A
magnetic field is a picture that we use as a tool to
describe how the magnetic force is distributed in the
space around and within a magnet. Wikipedia
says that magnetic field lines form in concentric circles
around a cylindrical current-carrying conductor, such as a
length of wire. When we speak of the force due to a magnet
(or any force for that matter) it has to be on something.
This something is what we can call a force vector field.
It can describe the magnitude and direction of a particle
at any point.
"The field-line description has some useful properties:
- Magnetic field lines never cross.
- Magnetic field lines naturally
bunch together in regions where the magnetic field is
the strongest. The closer the lines are bunched
together the stronger the magnetic field.
- Magnetic field lines don't start
or stop anywhere, they always make closed loops and
will continue inside a magnetic material (though
sometimes they are not drawn this way).
- We require a way to indicate the
direction of the field. This is usually done by
drawing arrowheads along the lines. Sometimes
arrowheads are not drawn and the direction must be
indicated in some other way. For historical reasons
the convention is to label one region 'north' and
another 'south' and draw field lines only from these
'poles'. The field is assumed to follow the lines from
north to south. 'N' and 'S' labels are usually placed
on the ends of a magnetic field source, although
strictly this is arbitrary and there is nothing
special about these locations.
https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-field-current-carrying-wire/a/what-are-magnetic-fields."
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