Having shown the forces that result from a given magnetic field, we must now complete the picture of magnetic forces and fields by describing the source of those fields. Such a topic is complex, as magnetic fields come from sundry sources. Magnets, compasses, straight wires, curved wires, and solenoids are just some of the sources we will study. Such diverse sources give rise to complex phenomena, only explainable through vector calculus and difficult mathematics. This SparkNote will try to cover most sources on a basic level, but also provide the necessary mathematics to provide for a complete understanding of the topic.
We begin by describing magnets. Though they are easily describable in terms of north and south poles, their magnetic fields are actually quite complicated, and are not examined on a quantitative basis. In the same section, we move on to perhaps the simplest source of a magnetic field, a straight wire. From this point we must develop some calculus regarding magnetic fields before analyzing more complex phenomena. Equipped with this mathematics, we can then examine the fields of rings, coils, and solenoids.
By the end of this SparkNote, one should have a fairly complete understanding of magnetic phenomena. We will have described both the cause and effect of magnetic fields. With this complete understanding we can then examine magnetism on a theoretical basis, using vector calculus as our guide.