Notwithstanding, for the sake of explaining
24-hr E.M revolution, Ampere’s circuital law (with Maxwell’s addition) in
differential equation is applied. That equation is to be reviewed.
II-Problem of 𝜵*B=µ0*(J +Ɛ0* δE/δt):
1-Twin graph of J and gradient of E:
The following graph is built out of real
data that observed at Tirunelveli (South India). Both plots on this graph (gradient
of atmospheric electric potential ‘’E’’ and density of air-earth current‘’J’’)
are averaged in every minute; one is in proportion with the other (fig. 02).
Figure 2- The air-earth current ‘’J’’
is averaged in every minute, observed with Wilson antenna(broken line).The
continuous line is performing the gradient of atmospheric potential that
measured with passive antenna at Tirunelveli on 25 April 2007 (reference to
Atmosphere Electric of NOAA).
After every 24hr interval, both ‘’J’’ and
‘’E’’ (refer to the graph of figure 2) vary and especially their fluctuation
repeat (24hr) on global scale except at locales where some specific matter effects
on those 2 figures.
We may ask whether the fluctuations of
‘’J’’ and ’’E’’ contribute to Earth Magnetism and explained by Ampere-Maxwell
equation?
Definitely the answer must be ‘’yes’’, and
it is right in the Wikipedia for ‘’Ampère's law with Maxwell's addition the Ampere
rule with Maxwell addendum says that magnetism can be created by both electric current(Ampere)
and changing electric fields. This
statement affirms that the fluctuations of both ‘’E’’ (potential gradient) and ‘’J’’
displacement current are inducing Earth Magnetism.
For Earth Magnetism, the contribution from
atmospheric electric is obviously as mentioned above. But we need more argument
anyway, if the terrestrial magnetic field is belonging to one of an individual
magnetic bar, the above mentioned reason for Earth Magnetism ‘’Electric field
change’’ may be accepted as the major; or implies: the atmospheric electric
potential and displacement current vary to induce Earth Magnetism.
Actually the Earth Magnetism is a set of fields
that induced by the moving of many electric charges, definitely neither just the
fluctuations ‘’J’’ and ‘’E’’ nor a field of such a powerful magnetic bar inside
the Earth core. But the Earth is magnetized by magnetic fields and then the
fields expand outward from the Earth.
Notwithstanding we do carry out an express
review to Ampere-Maxwell once as to consider ‘’J’’ and ‘’E’’ in the graph on
figure 2.
General description in brief:
-The homographic plots are built out of
real data that observed at Tirunelveli (South India). Both two quantities,
air-earth current and gradient of atmospheric voltage, are fluctuating, and its
fluctuation is repeated after every 24 hrs.
-The horizontal line is for time that calibrated
in 60 minutes (1hr.)or 1440 minutes in 24 hrs.
-Assumption: Each 60 minute segment equals
to 1 segment of 10 V/m on vertical line that performs gradient of atmospheric
voltage, meantime equals to ½ of a segment on another vertical line which
performs the density of air-earth current.
The world scientists spend a lot of time to
debate about this problem, eventually they all recognise what happened as
realities. I do explain about this question in ‘’Chapter I’’ of the book: ‘’the
Earth Magnetism and some basic problems with sea-land surface, atmosphere, Van-Allan
bell and Moon’’. The explanation in there also implies that the above graph may
changes a bit in accordance with the change of position of the Sun relative to
the Earth.
-The above graph is to apply worldwide
because the data are recognised as the same for everywhere in the world.
-There are always, within 24 hrs., 2
moments when air-earth current almost reaches zero while potential gradients
are still hung at 100V/m or a bit better (the minute 175th and
minute 785th). The plots are built of real data, therefore they don’t
look similar to any standard graph such as Sin, Cos or Tg...
-There are many parts of those plots likely
straight, some of the straight line is forward slash while some other is
backward slash.
Figure
04- ‘’J’’ and ‘’E’’plots-Red colour column indicate‘’rising up’’,
while
the grey is for falling down.
My way is to attribute a certain straight
line to each part of ‘’E’’ plot. Seek for specific differentiation of potential
gradient of ‘’E’’ on ‘’t’’ (time) in that part (
).
Some tiny problem will be setup and sorted
out during Q&A.
Q&A:
Q1-When
does 𝛛E/𝛛t reach 0 in each 24hr interval?
Throughout a 24hr interval, the ‘’E’’ and
‘’J’’ graphs are rising up and falling down many times, the values of 𝛛E/𝛛t at every peak and every bottom are zero because where the tangent
line are horizontal or parallel to (t) line.
Figure
05 –At every peak or bottom, the value of 𝛛E/𝛛t may reach Zero
Approximately 𝛛E/𝛛t may reach zero value at the following times 60, 90, 180, 400, 510,
640, 785, 1085, 1145, 1265th minutes.
When 𝛛E/𝛛t reaches zero, the value of 𝜵*B may be considered as function of ‘’J’’ only:
𝜵*B=µ0*J
As matter of facts, in the circumstances
when 𝛛E/𝛛t=0, when 𝜵*B= µ0*J; the value of ‘’J’’ plays no
important role, while the trend of electric field does. Refer to figure 04 above,
right after minutes 179-180th, or at 510th, 785th, 1145th the
value of 𝜵*B or gradient of B almost
rocketing of falling down sharply.
Q2-The
value of 𝜵*B at minute 960th GMT
(The popular slope within 24hrs.)?
On figure 4, the minute 960th is
belonging to a red part of the graph, it is rising. To solve this problem, we
need the homographic graph for ‘’J’’ and ‘’E’’ (From NOAA), with some
additional lines on it.
+We can find the value of ‘’J’’ at minute
960th by drawing a vertical-straight line through 960, we get Nand M
when it meets the plot of ‘’J’’ and ‘’E’’.
From N, draw a horizontal line parallel
with time line, it meets O’E’ at K; Position of K on O’E’ is to indicate value
of ‘’J’’ which is approximately 0.62*10-12 Amp/m2.
+From M, graph of gradient E is
approximately on a line that meets time line at D(approximately it is t=730).
The line in 2D coordinates should be:
(y=ax+b).
+In order to find out 𝛛E/𝛛t, we consider a function of ‘’E’’ in the form y=ax+b at minute 960
GMT.
E=at+b (‘’t’’ is short for ‘’time’’), a=tg
(MDH)) (This function is set up for M and its adjacency only).
𝛛E/𝛛t = a (Applied for the function of E=at+b).
Figure
6-Gradient E and displacement J with some additional lines at minute 960th.
The point M is chosen at a positive part of
(forward and popular slope) of 24hr plot of gradient ‘’E’’.The line MD coincide
with a part of the above plot and its function is: y=ax+b.
We got to set and solve a problem.With t=960,
E=Em≈168 V/m and whent=730th, E=80 V/m. The results are:
a≈(168-80)/(960-730)=0.3826 and b≈-199.296
Thus, the function for E at t=960thcan
be:
E=0.3826t - 199.296
Value
of 𝛛E/𝛛t=0.3826 (indicates
the slope of the line tangent to a curve at the intended point). The function
for E as mentioned is applicable to the point M and its adjacencies only. For
other parts of that plot, both ‘’a’’ and ‘’b’’ will be attributed with some
different values.
With ‘’J’’=0.62 pA*m-2 at t=960
(1 pAmp/m2=10-12 Amp/m2, µ0=4π*10-7,
Ɛ0 =5*10-15 (average between 3*10-15and8*10-15. Furthermore,
we should note that 1 pA=10-12 Ampere).
𝜵*B=µ0*(J +Ɛ0*
)=4π*10-7*(0.62*10-12+5*10-15*0.3826)=
=12.56637*10-7*(620*10-15+5*10-15*0.3826)=12.56637*10-7*621.913*10-15
=7.81519*103*10-15*10-7=7.81519*10-19
𝜵*B=7.81519*10-19
This is value of 𝜵*B at minute 960th GMT on
daily basis.
-The
value of 𝜵*Bat
minute 960th GMT is found as an example that indicates that we are
capable to find out value of 𝜵*B at any time in a day.
As long as ‘’E’’ and ‘’J’’ fluctuate with 24hr revolution, the value of 𝜵*B does the same, and it
can be considered as daily revolution of Earth Magnetism.
Q3-When
and where we find 𝜵*B<0?
𝜵*B=µ0*(J +Ɛ0* δE/δt)
Let’s solve this problem:
If (J +Ɛ0*
)<0
Then
< -J/Ɛ0
When the value of ‘’E’’ is falling down,
definitely δE/δt
<0, but this problem
requires a certain ‘’J’’.
The quantity ‘’J’’ varies within 0 and
1.25*10-12, while Ɛ0 does not change often, we supposed that
Ɛ0 is average between 3*10-15 and
8*10-15, and assumed as 5*10-15.
When ‘’J’’ is rather high, let’s consider
J=1.25*10-12 Amp/m2 in our example, then: Then
≈-250, this is a slope
of the ray that nearly vertical downward (890 43’).
If we consider ‘’J’’ at sometimes when its
value is low, such as the duration from minute 150th to minute 160th,
J ≈
0.05*10-12 Amp/m2. The same calculation as above is applied,
we obtain:
≈-10, equivalent to tg
of an angle 84015’ downward.
Figure
6a-Angle of 84015’ downward.
In brief, we can realize that the lower
‘’J’’ the more possible for 𝜵*B<0. Nonetheless, no
matter how much the value of 𝜵*B gets lower under zero,
this is to indicate that the amplitude of Earth Magnetism is getting down due
to the fluctuation of displacement current ‘’J’’ and potential gradient ‘’E’’, they
expect to be the same in the next day; and nothing else about the average of
Earth Magnetic Magnitude.
Anyhow, this is not more than a calculation
for 𝜵*B,some more attract our attention are the sources that induce the
Earth Magnetism, someone are from the electric charges on the Earth and in the
atmosphere;while some other ones are in Near Earth Space.
Q3-How is the influence from
potential gradient ‘’E’’ and displacement current ‘’J’’ to Earth Magnetism?
By Maxwell, as matter of facts, the
variation of electric field can induce the magnetism. We even do some review
for questions 1 and 2. However, for a better pragmatic concept, another figure
is to be considered: The fluctuation of total area of thunderstorm in the
world.
Figure
7–The fluctuation of global thunderstorm area (km2).
Almost every electric and magnetic incident
in the world is created and developed by‘’J’’ and ‘’E’’ as discussed in several
paragraphs before, and even in this essay. But the conspicuous subject is the total
area of thunderstorm in the world, the figure 7 above is an important reference
from NOAA.
In general, the fluctuation of total
thunderstorm area in above graph is explained as consequence of ‘’E’’ and ‘’J’’
fluctuation, the displacement current ‘’J’’ variation makes the value of charge
on Earth surface changed, and then one place is different from the other.
Consequently, the charge on land surface contributes to Earth Magnetism
(Chapter I-Air-Earth current and Chapter II-Contributions from Land & Sea
surfaces to Earth Magnetism by Biot-Sawart laws.)
The move that makes the electric charge on
the Earth surface changed in order to change the Earth Magnetism at all time.
(Problem
(this can be a reference to student or lecturer): The contributions from sea
surface and land surface to Earth Magnetism at 13hrs GMT? If The Earth is
neutral or total charges on land surface and sea surface is null, every land square
km under thunderstorm cloud is charged with 106 Coulomb.)
Q4 – Is any electromagnetic wave created from atmosphere electric?
Electric field fluctuation is to induce
magnetic field and vis-a-versa. This is traditional electromagnetic theory in
science, it is also fundamental theory of electromagnetic wave transmission,
and it is known to the world.
By the theory mentioned above, the fluctuation
of electric field described in figure 2 can be viewed as an oscillation which
produces one or several electromagnetic waves. The waves are emitted into
universe with such a huge power that nothing can stop or consume them all…
The electromagnetic wave detectors on board
spaceship can realize these waves from Earth.
Figure
8-Basic frequency (Left)and the form of original wave (Right) incorporated in 1
coordinate for comparison(Cited from Fourier manual)
All waveforms, no matter what you scribble or observe in the
universe, are actually just the sum of simple sinusoids of different
frequencies.(Fourier)
My own speculation, the 2 obvious waves can
be detected from outer space are wave of T≈k1*640’, and T≈k2*1600’are
popular with huge output regardless the capacitor-coil are found or not.
Figure
9 – Principal description of electromagnetic wave creator.
CONCLUSION:
-Although the homograph of E and J are
applied everywhere in the world.
-Although the differential equation of Ampere-Maxwell
does not bring us an accurate outcome for Earth Magnetic magnitude at any time.
But the gradient of Earth Magnetism (𝜵*B=µ0*(J +Ɛ0*δE/δt)) at any time is found throughout every 24hrs
to affirm that:
if revolution of the two quantities (E
and J) is 24 hr. time, then the revolution of Earth Magnetism revolution is
24hr too.
There are several magnetic inducers to
Earth Magnetism found, therefore every calculation depending on functions of
atmospheric electric field and displacement current can’t bring satisfactory
result. So, we can’t claim Ampere-Maxwell equation a perfect instrument for predicting
the current value of Earth Magnetism.
Another reason for above negative comment
is that the Earth Magnetic vector does not just vary in time, but also at
location where the vector is observed; while Ampere-Maxwell may give out a result
that depends only on GMT.
-Although the fluctuation of ‘’E’’ and
‘’J’’ –as above considered with Ampere-Maxwell equations--may influence to
Earth Magnetism ambiguously. But consequence of the fluctuation--the
thunderstorm area--is an important figure that contributes enormously to Earth
Magnetism and makes it varying with revolution of 24hr (discussed in chapter
III).
-The Earth in its atmosphere with Ion
layers establish a unit in the universe, that unit is creating electromagnetic
waves and emitting them into the universe.
I hope that one day, a certain satellite in
outer space will detect those emitting waves; these are created by nature and
from Earth. Unlike the known waves from Earth, these mentioned waves are
produced in Earth atmosphere with unknown output. The waves are produced
continuously, unlimited power and non-stoppable. They are voices broadcasting
from our Earth.
Hanoi Nov. 30th 2018
Nguyen Van Cuong
Advisor/Editor: Phd. Vu Bang
