## Sunday, May 3, 2020

### Unizor - Physics4Teens - Electromagnetism - Magnetic Field

Notes to a video lecture on http://www.unizor.com

Magnetism - Magnetic Field

Magnetic forces act on a distance, so there must be a field that exists around each magnet - magnetic field.

When studying Electrostatics, we started with the simplest
electrically charged object - a point-object with certain excess or
deficiency of electrons to make it negatively or positively electrically
charged.

The electrostatic field around it was spherical in shape and the only
important parameter that determined the relative position of a probe
object (also a point-object, positively charged with one coulomb of
electricity) was a distance of this probe object from the source of
electrostatic field.

If we wanted to analyze the electric properties of a more complex source
of electricity, like a rod or a sphere, we could always resort to some
relatively simple geometry and calculus to achieve our goal by breaking a
larger object into smaller parts.

Looking at the electrostatic field, the forces acting on a probe object
are always unidirectional, either attracting or repelling. To calculate
the resultant force, we used a vector sum of them, and in simple cases
of sources of electrostatic fields (a point-object, a rod, a sphere) it

With magnets the situation is much more complex. We cannot have a
point-object because each magnet has two poles and each of them act in
some way. Even more, the magnetic force exhorted by a magnet is changing
as we move from North pole to South, first diminishing to zero in the
middle and rising again at the other pole.

Probably, the simplest magnet we can deal with, as a source of magnetic
field and a probe object, is a thin rod with poles at its ends. But even
in this case we have to take into account all the different forces,
attracting and repelling, of different magnitude and directions that act
on probe magnet.

Let's experimentally visualize the magnetic field in this simplest case.

For this experiment we need a bar magnet and iron shavings. Each shaving
is a little temporary magnet that forms its poles based on the forces
of the magnetic field. Then different shavings will attach to each other
by opposite poles and form lines. The picture obtained will represent
the vectors of forces in the magnetic field of a bar magnet. Along each
line on a picture below lie iron shavings, each with North and South
magnetic poles, linked by opposite poles and directed with their South
pole closer to North pole of a bar magnet. The picture below schematically represents these field forces. Direction of forces from North magnetic pole to South was traditionally
chosen, similarly to a direction of the electric current was chosen from
a positive terminal to a negative one, regardless of the flow of
electrons, unknown at the time of early experiments with electricity.

Let's discuss a concept of a magnetic field.

As usually, the following explanation is the model, which to some
degree corresponds to experimental and theoretical data, but we do not
claim that in reality the things are arranged in exactly this way.

However, we offer it as an aid to understanding the concept of a magnetic field.

Imagine a small particle rotating within a plane with certain speed on a
certain radius around an axis that is perpendicular to this plane. On
the same axis in a plane parallel to the first one another particle is
rotating. Generally speaking, it might rotate on a different radius, in
the same or opposite direction and with a different speed.

Consider a distance between these two parallel planes of rotation of
these two particles. When it's large, particles don't really have any
interaction. But, when we make this distance small enough, the particles
will "feel" each other.

If the particles rotate in the same direction, there will be some
attracting force between them and the planes of rotation tend to get
closer to each other.

If the particles rotate in the opposite directions, there will be some
repelling force between them and the planes of rotation tend to increase
the distance between them.

The rotating particles in this model behaves like a bar magnets
positioned along the axis of rotation with poles determined by a
direction of rotation. We can assume that the North pole is defined by a
rule, that, looking from it towards the rotating particle, this
particle rotates counterclockwise.

If two particles rotate around the same axis in the same direction, each
behaving like a bar magnet, the magnets will attract to each other
because they will be facing by opposite poles.

If the particles rotate in opposite direction, the corresponding magnets
will be facing each other by the same pole and will repel each other.

Now let's assume that these particles are electrons rotating around a
nucleus in the atoms inside some object. According to this model, if all
planes of rotation of electrons inside all atoms are parallel and the
rotation is such that all North poles of all atoms are directed in the
same way, we have a perfect permanent magnet.

If planes of electron rotation in some object are randomly directed and
are insensitive to outside forces exhorted by magnets, we have a
diamagnetic object - the one that cannot be magnetized.

If planes of electron rotation in some object are randomly directed, but
outside magnetic forces, interacting with atoms of this object, align
all planes of rotation in a parallel fashion with the same direction of
the poles, we have an object that can be a temporary magnet.

In all those cases our model of rotating electrons, producing a force
that in some way acts like a bar magnet positioned along the axis of
rotation, seems to explain all the magnetic properties.

It also prompts to a connection between the electricity and magnetism
because both are caused by position and movement of electrons.