Magnetic field lin
Mapping the magnetic field of an object is simple in principle. First, measure the strength and direction of the magnetic field at a large number of locations. Then, mark each location with an arrow (called a vector) pointing in the direction of the local magnetic field with a length proportional to the strength of the magnetic field.
A simpler method to map the magnetic field is to 'connect' the arrows to form magnetic field lines. On a magnetic field line diagram, the direction of the magnetic field at any point is represented by the direction of nearby field lines. Further, if drawn carefully, a higher density of nearby field lines indicates a stronger magnetic field.
Magnetic field lines are no more real than (for example) the contour lines (constant altitude) on a topographic map. A different mapping scale could show twice (or half) as many "lines", for example. An advantage of using magnetic field lines, though, is that many laws of magnetism (and electromagnetism) can be stated completely and concisely using simple concepts such as the 'number' of field lines through a surface. These concepts can be quickly 'translated' to their mathematical form. For example, the number of field lines through a given surface is the surface integral of the magnetic field.