Flux lines

Perhaps you have seen the experiment in which iron filings are placed on a sheet of paper, and then a magnet is placed underneath the paper. The filings arrange themselves in a pattern that shows, roughly, the “shape” of the magnetic field in the vicinity of the magnet. A bar magnet has a field with a characteristic form (Fig. 1).

Fig. 1: Pattern of magnetic flux lines around a bar magnet.

Another experiment involves passing a current-carrying wire through the paper at a right angle, as shown in Fig. 2. The iron filings will be grouped along circles centered at the point where the wire passes through the paper.
Physicists consider magnetic fields to be comprised of flux lines. The intensity of the field is determined according to the number of flux lines passing through a certain cross section, such as a square centimeter or a square meter. The lines don’t really exist as geometric threads in space, or as anything solid, but it is intuitively appealing to imagine them, and the iron filings on the paper really do bunch themselves into lines when there is a magnetic field of sufficient strength to make them move.

Fig. 2: Pattern of magnetic flux lines around a current-carrying wire.