Lines that close on themselves

Sketch a bar magnet's field and finish the job: the lines outside run from the north end around to the south end, and inside the material they continue from south back to north. Every line is a closed loop.

That is why cutting a magnet cannot separate the poles. Saw a bar magnet in half and you do not get a north piece and a south piece; you get two complete magnets, each with its own north and south. Cut again and it happens again, all the way down.

The reason is where the magnetism comes from. It is not a supply of magnetic charge sitting at the tip: it is circulating charge inside the material, the orbital and spin motion of electrons. Cut through a region of circulating charge and both halves still contain circulating charge, so both halves are still dipoles. The word "pole" names an end of the object, not a substance located there.

"Metal" is not the sorting criterion. What matters is how the material's magnetic dipoles behave in an applied field.

1. Ferromagnetic: iron, nickel, cobalt. The dipoles align in domains and stay aligned after the field is removed. Strong attraction, and these are the materials a permanent magnet can be made from.
2. Paramagnetic: aluminium, titanium, magnesium. The dipoles align weakly and relax the instant the field is gone. The attraction is far too weak to notice.
3. Diamagnetic: everything, including water, copper and graphite. A faint alignment opposite the applied field, so a very weak repulsion.

So a magnet lifts an iron nail and ignores an aluminium can, even though both are metal and both conduct. Conduction and magnetic response are different properties of a material: copper is one of the best conductors there is and a magnet does not pick it up.

A compass needle is a small magnetic dipole. The field exerts a torque on it, turning it until it lines up with the local field vector at the needle's own position. So the needle lies tangent to the field line passing through it.

On the axis of a bar magnet the tangent happens to point along the line to the magnet, which is why the error survives. Move the compass off the axis and the two directions separate, sometimes by a lot: a compass held above and to the side of a bar magnet can be nearly perpendicular to the straight line toward the pole.

Two more consequences of it being a torque and not a pull. A compass in a uniform field feels no net force at all, only a turning effect. And the field weakens as the compass is moved away, so the needle turns more sluggishly, but its final direction depends only on the field's direction there, not on its strength.

The same reading conventions from the electric-field topic carry over, with the closed-loop rule added.

1. Direction: the field at a point is tangent to the line through it, in the direction of the arrows. Outside a magnet, arrows run away from the north end.
2. Strength: carried by line density. Lines crowd near the poles, which is where the field is strongest.
3. Lines never cross, since the field has one direction at each point.
4. Every line closes. A drawing whose lines stop at the magnet's surface is incomplete.

Iron filings show the pattern because each filing becomes a tiny magnet and aligns with the local field, which is the compass argument repeated a few thousand times. The filings chain into lines because each one's own field then attracts the next.