Earth's Magnetism

It is common everyday experience that a bar magnet or magnetic needle, suspended freely in air, always aligns itself along the geographic North-South direction; and if it additionally has the freedom to rotate about a horizontal axis, it settles at some fixed angle to the horizontal rather than lying perfectly flat. This behaviour is direct evidence that a magnetic field is present everywhere on (and around) the Earth -- called Terrestrial Magnetism -- and it is precisely this field that makes navigation by compass possible. The Earth's magnetic field lines enter the Earth's surface near its (north) magnetic pole and emerge near its (south) magnetic pole, exactly matching the external field pattern of a bar magnet. Unless stated otherwise, every direction mentioned below (North, South, etc.) is the GEOGRAPHIC direction, not the magnetic one.

The Earth is treated, to a good approximation, as one huge bar magnet. Its magnetic north pole (N) -- the pole where field lines converge, matching a bar magnet's own south-type behaviour -- is located below Antarctica, while its magnetic south pole (S) is located below northern Canada; the straight line NS joining these two poles is called the Earth's magnetic axis, labelled MM'. A great circle lying in the plane perpendicular to this magnetic axis is called the magnetic equatorial circle, labelled AA'; it happens to pass through India close to Thiruvananthapuram (Fig. 12.5).

Two reference planes are needed to describe how the Earth's field is oriented at any particular place. The geographic meridian is the vertical plane, perpendicular to the Earth's surface, that passes through the geographic (rotation) axis -- it defines true geographic north. The magnetic meridian is the vertical plane, also perpendicular to the surface, that instead passes through the Earth's magnetic axis; the direction of the Earth's resultant magnetic field at a place always lies along, or parallel to, this magnetic meridian plane (Fig. 12.6). The angle between the geographic meridian and the magnetic meridian at a place is called the magnetic declination, $\alpha$. This declination is small in India: about $0^\circ58'$ west at Mumbai and about $0^\circ41'$ east at Delhi, so a compass at either city already shows very close to true north.

Within the magnetic meridian plane at a place, the Earth's resultant field $\vec B$ generally makes some angle with the horizontal, called the magnetic inclination or angle of dip, $\phi$ (Fig. 12.7). Resolving $\vec B$ into a horizontal component $B_H$ and a vertical component $B_V$ gives $B_H=B\cos\phi$ and $B_V=B\sin\phi$; the vertical component is comparatively easy to measure directly. From these, $\tan\phi=\dfrac{B_V}{B_H}$ (Eq. 12.10) and $B=\sqrt{B_H^2+B_V^2}$ (Eq. 12.11). Three special cases follow directly: (1) at the magnetic north pole, $B=B_V$ (directed straight upward), $B_H=0$, and $\phi=90^\circ$; (2) at the magnetic south pole, $B=B_V$ (directed straight downward), $B_H=0$, and $\phi=270^\circ$; (3) anywhere on the magnetic (great-circle) equator, $B=B_H$ (directed from geographic South to North), $B_V=0$, and $\phi=0^\circ$.

Because the horizontal component $B_H$, the declination $\alpha$, and the dip $\phi$ all vary from place to place (and slowly with time, as the Earth's own magnetic poles drift), magnetic maps -- drawn by joining places that share the same value of a given magnetic element -- are essential for accurate navigation. These are called iso-magnetic charts: lines joining places of equal horizontal component $B_H$ are Isodynamic lines; lines joining places of equal declination $\alpha$ are Isogonic lines; and lines joining places of equal inclination (dip) $\phi$ are Aclinic lines. …