF model does). The two positions where the the axis of this dipole crosses the surface are called the geomagnetic poles. These are located at 80.31°N and 80.31°S.
The geographical axis (or rotational axis) crosses the surface of the Earth, by definition of geographical latitude at 90°N and 90°S. Thus the angle between the magnetic dipole axis of the Earth and the geographic axis is thus 90°-80.31° = 9.69°.