Representing magnetic fields: in theory
Physics Narrative for 11-14
Magnetic field diagrams
Magnetic fields are represented by diagrams which show patterns of magnetic field lines.
The magnetic field lines show the direction in which the magnetic force is acting at any particular point. The density of the magnetic field lines shows the strength of the magnetic force acting. If the lines are close together the magnetic force is great, if the lines are spread out the force is weak. From the magnetic field pattern you can see that the magnetic field is strongest (greatest magnetic force acting on any magnetic object) at the poles of a magnet.
No two dimensional picture can replace the full understanding that can be gained by exploring the field around a magnet with a carefully gimballed magnet. These images are a poor substitute for trying it for yourself.
The direction of the magnetic field
The arrows on the magnetic field lines show the direction of the magnetic field, but what precisely does this mean?
In the case of gravity we can use any object (with mass) as a field detector; the direction of the field is given by the direction of the force that the object experiences when placed in the field. For example, hold a book in your hand and it is obvious that the gravity field is acting in a downwards direction on the book.
With magnetism, there are two contenders for the role of field detector, north and south poles. Deciding on north or south is a matter of convention, and the convention that is used throughout the world of physics is that the arrow drawn on a magnetic field line shows the direction in which a free north pole would move, that is from north towards south.