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3B. Entity Field Electromagnetism (Part B)

__3.8. The
Origin of Magnetic Phenomenon__

__3.9.
Entity Magnetic Field Is a Relative, Relativistic and Quantified Field__

__3.10. Magnetic Force and
Its Force Field__

__3.11.
Magnetic Action of a Current__

__3.13.
Inductance and Magnetic Energy__

__3.14.
Magnetic Properties of Matter__

All experiments prove that there is no
magnetic monopole to form the source of a magnetic force. The so-called
“magnetic field” is the result of a moving electron or proton. In term of
entity field, a magnetic force is originated from a moving entity field. To get
a clear picture of this new way of understanding magnetic phenomenon, let’s start
with some simple experiments.

Figure (3.8.1c) An electron moves in free
space

Figure (3.8.1a) is a stationary electron
in a magnetic force field **F**_{B}. There is no magnetic force on
it. In fact, it is nothing but a normal electron. This means that a magnetic
force does not interact with entity electric field.

Then, we can imagine that this electron is
moving perpendicularly in the magnetic force field **F**_{B} with speed **v**, as shown in figure (3.8.1b). As the result of this motion, there
is a magnetic force on the electron. This means that the moving electron
produces a magnetic force **F** to
interact with the external **F**_{B}. By using right hand rule we
can find out that the force on the moving electron is pointing out from the
screen, or can be symbolized as ʘ.

Comparing with a rest electron, a moving
electron not only gets a kinetic energy for its particle, but also gets a
magnetic energy for its entity field to form the source of the magnetic force.
Both energies are transformed from an accelerating energy.

As we know that the source of an electric
force is the entity electric field of an electron. Similarly, the source of a
magnetic force can only be the entity field of a moving electron. There is no
other possible source involved. Thus, a magnetic force is the result of an
entity field with magnetic property. We can simply call it an entity magnetic
field.

As the electron moves on, it passes the
area of magnetic force and gets into a free space, as shown in figure (3.8.1c).
Since the magnetic energy is stored inside the moving electron as an entity
magnetic field, the disappearance of the external magnetic force field **F**_{B}
only withdraws the interaction and does not affect the existence of its entity
magnetic field. So, this moving electron should carry the same entity magnetic
field and has the same magnetic force field around it.

A question here is that if a moving
electron carries a magnetic force field, what is its direction? As we can see
that it doesn’t have direction yet since there is no interaction occurred. The
direction of a magnetic force field will be defined according to its
interaction with other magnetic force. Like an electric force field, a magnetic
force field has no absolute physical direction.

The electron then moves into another
external magnetic force field as shown in figure (3.8.1d). But this time the
external magnetic force **F**_{B} is parallel to the electron’s
moving direction. Although the electron still carries a magnetic force field
caused by its entity magnetic field, it does not interact with the external
magnetic force **F**_{B}. Again, we cannot decide its direction.

Finally, the electron is decelerated to
its original state – stationary state. The speed of its particle is dropped to
zero and the entity magnetic field is emitted as quantified photons carrying
electromagnetic wave, which we will discuss later. There is no more magnetic
force field around it.

We understand now that an entity magnetic
field is, in fact, an extra entity field with magnetic property gained by
moving entity electric field of an electron. Thus, both entity magnetic field
and entity electric field are unified as entity field. From the viewpoint of
entity field, an electric field is an entity field with electric property and a
magnetic field is an entity field with magnetic property.

Since an entity magnetic field is only
related to a moving electron, its image is also related to a moving electron.
This is shown in figure (3.8.2).

It is quite clear that an entity magnetic
field co-exists with its moving electron and emits out as a photon carrying electromagnetic
wave once the speed of its electron is reduced. In some situations such as in
figure (3.8.1c) and figure (3.8.1d), entity magnetic field of a moving electron
cannot be detected.

A moving proton also carries an entity
magnetic field as the source of its magnetic force field. The direction of this
force field is opposite to the direction of which of an electron. A photon is
emitted if the proton is decelerated.

A moving atom also carries entity magnetic
fields due to the contributions of its electrons and protons. Normally, no
magnetic force can be detected from out side of a moving atom for the magnetic
forces are interacting within the atom. It emits photons if its electron,
proton or the whole atom reduces speed.

Every moving object carries entity
magnetic fields. Normally, magnetic forces are interacting within the object so
that there is no magnetic force field can be detected. If the moving object is
stopped, entity magnetic fields are emitted as photons in the form of electromagnetic
wave.

In the case of magnetic force fields of
moving electrons are aligned in one direction, strong magnetic force can be
detected and the object is called magnet.

If a moving object has rest mass m_{0},
increased mass m and kinetic energy E_{K}, its magnetic energy E_{M}
is decided by special relativity

mc^{2}=m_{0}c^{2}+E_{K}+E_{M} (3.8.1)

Where m is

(3.8.2)

In most situations, magnetic energy E_{M}
is kept inside the object without our notice.

By the way, there is no gravitational wave
can be emitted. So, there is also no such thing as graviton.

As we explained before that the source of
a magnetic force field is an entity magnetic field inside a moving electron or
proton. Since any motion is relative to the observer, an entity magnetic field
is a relative field. Since any motion is related to a certain energy level, an
entity magnetic field is a quantified field. Since any motion obeys special
relativity, an entity magnetic field is a relativistic field.

There are two frames of reference O and O^{’}
in figure (3.9.1). O^{’} is moving to the right with speed v along the
positive X-axis of O system. Conversely, O is moving toward negative X^{’}-axis
with the same speed v as measured in O^{’} system. If electrons e_{1}
and e_{2} are stationary in O and O^{’} respectively, the two
electrons have relative notion with respect to one another with the speed v. An
observer in O system finds that the moving electron e_{2} carries
magnetic field and the stationary electron e_{1} doesn’t. Meanwhile,
another observer in O^{’} system finds e_{1} has magnetic field
and e_{2} hasn’t.

One way to find out which electron really
has relatively higher-level energy is to transfer electron from one system into
the other. If an accelerating force is needed to transfer an electron from O to
O^{’}, we know that e_{2} is at higher energy level in
comparison with e_{1}. Therefore, to the observer in O system, e_{2}
has real kinetic energy and real entity magnetic field. Meanwhile, observer in
O^{’} finds that e_{1} has_{ }imaginary kinetic energy
and imaginary magnetic field. This is to say that an entity magnetic field is a
relative field.

Since an entity magnetic field is a
relative field, an observer can never detect any entity magnetic field if an
object is at rest in his reference system. In fact, this resting object is
indeed carrying entity magnetic field due to the relative motion of his
reference system.

On the other hand, to move an electron,
the accelerating force has to provide a kinetic energy to its particle and a
magnetic energy to its entity field. The result of the kinetic energy is to
increase the speed of the electron and the result of the magnetic energy
(stored as entity magnetic field) is to increase the mass of the electron. The
distribution of the two kinds of energy is decided by special relativity. Due
to the involvement of the entity magnetic field, an electron can never be
accelerated into speed c. This is to say that an entity magnetic field is a
relativistic field.

Since entity magnetic field links electron
directly with special relativity, entity field theory provides us the real
reasons of special relativity. This means that the principles of special
relativity can be better explained by entity field theory, so they are no
longer necessary.

In ordinary situation, there is
v<<c, the effect of special relativity can be ignored.

A well known fact in quantum-mechanics is
that the speed of a moving electron is decided by its energy level
distribution. This means that the entity magnetic field is also quantified
according to its energy level. In low speed situation, the difference between
two energy levels is too small to be calculated and the quantum effect of an
entity magnetic field can be ignored.

Since an entity magnetic field is a
relative field, it has no absolute value. Once an electron has relative motion in
a reference frame, its entity magnetic field becomes the source of a magnetic
force and create a magnetic force field around it. This magnetic force field
was misunderstood as magnetic field in classical physics. On the other hand, an
observer moving with the same electron finds that there is no magnetic force at
all.

Historically, magnetic phenomenon is
studied by observing mature magnet. Our earth is considered to be a big magnet.
If we hang up a piece of magnetic bar from its middle with a string, it
automatically aligns with the magnetic force field of the earth. The end that
points northward is called north-seeking pole. The end that points southward is
south-seeking pole. A magnetic bar is shown in figure (3.10.1). Normally, they
are simply called North Pole and South Pole, or N pole and S pole.

If two magnets are put near by, there is a
magnetic interaction between them. The rule for this interaction is: like poles
repel; unlike poles attract. As a tradition, the direction of magnetic force is
defined from N pole pointing to S pole. So, the magnetic force is also shown in
figure (3.10.1).

Although entity magnetic fields exist in
every moving object, we can not detect any magnetic force if the forces are
interacting within the object. Our study is only concentrated on the one can be
detected and can be used – charged moving object. Since magnetic field is
originated from a moving electron or proton, our study should also start from
there.

Figure (3.10.2) shows a moving electron e_{1}
in O system.

Figure (3.10.2) Magnetic
field of moving electron

Suppose at the time t=t_{0} the
electron is passing point O with speed v along positive Z-axis. By setting up
another magnetic force near by and checking the interaction between the two, we
can get the result of its magnetic force. Testing results show that any point
in X-Y plane gets maximum magnetic force; any point along both sides of Z-axis
gets zero force. The magnetic force at any other point is between the maximum
and zero.

If there is another moving electron e_{2}
traveling in the same direction near e_{1}, the two electrons will have
magnetic force interaction. If we define the direction of magnetic force is
along straight line connecting the two electrons, magnetic force of e_{1}
could point to any direction around it.

Figure (3.10.3) shows that there is a
magnetic force **F**_{B} between two moving electrons. In the first
picture, **F**_{B}=0. In the third picture, there is a maximum
magnetic force **F**_{B}.

We now have to find out the direction of
magnetic force **F**_{B} between two moving electrons. From figure (3.10.3)
we know that, for a moving electron, there is magnetic force around it except
in its moving direction. We can imagine that this magnetic force builds up a
magnetic force field around the moving electron as shown in figure (3.10.4).

Since this is a picture in two dimensions,
the magnetic force field needs to be rotated about the axis of the electron’s moving
direction to form a three dimensional magnetic force field. Classical physics
failed to recognize this kind of magnetic force field.

If an electron does not move along
straight line, it will form a different magnetic force field. For example, if
an electron is moving in a circle, as it does in an atom, it will form a
magnetic force field as shown in figure (3.10.5). It is this kind of magnetic
force field we studied in classical physics as magnetic field by mistake.

The magnetic force field of a moving
electron changes according to its moving track.

All experiments about magnetic force field
show that N pole and S pole are symmetrical about a center plane. For the
moving electron in figure (3.10.4), the center plane “A” and its N pole and S
pole are shown in figure (3.10.6). We have to emphasize that the N pole and S
pole are defined concepts to simplify our study. We cannot mix them with
physical reality. Since classical physics failed to recognize the magnetic
force field of a moving electron, its N pole and S pole can never be identified
there. In modern physics, the two different magnetic properties of a moving
electron are rediscovered as its spin of +1/2 and -1/2.

Figure (3.10.7) shows that two electrons e_{1}
and e_{2} move in the same direction with the same speed **v**. If e_{2} is behind e_{1},
the S pole of e_{2} and the N pole of e_{1} tend to attract the
two together. If e_{2} is ahead of e_{1}, the N pole of e_{2}
and the S pole of e_{1} will attract the two together. As for e_{2}
is at the side of e_{1}, magnetic force still attracts the two together
due to that the function of a magnetic force is opposite to the function of an
electric force.

Suppose two electrons moving side by side,
there are three forces between the two: an electric repelling force, a magnetic
attracting force and a gravitation which is much weaker then the other two.
These forces form perfect wave condition and force electrons move in wavelike
track. This wave aspect of particles is the
basic principle of quantum-mechanics.

Since a moving electron carries entity
electric and magnetic fields, it has electric and magnetic force fields around
it. In modern physics, especially in QED, the entity fields of a moving electron
are treated as its virtual photon; the force fields of which are treated as its
wave.

In order to study the magnitude of a
magnetic force, a magnetic action **B** can be introduced and is defined in
terms of the magnetic force **F** exerted on a positive test charge q_{0}
whose velocity is **v**. That is

(3.10.1)

In which q is the angle between **v** and **B** as shown
in figure (3.10.8).

As we noticed that, in classical physics,
this **B** is believed to be
representing the magnetic field by mistake. In fact, it reflects the strength
of a magnetic force field. After correcting magnetic field **B** as magnetic action **B**,
the magnetic theory of classical physics can be re-discussed based on the same
structure but with entity meaning.

The directions of **v**, **B** and **F**_{B}
obey right-hand rule. It says:

Open your right hand so that the fingers
are together and the thumb sticks out. When your thumb is in the direction of **v**
and your palm faces in the direction of **F**, your fingers are in the direction
of **B**.

In fact, test charge q_{0} in
figure (3.10.8) is trying to form a magnetic action of its own to against the
external magnetic action **B**.

Figure (3.10.9) shown that a test charge q_{0}
travels in a circle under the influences of **B**, **v** and **F, **and
forms its magnetic action **B**_{0} to against **B**.

The direction of magnetic action **B**_{0}
can be worked out by using another right-hand rule:

Grasp the loop so that the curled fingers
of the right hand point in the moving direction of the test charge, the thumb
of that hand then points in the direction of **B**_{0}.

On the other hand, if test charge q_{0}
moves in a magnetic action **B** with speed **v**, a magnetic force **F**_{B}
on it is

(3.10.2)

Here the direction of **F**_{B}
obeys the right-hand rule for cross products of **v**_{0} and **B**.

If test charge q_{0} moves in both
magnetic action **B** and electric action **E** with speed **v**, the
force on it is

(3.10.3)

In the case of electric current in a
conductor, every moving electron will build up a magnetic action around itself
so that there is a magnetic action around the conductor. If a current-currying
wire is put in a magnetic action **B**, there is a magnetic force **F**_{B}
on the wire due to the interaction of magnetic forces. This is shown in figure
(3.10.10).

Suppose a charge dq
is passing through the wire with average speed **v**_{d}, magnetic force on it is

(3.10.4)

Considering equation
(3.7.1), the above equation can be changed as

(3.10.5)

Because **v**_{d}•t is the distance that a charge
is moved. Thus

(3.10.6)

If the length of the wire is
*l*,
the total force of the wire is

(3.10.7)

For normal situation, we
have

(3.10.8)

By distinguishing magnetic action **B**
from entity magnetic field itself, entity field physics not only unified
electric field and magnetic field as entity field, but also ensured that entity
magnetic field obeys conservation laws at all time.

Since a piece of current-currying wire has
magnetic force field around it, is has magnetic action **B**.

In figure (3.11.1) we consider that a current element
Id** l** is the source of magnetic action d

(3.11.1)

In which m_{0}=4p´10^{-}^{7} T·m/A is permeability constant; **r** is vector distance
pointing from Id**l**
to the arbitrary point. The total magnetic
action **B** is

(3.11.2)

Equation (3.11.2) can be used to solve
many different kinds of current-currying problems.

For a long, straight current, we can get

(3.11.3)

The direction of this magnetic action **B**
is decided by the right-hand as:

Grasp the wire with the right hand so that
the thumb in the direction of the current, the curled fingers in the direction
of the magnetic field. Please refer to figure (3.11.1).

For a solenoid or a toroid,
we can get

(3.11.4)

In which N is the number of
turns; *l* is the total
length and n is the number of turns per unit length.

Figure (3.11.2) shows a long straight current I flowing
form the screen. According to equation (3.11.3), the integral of its magnetic
action **B **is

(3.11.5)

If we change reference system into polar
one

(3.11.6)

Equation (3.11.5) then can
be written as

(3.11.7)

The result of ∮dq for
close path L_{1} is 2p, and for close path L_{2}
is zero.
So, we have

(3.11.8)

In
which I_{p}
means
that the current must be within the close path.

From section 3.7 we know that a current
can be expressed in terms of current density **J** and the cross-sectional
area dA it through. That is

(3.7.2)

The
integral of I_{p}
is

(3.11.9)

Then, equation (3.11.8) can
be written as

(3.11.10)

It implies that the magnetic
action **B** could be produced by a changing electric flux.

On the
other hand, the flux j_{m} of magnetic action **B**
is defined as

(3.11.11)

Since any magnetic action
can be identified to have N pole at one end and S pole at the other end, the
net magnetic flux j_{m} through any closed
surface is always zero

(3.11.12)

This means that there is no
magnetic monopole in our physical world.

The magnetic action **B** is, from the viewpoint
of magnetic force, the ability to interact with another magnetic action. For
example, if two long straight parallel
current I_{1}
and I_{2}
are separated by a distance a, magnetic action
of wire 1 due to I_{2}
is

(3.11.13)

Figure (3.11.3) two long,
straight parallel currents

If we consider only a certain length *l*
of wire 1, magnetic force from I_{2} is decided by

(3.11.14)

Substituting B_{2}
with equation (3.11.13), we have

(3.11.15)

Similarly, magnetic force on wire 2 from I_{1} has the same magnitude as F_{12} but to the
opposite direction. Thus, we have

**F**_{21}=−**F**_{12} (3.11.16)

Further more, from right-hand rule we can
find out that the interaction of two long, straight current are: Parallel
currents attract and anti-parallel current repel. Considering a current
contains a lot of individual moving electrons, the same rule can be used for
the magnetic force between moving electrons. This is another way of
understanding the wave of moving electrons.

So far, we have got a clear picture of
magnetic field and its interaction. The basic idea is that a magnetic field is
an entity field caused by a moving entity electric field. In the language of
unified entity field: an electric field refers to an entity field with electric
property and a magnetic field refers to an entity field with magnetic property.

According to the principle of relative
motion, the motion of an object is related to a certain reference system. Since
a moving electric field can produce an additional entity magnetic field, a
moving magnetic field should be able to produce an additional entity electric
field, which is called induced electric field. This induced electric field then
has interaction with another electric field and cause an induction.

Figure (3.12.1) shows a moving magnetic
action **B **along negative Z-axis with speed **v**. The electric field
produced by this motion causes an electric action to interact with the rest
charge q. So, there is an electric force **F** on charge q.

To check out this induced electric action **E**,
we can first change our reference system into a one fixed on the moving magnet.
Then the problem becomes a moving charge q in a stationary magnetic action **B**,
which is familiar to us.

An observer now finds that the charge q is
moving along the positive Z-axis with speed **v**. This moving charge
produces a magnetic field. Magnetic force on the charge is decided by equation
(3.10.2) as

(3.10.2)

The observer then changes back to his
original reference system in which the charge is stationary while the magnetic
action **B** is moving along negative Z-axis. He now finds that the magnetic action **B**
has an additional electric action **E** interacting with the electric action
of the charge q

**F**=q**E**
(3.12.1)

Since both reference systems are inertial
system, the physical result must be the same. So, we have

**F**=q**v**×**B**=q**E** (3.12.2)

In which **v** is along
positive Z-axis as equation (3.10.2) required. Considering **B** is actually
moving along the negative Z-axis, from equation (3.12.2) we can get

**E**=**B**×**v**=−**v**×**B** (3.12.3)

This electric action **E** can only be
caused by entity electric field. It means that a moving entity magnetic field
produces an entity electric field.

If we try to limit the above discuss to an
electron, this electron now has two relative motions. The structure of this
moving electron now has four entities: the particle and the unit entity
electric field of a stationary electron, an entity magnetic field caused by the
first relative motion, and an entity electric field caused by the second
relative motion. Each of the four entities has its force and forms its force
field.

Since a moving magnetic action can force
an electron move, it can cause current flow in a circuit. Figure (3.12.2) is an
experiment to demonstrate how this can be done.

The circuit is connected with an ampere
meter to check any current flow in it.

As the magnet approaches the center of the
coil from left, an induced current in the coil is established to against the
approaching N pole. The direction of the current is in the same direction of
the arrows in figure (3.12.2a) according to right hand rule. And the current is
plotted as the left half of figure (3.12.2b)

When the middle of the magnet reaches the
center of the coil, magnetic actions form N pole and S pole are counteracted.
There is no current in the coil.

As the magnet passes the center of the
coil, an induced current is established again to hold the leaving S pole. The
direction of this current is opposite to the arrows in figure (3.12.2a). The
current is show as the right half of figure (3.12.2b).

Figure (3.12.3) is two parallel coils.
Coil 1 is connected with a battery V and a switch K. Coil 2 has an ampere meter
to check it’s current.

When switch K is turned on, coil 1 has an
increasing N pole at its right due to the increasing current in it. The induced
current in coil 2 responds with N pole at its left to against the increasing N
pole from coil 1. The direction of induced current is shown by the arrows in
coil 2 according to right-hand rule.

At the moment switch K is turned off, coil
1 has a decreasing N pole at its right due to the decreasing current in it. The
induced current in coil 2 then sets up S pole at its left to hold the
decreasing N pole form coil 1. The direction of this induced current is opposite
to the arrows in coil 2.

The above two experiments show that both
moving magnetic action and changing magnetic action can produce entity electric
field, and then, can cause induced current in other circuit. This means that
the real source of an induced current is the electric action **E**. We can
define an electromotive force e (also called emf) of induced current as

(3.12.4)

From equation (3.12.3) we can change the
above equation into

(3.12.5)

In which **n** is normal vector of area A.
Combining it with equation (3.11.11) we have

(3.12.6)

This means that an induced
current can also be understood as the result of the rate of changing magnetic
flux j_{m} through a coil.

As the same entity field, if a
time-varying magnetic field can produce an electric field, a time-varying
electric field can surely produce a magnetic field. This is the principle of a
capacitor.

Let’s consider a RC circuit in figure
(3.12.4). At the moment the switch is turned on, the battery starts charging
the capacitor C. the surface charges on both plates are time-varying quantities
±Q(t) and the charges increase from zero to the maximum.
Correspondingly, the current in the circuit decreases from the maximum to zero.
So, the current can be expressed as

(3.12.7)

The time-varying charges ±Q(t) indicate that there are time-varying electric
actions between the two plates. By using electric displacement **D** and
equation (3.6.17), Q(t) can be expressed as

(3.12.8)

This means that a
time-varying electric displacement, which marks the present of an entity
electric field, provides substantial linkage in the broken space of a
capacitor.

For the complete RC circuit, the existence
of current I(t)
during charge and discharge periods means that
there is a current flowing through capacitor. As we know that electron cannot
pass through capacitor. This current is formed by time-varying entity electric
field, and can be described as electric displacement current I_{c}(t)

Combining equation (3.12.8) and equation (3.7.1), we can get

(3.12.9)

For free space situation, there is **D**=e_{0}**E**. The above equation can be changed into

(3.12.10)

Figure (3.12.5) is a circuit unit of a
capacitor in a long, straight wire. To simplify the problem, we suppose there
is a free space in the capacitor.

If there is a time-varying current I(t) in
the wire, there is also a time-varying displacement current I_{c}(t) in the capacitor. The total current is the sum of the two. The magnetic
action **B** of this circuit is contributed by both I(t) and
I_{c}(t). Thus, equation (3.11.8) should be expressed as

(3.12.11)

Combining equation (3.7.2)
and equation (3.12.10) we have

(3.12.12)

In which time-varying
electric action d**E**/dt becomes a source of
magnetic action **B**. In other words:
time-varying entity electric field produces entity magnetic field.

For two parallel coils, a changing current
in coil 1 causes an induced current in coil 2. Since the induced current is
also a changing current, it can cause induced current in coil 1 again. This is
called mutual induction.

Suppose coil 1 has number of turns N_{1},
current I_{1}
and magnetic action **B**, it produces flux to each turn of
coil 2. If coil 2 has number of turns N_{2}, its flux linkage is N_{2}j_{21}. An
induced emf in coil 2 is given by equation (3.12.6) as

(3.13.1)

For a given coil, its flux linkage is in
proportion to the current of causing the induction. So, we can change the above
equation into

(3.13.2)

In which M_{21} is
mutual inductance of coil 2 in respect to coil 1. It is defined as

(3.13.3)

In return, the induced current I_{2} in coil 2 will cause an induced emf
in coil 1 as e_{12}. With similar procedure we can get

(3.13.4)

In which M_{12} is
mutual inductance of coil 1 with respect to coil 2.

Experiments show that constant M_{21}
equals M_{12}. That is

M_{12}=M_{21}=M (3.13.5)

A changing current not only causes induced
current to other coils, but also causes induced current in its own coil. This
is called self-induction. If a coil has number of turns N, its self-induced emf is

(3.13.6)

Where flux linkage Nj_{m} is in
proportion to its current. So, we have

(3.13.7)

In which L is
self-inductance. It is defined as

(3.13.8)

The power of induced emf
and induced current is

(3.13.9)

Its total energy is

(3.13.10)

If we define magnetic energy density as w_{m}=W_{m}/V,
by studying a solenoid (L=m_{0}n^{2}V
and B=m_{0}In) we can get

(3.13.11)

Since the entity magnetic field is in the
structure of every moving electron and moving electrons exist in atoms of every
object, so magnetic field exists in any object. In normal situation, magnetic
fields are randomly oriented inside an object so that no magnetic force can be
detected from outside.

When an external magnetic action is
applied on an object, its atomic magnetic actions tend to be aligned with the
external one. For some materials, this alignment remains even after external
magnetic action is withdrawn.

Different names are used for magnetisms
with different magnetic effects. A magnetism has internal magnetic action
against the external one is called diamagnetism; The one has internal magnetic
action along with the external one is called paramagnetism;
The one has very strong magnetic action along with the external one is called
ferromagnetism.

If a magnetism is
put in an external magnetic action **B _{0}**, the total magnetic
action will be changed to

(3.14.1)

For diamagnetism, there is m_{r}<1.
For paramagnetism or ferromagnetism, there is m_{r}>1.

A magnetic permeability m can be defined as

m=m_{0}m_{r} (3.14.2)

Because m_{r} is a
constant for most magnetism, it can be expressed with another constant called
magnetic susceptibility c_{m}

(3.14.3)

Comparing equation (3.14.2)
and equation (3.14.3) we can get

m =
(1+c_{m})m_{0} (3.14.4)

To study the internal magnetic action of
magnetism, a magnetic dipole moment **m** can be used to describe its atomic
magnetic action. If we define a magnetization **M** as density of magnetic
dipole moments, **M** can be expressed as

**M**=n**m** (3.14.5)

In which n is the number
density of **m**.

For magnetism, the contribution of its
internal magnetic action can be generally expressed as

m_{0}**M**=**B**-**B**_{0} (3.14.6)

And the relationships among **M**,
**B** and **B**_{0} are shown in figure (3.14.1).

Figure (3.14.1) Relations
of

**B**_{0}, **B** and μ_{0}**M**

Considering equations (3.14.1) and
(3.14.3), equation (3.14.6) can be changed as

(3.14.7)

For a long, straight current described by equation (3.11.8), we have

(3.14.8)

To simplify above equation, a magnetic
force field strength **H** is introduced and is defined as

(3.14.9)

Substituting equation
(3.14.9) to equation (3.14.8) yields

(3.14.10)

Where I_{T} is the sum of electric current I and
displacement current I_{c}. Substituting equation
(3.11.9) and equation (3.12.9) into
above equation gets

(3.14.11)

Combining equation (3.14.1) and equation
(3.14.2) with equation (3.14.9) can get

(3.14.12)

For a solenoid with magnetism inside, its magnetic
energy density is given by equation
(3.13.11) as

(3.14.13)

So far, we have successfully restructured
the whole electromagnetism by using entity field theory. Based on the correct
understanding of entity fields and their force fields, Maxwell’s equations can
be written in the same form but with entity meaning

(3.15.1)

(3.15.2)

(3.15.3)

(3.15.4)

Equations (3.15.1) – (3.15.4) can also be
expressed as

(3.15.5)

(3.15.6)

(3.15.7)

(3.15.8)

There are three supplementary equations

(3.15.9)

(3.15.10)

(3.15.11)

And the density of
electromagnetic energy

(3.15.12)