If I have an irregularly shaped magnetic material and want to find which way is the north and south. How do I do it?
And more importantly, why are the north and south poles of a magnet situated where they are?
[Physics] Determining North and South pole of magnet
dipolemagnetic fields
Related Solutions
You van have two pairs of north/south if you wish.
Earth's magnetic field isn't really a dipole, but a dynamic field due to the convection occurring in the planet's core (consists of molten iron). The model below shows a simulation of the magnetic field (blue is pointing towards the core while yellow points away), the cluster of curves in the middle is the planet's core.
The geomagnetic pole is the location of the pole if earth's magnetic field were a simple dipole (no convection-driven fields).
Note also that, in your image, the geomagnetic pole hasn't moved much in the last century while the magnetic pole has. This is because every several thousand years, the magnetic poles flip sides (a non-constant rate of reversal, so we can't really say a definitive time-frame).
Best Answer
A typical magnetic material is made up of magnetic domains. These are regions of the material where all the electron spins are aligned to give the domain an overall magnetic moment. Typically these domains will be around 10 microns in size.
The total magnetic field of the chunk of iron, or whatever, is the sum of the individual fields of all the domains within it. In the unmagnetised state the domains are randomly aligned so their fields cancel out. When you magnetise the iron you are changing the alignment of the domains so they are partially aligned. This makes their fields reinforce instead of cancelling so we get an overall macroscopic magnetic field.
So to understand the field of an irregularly shaped piece of iron you need to consider the domains within it and add up their magnetic fields. In effect it's like making up your shape by gluing together lots of tiny bar magnets. An individual magnetic domain has a dipole field and in a bar magnet these fields sum to give a total field that is also approximately dipolar. However for some random shape the total field is going to be more complicated so it can't simply be described as a dipole.
The North and South poles we associate with magnets are the two directions in a dipolar field, so a randomly shaped magnet doesn't necessarily have distinct North and South poles. When you are far enough away from the magnet the field will usually look approximately dipolar, with distinct poles, but as you get closer to the magnet the field will become more complex.
I have written a related answer in What happens to the poles of a bar magnet if it isn't completely broken in two, but only partially broken? and you might be interested to read that as it also talks about irregularly shaped magnets.