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

The force on a magnetic monopole, if one existed, would be proportional to the product of its magnetic “charge” and the magnetic field. So it’s acceleration would be in the tangential direction, and the magnitude of its acceleration would decrease as the reciprocal of the distance from the wire.

Using $$a\sim\hat{\phi}/r$$, you can work out how it moves.

• will the north magnetic monopole follow the magnetic fields lines of electromagnetic lines ? Aug 29 '19 at 19:51
• No. “Accelerate along” not the same as “follow”. For example, the Earth accelerates radially toward the Sun, but its elliptical motion certainly doesn’t follow that that radial line. (If the Earth started from rest, it would move radially.) I haven’t solved the equations of motion, but I doubt that, even if you released a magnetic monopole from rest, it would follow a field line. Aug 29 '19 at 20:52
• You seem to have a misunderstanding of field lines. They tell you about force and therefore acceleration, not about velocity and thus direction of motion. Aug 29 '19 at 20:56
• 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
• As I have already explained, the “direction of the motion” and the “direction of the force” are two different things. I have also already explained that the force on a monopole is proportional to the magnetic field, so the force on it is along the magnetic field lines. Its motion is not along the magnetic field lines. Furthermore, the electric field lines and the magnetic field lines typically point in completely different directions. There are no “electromagnetic field lines”. Aug 30 '19 at 2:04