Explain the magnetic field of the Earth and give the order of magnitude of the Earth's magnetic field.

(N/A) To describe the magnetic field of the Earth at a point on its surface,we need to specify three quantities,which are known as the elements of the Earth's magnetic field:
$(i)$ The magnetic declination $(D)$: The angle between the geographic meridian and the magnetic meridian.
$(ii)$ The angle of dip or magnetic inclination $(I)$: The angle that the total magnetic field vector of the Earth makes with the surface of the Earth.
$(iii)$ The horizontal component of the Earth's magnetic field $(H_{E})$.
From the geometry of the magnetic field components:
$H_{E} = B_{E} \cos I \quad ...(1)$
$Z_{E} = B_{E} \sin I \quad ...(2)$
Where $Z_{E}$ is the vertical component of the Earth's magnetic field.
Dividing $(2)$ by $(1)$,we get:
$\tan I = \frac{Z_{E}}{H_{E}} \quad ...(3)$
Squaring and adding $(1)$ and $(2)$,we get the total magnetic field intensity $B_{E}$:
$B_{E} = \sqrt{H_{E}^{2} + Z_{E}^{2}} \quad ...(4)$
The order of magnitude of the Earth's magnetic field is approximately $10^{-5} \text{ T}$.