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: The field lines always point away from the north end, and toward the south end, in a shape similar to the electric field between two oppositely charged particles. As we will see, this field is quite similar to the field created by a coil of wire with a current running through it (see solenoid). Permanent magnets are often used to create magnetic fields; these magnets are usually oriented in a manner that causes a uniform field, so we do not have to concern ourselves too much with their field shape.
The Magnetic Field of a Straight Wire
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.
Shape of the Field
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. Given that the field lines travel in a circle around the wire, as shown, how do we decide which way the field lines point? We use our hands again, relying on the second right hand rule. Take your right hand, stick your thumb up like a hitchhiker, curling your fingers around. If you point your thumb in the direction of the current, your fingers will curl around in the direction of the field lines. Try it with the figure above--in many ways this right hand rule is simpler than our first right hand rule.