THE MICROSKOPIC ANALYSIS OF THE ELECTRIC CURRENT AND ITS
CONSEQUENCES, THE RADIUS OF THE ATOMS OF THE CONDUCTORS,
THE COSTRUCTION OF THE ELECTRIC AND MAGNETIC COUNTERS
Spiritual Property
Number of application of patent at Greek Organization of Industrial Property
20130100410/12/7/13
By Alekos Charalampopoulos
The consequence microscopic analysis of the electric current , will bring new means and
different theory, that it will moderates the old one and it will bring new construction of the
electric current counters of voltage, power, resistance and current. It will calculate the radius
of the atoms of the current conductors.
THE MICROSCOPIC ANALYSIS OF THE ELECTRIC CURRENT
Into an electric conductor, the electrons move under the reaction of the voltage. The
Millikan experiment fixed that the electron charge is e=1.6x10-19 Cb. Was used voltage that it
will be moderated at the follows and it is in force, it will absolutely change the size of e.
It has been fixed that the electric current is Ι=q/t and the density of the current is J=I/A,
where Α is the surface (the vertical section of the conductor), where the current pass. The J
we will call surface density current.
If nV= N/cm3 , the number Ν of the conductive electrons in a unit of conductor’s volume,
then into the unit of the conductor’s volume , it is, because of q/cm3=nVe,
I= q/t =Nev/L
/v=the velocity of the electrons, it called the drift
3
velocity and AL=Vol=unity volume =cm , and then,
v=ILA/ANe=I/AnVe=J/nVe= (I.cm3)/NeΑ
(1)
It had been fixed the unit of current us Ι = 1Amp. We do fix Ι.cm3 = 1Amp.cm3= 1El και El
is the unit currentvolume ΙV. It comes from, for every current conductor, the currentvolume is
analogous to the electrons velosity.
When every copper’s atom has one conductive electron, it is up today estimated nV=
8.4x1023 electrons/cm3 και v= 3.6x10-2 cm/sec into a copper wire with Α= 0.0032 in2.
The (1) gives,
v=at = (L/v)a = (eV/m)1/2 = IV/NeΑ and
v2 = eV/m = (IV/NeΑ)v
and
mv2=eV, the kinetic energy, but and
V= (IV/NeΑ)2 (m/e) = (m/N2e3Α2) IV2
(2)
That is, the voltage is analogous to the electrons square velocity and of the currentvolume
square for every fixed conductor.
THE OVERTURNING OF UP TODAY MICROSCOPIC CURRENT ANALYSIS
Up the stated considerations, the electrons have elastic collisions with the conductor’s
atoms and they have velocity v that above we informed it, but and they have a large velocity,
that they plan crooked lines and they have drift velocity v.
The collisions of one electron. The white line is planed of the electron collision to the
conductor’s atoms, when it is applied voltage and the electric field E. Then it is not in force
eV=mv2 for the velocities are not parallels to the field E.
Let’s have the mono-atomic atom of copper Cu. It is up today, that it has one electron on
the conductive zone (valence electron). It is a very much weak positive electric field of the
nuclei, on conductive zone, and the electron is attracted of the nuclei. It happens, side the
defence of nuclei strong positive field, of the negative field of the electrons accumulation.
Well, when we apply voltage on the edges of the conductor, then every conductive
electron, it comes off of the atom and it “travels” into the conductor. But, if it collides with an
atom, the collision will be the plastic one, because of the meeting of the very much weak
positive electric field of atom nuclei and it will collide to the atom. Then it will,
𝐿̅
v= 𝑣̅ = 𝑡̅ = L/t
and 𝐿̅, 𝑡̅ are the average distance of the successive collisions and the average time of them.
That is, it is the same the velocity v with the average velocity, and it is the one. But, the
applied voltage is very weak, us the formula (2) gives it.
THE RESISTANCE OF THE ELECTRIC CURRENT
It is axiom that V/IV =RV the volume-resistance and then the (2) gives,
RV = (m/N2e3Α2) IV =(m/Ne2A)v
That is, the volume-resistance of the electric current is analogous to the currentvolume, again,
of the electrons velocity. In the circuit, we have volume-resistance (m/N2e3Α2) IV ohm/cm3.
The unit of volume-resistance we call Al=x.ohms/cm3 and V/RV =IV. We double the
resistance, 2RV and then we have ΙV2R=2ΙV.
But V4= (m/N2e3Α2)4 IV2 , we must to apply fourfold voltage to we have the currentvolume
ΙV. In this voltage, but to we have the initial currentvolume ΙV, we must come into circuit,
volume-resistance 4RV, four initial volume-resistances, but with 2RV we will have ΙV2R.
The unit of the voltage will be V= x.volt =1 Hellas= El.Al and 1Al is the volume-resistance
of 1 cm3 of copper (the standard of volume-resistance at 20 C0)
By fixing, the special resistance is,
ρ=Ε/J =ΕΑ/Ι
It found ,
=VA/LI =RA/L
ρ=ρ0[1+α(Τ-Τ0)] and then,
V=IVRV =IV ρV L/A=IVρV0[1+α(Τ-Τ0)] L/A
volume-resistance at 0 C0.
/ ρV0 the special
That is, it is needed more voltage at larger temperatures than the special one, into a conductor
to have the same IV.
But,
RV =ρV0[1+α(Τ-Τ0)]L/A=(m/N2e3Α2) IV =(m/Ne2A)v
It means that, when the temperature the conductor will be increased, it will be increased the
carrentvolume and the electrons velocity. And this it is, because of the increase of the
temperature and the heat, will be increased the kinetic energy of electrons (the heat transforms
to the kinetic energy).
THE FIXING OF THE El
We considerate the two parallel conductors of Ampere. We arbitrary count a force,
F=μ0Ι2L/d =2πx10-7 Nt,
/ d=it is the distance between two conductors and L=it is the length of them. We considerate
that the electric current into the conductors is 1Amp and then μ0=4πx10-7. This 1Amp/cm3
will fix and the 1 El.
But so, it cannot count the force, and it will count as the experiment in the next plan,
Look out, the current was flowed in the coils, it was fixed of the formula V=IR, but we
fixed the formula V = (m/N2e3Α2) IV2 . So, if it applied different voltage of formula V=IR in
the experiment, then the IV of the formula V= (m/N2e3Α2) IV2 it is different of the Ι, and they
must become the necessary corrections. And if by the formula V=IR is trued the law of
parallel conductors attraction, with new data it is no in force. Then the constant μ0, it is no
constant, but it will in force different μ0 for different ΙV.
THE COUNTING OF THE MAGNETIC FIELD
It come from the law F=qvB for vertical v, B, the formula F=ILB. The counting of the
magnetic field became as the next plan,
A part of the current loop i=I, it is found into the magnetic field, that it forces on the
section L of the loop, the force F. But really the loop was coil with 9 spirals.
It is the same here, in force. It was not correctly counted the B, if the voltage was changed
and now, we ought to correct it.
THE COUNTING OF THE ELECTRIC FIELD
It comes from the formula E=V/L. And the V was not correctly counted, the volt-counters
give error voltage. So, the Ε is not correctly counted at any case. But into a conductor, it
happens
E=V/𝐿̅ and 𝐿̅ is the average way of plastic collisions of electrons with the
conductor’s atoms
THE COUNTING OF n
From the formula eΕ=evB, we have Ε=(I/neA)B of the stated physics, that is,
n=(I/eVAL)B and if n=nV in connection to the (2), nV=Im/(eA)2, which is very smaller than
the estimated. And because of Ε= V/L the Β was not correctly counted, so and the n=nV was
not correctly counted. The V is the applied voltage in the conductor, at Hall’s effect.
THE COUNTING OF q
It comes from formula q=CV, C= the capacity of a capacitor. And this has an error in its
counting.
THE COUNTING OF ATOM MASS
In mass spectrograph, it is counted the mass of the ions and the atoms,
The Β and V were not correctly counted, so the ions and atoms masses it must be counted
again and they are very much larger than the estimated.
It will change the relation 1/1831 of the electron to the proton mass.
THE COUNTING OF THE PARAMAGNETIC-DIAMAGNETIC
-FERROMAGNETIC SIZES
With Rowland ring, they were counted the Η, Β and Μ of the ferromagnetic materials,
The sizes μ, χ (=magnetic susceptibility) are wrong.
THE SIZE OF CONDUCTORS ATOM RADIUS
We have nV=N/cm3 and nA =(Ν/cm3)2/3 the number of atoms on vertical section of the
conductor and ΝΑ the relative number of atoms .
πr2 is the effective section of the atoms. πR2 the vertical section of the conductor. (r/R)2 is the
possibility of the conductive electron to collide plastic collision with an atom. This becomes
with possibility 1 for every electron, on distance 𝐿̅=v𝑡̅ and then,
nL= nV 1/3 the linear density of conductor’s electrons , and
PA= (r/R )2 is the possibility of collisions on the effective section of the
atom πr2 . PL=NL =nLL is the linear possibility of collisions and Ν1/3 =ΝL.
The πR2L=cm3 and L=cm3/πR2=(1/IV)I/πR2=(1/IV)J that is, the surface density of the
current to the currentvolume (J/IV) is the L=cm3/πR2
PAPL=1=(r/R)2ΝL =(r/R)2nLL and
r=R/ (nLL)1/2
the radius of the atom. It is concreted on this radius, the mass of the atoms, in the crystals. Up
today, they were estimated that they have diatomic distances of 10-10 m= 10 nm (but of our
theory, such distances are in force between the atom’s electrons ) .
THE CONSTRUCTION OF THE ELECTRIC COUNTERS
We give the plan of moderation of the existed counters of the electric current, voltage and
power. They will be more complex and more volume. Obviously, because of the voltage is
analogous of the square of IV, then the alternated voltage will the average voltage,
𝑉̃ = 𝑉̅= ½(m/N2e3A2) IVm2 , IVmcos(ωt)=IV .
IVm is the maximum ΙV.
And the voltage is 𝑉̃ = 𝑉̅ it is the average term of cos2 (ωt)= ½ times the ΙVm2.
The 𝐼̃= (½ )1/2IVm is the effective intensity of the alternated currentvolume.
It is RV=(m/N2e3A2) IV
and for the alternated currentvolume, it is 𝑅̃V =(m/N2e 3A2)𝐼̃
ABSTRACTION
OF THE COSTRUCTION OF THE ELECTRIC COUNTERS
The new multi-meters must operate with the formulas,
V= (m/N2e3Α2) IV2
R = (m/N2e3Α2) IV
/ ΙV=Ι.cm3, /m,e are the mass and the charge
P=VI
of the electron.
The m/N2e3 =Η is the characteristic of every material, because every material has
different atomic mass and number N (Ν=nVcm3) and nV=N/cm3= the number of electrons into
a cm3 of a conductor.
So, the electric counter will have different Η and the switch of every material (Cu, Al, Ag,
etc) and it will have a computer to calculate the Η/Α2 and Α= is the vertical section of the
conductor.
The Η/Α2 that it will appear on the computer, on the formula,
V=(H/A2 ) IV2 and the formula
R=(H/A2 ) IV
and the formula,
P=VI=(H/A2 cm3 ) IV2
It comes in V, IV2 , R,IV ,and P,IV.
For the alternative sizes will be in force,
Average voltage
𝑉̃ = 𝑉̅= ½ IVm2 (Η/Α2)
Effective density of current 𝐼̃= ( ½ )1/2 IVm
Effective resistance
Average-effective power
𝑅̃= (Η/Α2) 𝐼̃
P= 𝑉̅. ½ IVm2 (Η/Α2)
And the ΙVm is fixed by the formulas of the constant maximum currentvolume.
Bibliography
PHYSICS ,D. Halliday-R. Resnick. From where the haved plans
ELECTROMAGNETISM, R. Serway