Lines Of Flux:

Physicists thought magnetic fields to be consist of flux lines, or the lines of flux. The intensity of the field is established according to the number of flux lines passing via a certain cross section, like a centimeter squared (cm²) or a meter squared (m²). The lines are not real threads in space, though it is intuitively appealing to visualize them this way, and their existence can be shown by simple experimentation.

Have you view the classical demonstration in which the iron filings are positioned on a sheet of paper, and then a magnet is placed under the paper? The filings arrange themselves in a pattern which shows, approximately, the "shape" of the magnetic field in the vicinity of the magnet. The bar magnet has a field whose lines of flux have a characteristic pattern which is as shown in figure below.

Figure: Magnetic flux around a bar magnet.

The other experiment includes passing a current-carrying wire via the paper at a right angle. The iron filings become grouped all along circles centered at the point where the wire passes via the paper. This show that the lines of flux are circular as sight through any plane passing via the wire at a right angle. The flux circle is centered on the axis of the wire, or the axis all along which the charge carriers move which is as shown in figure below.

Figure: Magnetic flux generated by charge carriers traveling in a straight line.