Earth's Magnetic Field and Magnetic Elements

The Earth as a giant bar magnet. A freely suspended magnetic needle anywhere on the Earth's surface settles, after any disturbance, pointing in a fixed direction -- clear evidence that the Earth itself is the source of a magnetic field. To a good approximation, this field is the same as that of a single short but very powerful bar magnet located near the Earth's centre, tilted at roughly $11.3^\circ$ to the Earth's rotation axis, with its (magnetic) S pole lying close to the geographic North Pole (this is WHY the N pole of a compass needle -- attracted toward an opposite pole, exactly as Section 1.4's poles attract -- points roughly toward geographic north) and its (magnetic) N pole lying close to the geographic South Pole.

The three magnetic elements. At any given place on the Earth's surface, the local magnetic field is completely specified by three measured quantities, the magnetic elements (Figure 1):

1. Angle of declination ($D$). The angle, measured in the horizontal plane, between the geographic meridian (the vertical plane containing the true, geographic north-south direction) and the magnetic meridian (the vertical plane containing the direction a freely suspended compass needle actually points). $D$ tells a navigator how much a compass reading must be corrected to obtain true geographic north.

2. Angle of dip or inclination ($\delta$). The angle the Earth's total field vector $\vec{B}_E$ makes with the horizontal, measured within the magnetic meridian plane. A magnetic needle free to rotate about a HORIZONTAL axis (a "dip needle") comes to rest along this tilted direction, not lying flat.

3. Horizontal component ($H$). The component of $\vec{B}_E$ that lies in the horizontal plane, along the magnetic meridian -- the component that an ordinary compass needle, free to rotate only about a VERTICAL axis, actually aligns with.

Relating the elements. Resolving $\vec{B}_E$ into its horizontal component $H$ and its vertical component $V$ (Figure 1) gives the standard right-triangle relations

used directly in Numerical 8. …