Earth's Magnetism

The Earth is a magnet. Its field is roughly that of a giant bar magnet at the centre, tilted from the spin axis, and three numbers describe it at any place.

A dipole inside the Earth#

Near the surface the field is roughly that of a dipole of moment about 8.0 × 10²² J/T at the centre, its axis about 11.5° from the rotation axis. Where that axis meets the surface are the geomagnetic north pole(near the geographic north pole) and the geomagnetic south pole. There the field is vertical: a freely hung magnet stands straight up and down (north end down at the geomagnetic north pole). That is how the geomagnetic poles are defined.

A hung magnet’s north end is attracted to the dipole’s south pole, so the imaginary bar magnet inside the Earth has its south pole toward the geomagnetic north.

The elements of the Earth’s field#

Declination

The geographic meridian at a point P is the vertical plane through P and the geographic poles; the magnetic meridian is the vertical plane through P and the geomagnetic poles. The Earth’s field at P lies in the magnetic meridian. The angle between the two meridians is the declination. A compass needle settles in the magnetic meridian, so navigators must correct its “north” by the declination.

Inclination or dip

The angle the field makes with the horizontal, in the magnetic meridian, is the dip δ. In the magnetic northern hemisphere the field slopes downward, so a freely hung needle’s north end dips.

Horizontal component

B_H is the field’s horizontal component, pointing to magnetic north. Declination and dip fix the field’s direction; with B_H they fix its size too:

Measuring dip#

A dip circle is a magnetic needle pivoted at the centre of a vertical circular scale (0°–0° horizontal, 90°–90° vertical), in a glass case that turns about a vertical axis over a horizontal scale.

1. Level the base. Turn the case until the needle stands vertical (90°–90°): the scale’s plane is now perpendicular to the magnetic meridian, so B_H can’t turn the needle and only B_V acts.
2. Turn the case through exactly 90°: the scale now lies in the magnetic meridian, the needle lies along B⃗, and its ends read the dip.

Errors and their cures: read both ends of the needle (off-centre pivot); rotate the circle by 180° (0–0 line not horizontal); turn the needle over on its bearing (magnetic axis ≠ geometric axis); remagnetize it the other way (centre of mass off the pivot). Averaging all 16 readings gives the true dip.

Apparent dip

If the scale’s plane is at angle α to the meridian, only B_H cos α lies in it, while B_V is unchanged, so the needle shows an apparent dip δ′:

Neutral points#

Near a magnet there may be points where the magnet’s horizontal field exactly cancels B_H. There a compass needle feels no horizontal field and stays in any position: a neutral point.