Magnetic fields and lines of flux

[DecayProduct]

I have several texts, some new, some from the turn of the 20th century, that are all packed with explanations and formulae for electromagnetic theory. In almost all of them, it is stated that the magnetic field or it's lines of flux, are an abstraction, a mathematical tool to aid in solving problems. If they are an abstraction, that is, not real, why do those iron filings form those neat lines when sprinkled over a magnet? And what are those huge plasma prominences following when they arc off the sun?

I guess what I'm asking is, a magnetic field is obviously a real thing, so why do these (and other) texts say it is a fictional construct?

 

[Dick]

The reason they are fictional is that there is also a magnetic field between the lines that the material subjected to the magnetic field traces out. The filings form discrete lines because they become magnetic dipoles in the field and like to minimize energy by spontaneously assembling into lines. A magnetic field with nothing in it doesn't have discrete lines. It's a continuous field.