We begin looking at the sources of magnetic fields by looking at the most simple cases: permanent magnets and straight wires.
Permanent magnets are the most familiar sources of magnetic fields. A compass needle is a permanent magnet, which itself reacts to the permanent magnet in the earth's axis. Unfortunately, the fields of permanent magnets are very hard to calculate, and require an understanding of complex ferromagnetic phenomena, belonging as much to atomic theory as to electromagnetism. Here we will simply give a qualitative description of the magnetic fields of permanent magnets.
In essence, a permanent magnet is a piece of metal with a "North Pole" and a "South Pole". Any magnetized piece of metal has both poles; no magnet can exist with only one pole. Since magnetic charge does not exist, there is no isolated concentration of magnetic charge in an object. So why not simply take a magnet and split it in half, thus separating the north and south ends? Well, when we try it, two smaller, identical magnets are produced, shown below. Again, the north or south end of a magnet cannot be isolated.
Even though we cannot describe quantitatively the field of a permanent magnet, we can show its shape:
Like magnets, current-carrying wires also create magnetic fields. Wires of and any and all shapes create a magnetic field, but straight wires are the easiest to work with. After going through some calculus we will tackle more complex situations, but for now we look at the most simple case: the straight wire.
As we know, the magnetic field must always be perpendicular to the direction of the current; in terms of a field around a wire, this means that the field lines must follow a circular path about the wire, as shown below.