Notes to a video lecture on http://www.unizor.com
Magnetic Field Lines
Magnetic field is a force field, which means that there is
a force, acting on a probe object positioned at a distance from the
source of this field, and a force is a vector that has a direction and a magnitude.
Let's examine this force and attempt to determine a direction and a
magnitude of vectors of force at different locations around a magnet,
acting as a source of a field.
Our first complication is a kind of a magnet at the source of a magnetic
field. Different shapes (bar, ring, horseshoe etc.) result in
differently arranged fields.
Recall that we model the permanent magnet as a set of electrons
circulating around parallel axes in the same direction on parallel
planes. Each of these rotating electrons we considered as a tiny bar
magnet with two poles located on an axis on two opposite sides of a
plane of rotation. This construction is called a magnetic dipole.
This magnetic dipole is the most elementary magnet possible, and we can use it in our study of the properties of a magnetic field.
Bar magnet would be the best choice for a source of a magnetic field for
our study, since it closely resembles each elementary magnetic dipole
created by one rotating electron.
The next decision we have to make is the shape of a probe object. It is
important since different shapes would behave differently in the same
magnetic field.
Here, again, we choose the bar magnet, as the simplest. Note that a
magnet is not a point-object because it has two poles. Therefore, we
have to consider two types of its motion - translational motion of its
center and rotation around its midpoint.
In the previous lecture we presented a two-dimensional picture of iron
filings dropped around a bar magnet. Schematically, it's represented as
Lines around this magnet represent the magnetic field lines,
along which the filings link to each other, and the direction of the
compass needle, if positioned at any point in this magnetic field.
The designation of which pole of a magnet is North and which is South is
traditional - if hanging freely, North pole of a permanent magnet is
the one pointing to geographical North of the Earth. After one magnet's
poles are defined, all other magnets' poles can be determined using
their interaction with previously defined, according to the rule
"similar repel, different attract".
By the way, it means that the magnetic pole of the Earth that is close
to its geographical North pole is, technically speaking, the South
magnetic pole of the Earth. So, when someone says "North magnetic pole
of the Earth", it, most likely, means "Magnetic pole of the Earth that
is close to its geographical North pole". Not always, though, so it
might lead to confusion.
Arrows on each line from North pole of a magnet towards its South pole
are the traditional definition of the magnetic force direction. It's
just the agreement among people similar to an agreement about the
definition of the flow of electricity from positive terminal of the
source of electricity (where, in reality, there is a deficiency of
electrons) to its negative terminal (with excess of electrons), in spite
of the real moving of electrons in the opposite direction.
Another important quality of these magnetic field lines is that,
if the source of a magnetic field (a bar magnet on the picture above) is
fixed on a flat surface and another very small and light probe magnet
could freely move without friction in the magnetic field on that
surface, its center would move along the magnetic field lines in
the direction of the arrows on the picture above, always oriented
tangential to a magnetic line it's moving along, pointing its North pole
towards the South pole of a magnet that is the source of the magnetic
field.
Magnetic field lines never cross, as they represent the
trajectories. If they cross at any point, the probe magnet would have
ambiguous dynamics at this point.
The density of the magnetic field lines visually represents the
strength of the magnetic forces at each point. The lines close to the
poles of a magnet are the most dense, as the field is stronger there.
Let's position our probe bar magnet on any line around a source of this
magnetic field. If we let it turn freely, as if this probe magnet is an
arrow of a compass, it will align along the tangential to a magnetic field line it is on.
The North pole of a probe object in this position will point towards the
South pole of a bar magnet in the center of the field and the South
pole of a probe magnet will point towards the North pole of a center
magnet.
Two attracting and two repelling forces from two poles of a center magnet, acting on a probe object, represent the torque that turns the probe magnet and holds it in a position along the magnetic field line.
The pole of a center magnet that is closer to a probe object forces the
probe object to turn the opposite pole towards it to a greater degree.
Obviously, there is a resultant force that ultimately moves the center of a probe object closer to a center magnet.
Also, in a special case of a probe object positioned exactly on the
continuation of the North-South line between the poles of the center
magnet both forces from two poles of a center magnet act along this same
line and can be added easily.
The above considerations are related to a direction of the forces acting on a probe magnet in the magnetic field of a bar magnet.
The magnitude of these forces is a more involved subject and is
related to techniques of measurement of the strength of a magnetic field
at different points. This will be a subject of the next topic.
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