Proving which way magnetic lines on a magnet travel
If you sprinkle iron filings around a magnet, the small iron filings react to the magnetic forces and position themselves along the magnetic lines.
To find which direction the magnetic lines travel, take a small compass and place it near one pole of the magnet and mark the positions of the ends N and S of the compass needle with pencil dots. Then move the compass so that the S end of the compass needle is over the dot you previously placed at the N end and mark the new position of the N end with a third dot. Keep repeating this until you reach the other end of the magnet.
We can now join the dots up.
This shows a field line of the magnetic field.
If we keep plotting the field lines around the magnet in different positions you should get the magnetic field plot above.
If you plot the field lines around a horseshoe magnet you should get the magnetic field plot above.