Earth's magnetic field

Evidence that Earth has a magnetic field. A freely pivoted compass needle, kept away from other magnets and large iron masses, always comes to rest pointing in essentially the same direction wherever it is placed. This repeatable, location-independent alignment cannot happen unless some field pervades the space around the compass and exerts a directing torque on it. That field is Earth's own magnetism, and the compass is simply the cheapest, most familiar detector of it.

The buried-magnet picture. Earth's field pattern outside the planet looks very similar to the field of a single enormous bar magnet tilted slightly from the rotation axis. Because a compass's north pole is attracted toward the pole in the Northern Hemisphere, that pole must behave as a magnetic south pole (unlike poles attract); the pole in the Southern Hemisphere behaves as a magnetic north pole. This is a classic "gotcha" fact examiners like to test directly.

Uniform versus non-uniform fields. Over a small region — a desk, a room, a school laboratory — Earth's field can be treated as uniform: the same magnitude and direction (roughly geographic north, tilted slightly by the local magnetic declination) at every point. Drawn on paper, its field lines over such a small area look like evenly spaced parallel straight lines, exactly like the field between two flat parallel plates. A bar magnet's field, by contrast, is strongly non-uniform: it is dense and strong near the poles, sparse and weak farther away, and the lines curve from the north pole around to the south pole. This contrast — uniform background field versus non-uniform magnet field — is the entire basis for what happens next.

where: $B_{\text{net}}(P)$ is the resultant field at a point $P$, $\vec{B}_{\text{Earth}}$ is Earth's field (treated as constant in magnitude and direction over the small region), and $\vec{B}_{\text{magnet}}(P)$ is the bar magnet's field at $P$, which changes in both magnitude and direction as $P$ moves. This is simple vector addition, not a numerical formula you need to plug numbers into — ICSE Class 9 keeps it entirely qualitative — but it is the idea that explains everything that follows, including neutral points.

Neutral points. When a bar magnet is placed on a table with its axis lying along the magnetic north-south direction, $\vec{B}_{\text{magnet}}(P)$ points in different directions at different places around it. There exist specific points where $\vec{B}_{\text{magnet}}(P)$ is exactly equal in magnitude and exactly opposite in direction to $\vec{B}_{\text{Earth}}$, so the vector sum is zero. Such a point is called a neutral point. Its location depends on which way the magnet's north pole faces: if the north pole faces geographic north, the two fields near the axis point the same way (they add, never cancel), so neutral points appear instead on the equatorial line (broadside-on, to the sides of the magnet); if the north pole faces geographic south, the fields cancel on the axial line extended beyond the poles, so the neutral points sit there instead.

Earth's field near its surface is, over the scale of a table top, effectively constant — a fixed magnitude pointing in a fixed direction, the way gravity near the ground is effectively constant even though it technically varies with height. A bar magnet's field, however, is created by two localised poles a short distance apart, so it falls off sharply with distance and swings in direction as you move around the magnet. When you superpose (vector-add) a constant field with a variable one, the sum is only zero at isolated points where the variable field happens to have crept down to exactly the right magnitude while pointing exactly opposite to the constant field. Move even a millimetre away from such a point and the cancellation breaks — the magnet's field has changed slightly in magnitude or direction, while Earth's field has not, so the balance is destroyed and a small net field reappears. This is precisely why neutral points are isolated points, not regions: the geometry of a rapidly varying field crossing a constant one only balances at specific locations, and the two configurations (equatorial-line points for one orientation, axial-line points for the other) are simply the two ways a bar magnet's field pattern can be made to point directly opposite to Earth's field on either side of the magnet.

Question: A bar magnet is placed on a horizontal table with its magnetic axis along the north-south direction, its north pole pointing toward geographic north. A compass is slid along the table, starting from a point beside the magnet, moving further from it. (a) Explain what the compass shows very close to the magnet, at the neutral point, and far away. (b) A second student repeats the setup but flips the magnet so its north pole faces geographic south. State how the location of the neutral points changes and why.

Solution: Step 1. Very close to the magnet, $\vec{B}_{\text{magnet}}$ is much stronger than $\vec{B}_{\text{Earth}}$, so the compass needle aligns almost entirely with the magnet's own field — it points toward the nearest pole of the magnet, ignoring Earth's field. Step 2. As the compass is moved outward along the sides of the magnet (the equatorial line, since the north pole faces geographic north), $\vec{B}_{\text{magnet}}$ weakens. At one particular distance it becomes exactly equal and opposite to $\vec{B}_{\text{Earth}}$: this is the neutral point, where the resultant field is zero and the needle can settle in any direction with no preferred alignment. Step 3. Moving still farther out, $\vec{B}_{\text{magnet}}$ becomes much weaker than $\vec{B}_{\text{Earth}}$, and the resultant field is dominated by Earth's field again — the compass returns to pointing roughly geographic north, just as it would with no magnet present at all. Step 4. For part (b): flipping the magnet so its north pole faces geographic south reverses $\vec{B}_{\text{magnet}}$ along the axis. Now it is along the axial line (extended beyond the poles) that the magnet's field points opposite to Earth's field, so the neutral points move from the equatorial line to the axial line.

Answer: Close to the magnet the compass follows the magnet's field; at the neutral point (on the equatorial line, for a north-pole-facing-north magnet) the resultant field is zero and the needle has no preferred direction; far away it reverts to pointing roughly geographic north. Reversing the magnet's orientation moves the neutral points from the equatorial line to the axial line.

• Confusing Earth's magnetic north pole with its geographic North Pole — they are close but not identical, and the magnetic pole in the Northern Hemisphere is actually a south-type pole.
• Assuming Earth's field is uniform everywhere on the globe — it is only treated as (locally) uniform over small regions like a table or a room, not across continents.
• Believing a neutral point means "zero magnetism exists there" in some permanent sense — it only means two specific fields happen to cancel at that exact spot for that exact magnet placement; move the magnet and the neutral point moves too.
• Forgetting that the neutral-point location (equatorial line versus axial line) flips depending on which way the bar magnet's north pole is pointed relative to geographic north.

Ask the tutor: Want to work through a case where the bar magnet is tilted at an angle to geographic north, or see how neutral points are actually plotted using a compass and iron filings?