What do magnetic field lines represent?

When magnetic field lines of permanent magnet were put, they supposed a north monopole magnet, so if you put a monopole north magnet it will follow the magnetic field lines.

But what about the magnetic field of a current flowing in a wire or solenoid, according to what did scientists put these lines?

What happens if you put a monopole in this magnetic field? • this might answer your second question. Aug 29 '19 at 17:54
• Magnetic monopoles do not exist. Aug 29 '19 at 18:19
• @my2cts , I know Aug 29 '19 at 18:49

Using $$a\sim\hat{\phi}/r$$, you can work out how it moves.
• I am just concerned about the direction of the motion, I know that $F=ma$ so the magnet applies a force on the monopole thus it will accelerate, However, What I am concerned about is the direction of the force applied on a north monopole By an electromagnetic field lines, Will it accelerate with the same direction of the field lines ? (By electromagnetic field ) Aug 29 '19 at 22:43