Do two distinct poles actually exist at two nearby points in a magnetic dipole?

Two like magnetic poles :

Magnetic poles always exist in pairs.

Consider two ‘postulates’ given below:(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.(ii) There exist at least three points that are not on the same line. Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.

Let the magnetic field on earth be modelled by that of a point magnetic dipole at the centre of earth. The angle of dip at a point on the geographical equator

A: Every magnetic configuration magnetic field north pole and south pole. R: North pole, south pole exists only if the source of the field has net magnetic dipole moment.

A: If a bar magnet is cut into two equal halves then magnetic dipole moment of each part is half that of the original magnet. R: magnetic dipole moment is the product of pole strength and magnetic length.

How many lines can pass through two distinct points on a plane?

Let the magnetic field on earth be modeled by that of a point magnetic dipole at the centre of earth. The angle of dip at a point on the geographical equator is

Show that the magnetic field at a point due to a magnetic dipole is perpendicular to the magnetic axis if the line joining the point with the centre of the dipole makes an angle of tan^(-1) (sqrt(2)) with the magnetic axis.

Let r be the distance of a point on the axis of a magnetic dipole from its centre. The magnetic fiedl at such a point is proportional to