Mime-Version: 1.0 Content-Type: TEXT/PLAIN; CHARSET=US-ASCII Content-Transfer-Encoding: 7BIT (By O. Tedenstig, Idungatan 37, 19551 Maersta Sweden) (continued from part 1(2) DEFINITION OF ELECTRIC VOLTAGE Electric voltage is by common theory defined as the length integral of the electric field strength, hence : 32a)==================== Voltage as defined by common theory s _ _ U = I E.ds.n 32b)------------------- or in differential form U = dU/ds = grad(U) 32c)----------------------------- Some mathematical _ manipulations div(E) = div grad(U) = 2 2 2 d U d U d U K.(---2- + ---2-- + ---2--) = dx dy dz _ __2 div(E) = !/ U (OBS "d" is here the partial derivative symbole ============================================== THE ELECTRIC VOLTAGE OVER A PLANE CAPACITOR In accordance with done definitions and results we will now calculate the voltage over a plane, parallel electric capacitor. We make use of the definitions of the electric field strength from formula 22) and the definition of electric voltage in 32), giving : 35a)=========================================== _ ' 2_ 3 E = qr.c = q.Kt.Ka/Kv.c.N.re.r/r ' s _ 2 _ 2 U = I E.ds = q.Kt.Ka/Kv.re.c.N.D.n/r = 2 1 4.Pi.D . Kt.Ka.c.re.N .2.sqrt(Pi/Kv) ---.-------2------------------------------ = Eo 4.Pi.r . Kv . 2.sqrt(Pi/Kv) Q.D 4.Pi -----. -------------- Eo.A 2. SQRT(Kv.Pi) 35b)------------------------------------------- ' Q.D U = --------. 2.SQRT(Pi/Kv) Eo.A =============================================== >From common theory U = Q.D/(Eo.A), givning that for exactness of U=U' : 35c)==================== For exactness between common theory and the new theory. 2.SQRT(Pi/Kv) = 1 ======================== ----------------------------------- ELECTRIC CURRENT Electric current usually is defined as the amount of "charge" passing a cross area of a conductor per time unit. Another way to define electric current would simply be by the number of unit charges passing the same area per time unit, hence not using the charge concept at all. Then there may be two ways of defining current in accord with these two principles, namely : 37)===================== Electric current as defined by i = Q/t common electromagneti theory 38)===================== Electric current defined as the In = N/t number of unit charged particles passing a cross area of a conductor per unit time. ======================== The relationship between these two ways of defining electric current then will be : 39)===================== The relation between In = N.i/Q the two ways od defining electric current in i = Q.In/N equation 38) and 39). ======================== 1 ampere is defined as this current which deposit 0.00111800 grams of pure silver each second from a silver nitrate solution, equivalent to N=6E18 electrons per second (approximately), passing the same cross area. Another method used to determine 1 ampere is to measure the force effect between two straight parallel conductors. 1 ampere is that current which produces a force of 2E-7N per meter on these conductors. That method mostly is founded on pure theoretical basis, on the relations between magnetic and electric field theory as derived by Maxwell and others. -------------- DEFINITION OF ELECTRIC RESISTANCE AND IMPEDANCE In common theory, resistance of a current flow in a conductor is defined as the quotient between the driving voltage and the resulting current flow, hence : 40)=================== Electric impedance and Z = U/i ; R= U/i recistance in accordance with common definitions ====================== We uses this definition to calculate the vacuum zero impedance. The idea of calculating this physical entity is to study this case where the limit value of a plane capacitor are two naked electrons and where the distance between these electrons is two times the electron radius, giving the relation : 41)============================== Z'= U'/i' = ' eo.Do eo. Do.2.SQRT(Pi/Kv) U = --------. 2.SQRT(Pi/Kv) = ------------2--------- Eo.Ao Eo. 4.Pi. re eo eo.c i' = ----- = -------- Do = 2.re te Kt.re eo.2.re.2.SQRT(Pi/Kv).Kt.re 1 Kt Z' = -----------2---------------- = -----. ----------- Eo.4.Pi.re .eo.c Eo .c SQRT(Pi.Kv) ============================================================ 1 In conventional theory, Zo har been defined to Zo = ---- and Eo.c the relation between this value and our calculated value : 42)========================= The relationship between the vacuum zero impedance and our ' SQRT(Pi.Kv) calcualted value, which may Zo/Zo = ------------- be equal to, or near equal to 1. Kt ============================ THE CAPACITANCE CONCEPT OF AN ELECTRIC CAPACITOR There is a need of describing a capacitor's ability of storing electric energy in terms of the capacitor's geometrical performance. We wish to express this ability as a function of f(x) by the following relation 43), and by use of results from 14),30a),35b). The searched result is in 44) : 43a)========================== 2 W' = 1/2.f(x).(U') ' 2 U = q.Kt.Kav.re.c.N.D.4.Pi 35a) ---------------------- A ' s _ 2 _ 2 U = I E.ds = q.Kt.Kav.re.c.N.D.n/r 2 2 2 W' = 1/2.Ka/Kv.me.c.re.N.(D/A) 29) 2 2 2 2 2 2 2 2 2 2 4 2 2 2 1/2.Ka/Kv.me.c.re.N.(D/A) = 1/2.f(x).q.Kt.Ka/Kv.c.N.D.re.4.Pi/A 2 2 A Ka A.Eo Ka f(x) = ----. -----2- = ------- .------2- q.D 16.Pi D 16.Pi ================================== In common theory, the function of f(x) is the same as the capacitance of the capacitor, given by the relation : A.Eo C = -------- D 44)========================== The relation between the 2 capacitance in a plane 16.Pi capacitor calcualted by C/f(x) = ----2--- common theory and our Ka theory ============================= ----------------------------------------------------------------- THE MAGNETIC FIELD AND ITS PHYSICAL CONSEQUENCES o dm= q.dV The moving charge . . in the conductor create . . a torsional effect in a . b . space element outside c = outflow . . C = inflow a conductor by reason . . of a time phase shift . . in and out streaming field . . . a . ----!------------------!-------- ! --------> v ! conductor ----!------------------!--------- ! ds=v.dt ! !<---------------->! FIGURE 5 When an charged particle move, the environment void will be effected in a very special manner. The phhysical phenomena and properties of the space associated to it has been given the name of magnetism. The electric field, as well as the magnetic field with associated physical properties are well described by existing electromagnetical theory resting on works by the great investigator of Ampere, Faraday, Maxwell and many others, all great pioneers and contributors of the fundamental physics. In particular Maxwell's work has been of significant importance since he suggested to demonstrate close relationships between the electric and the magnetic phenomena by arranging them in a common theory. Maxwell made clear that electric and magnetic phenomena had a common source, being only different sides of the same thing. A simple way to distinguish between electric and magnetic phenomena is to say that electric phenomena are result of charges in rest and magnetic phenomena are associated with charged particles when moving. Maxwell's theory was founded on existence of a mechanical aether, but when the theory was fully developed, this aether was taken away. Today only a barren mathematical formalism remains as result of his thinking. We shall here make an attempt to repair this damage and allot electromagnetism substantial properties of space and matter. We will do that by applying the same basic ideas as we have used before when treating the electromagnetic field and associated phenomena. We start from the most simple arrangement, a straight metallic wire in which an electric current flows. This electric current consists of free charges carrying the electric current, put forwarded by an external voltage source to the end point of the wire loop. In aim to demonstatrate this arrangement, we make use of the adjoining figure 5). The wire is placed out in a x,y,z coordinate system. The current carrying particles- here the electrons' are supposed to be smoothly distributed over the whole wire length. In a small section, ds, we suppose there are N free charging carrying particles with unit charge, then we find that the relation N/s will be a constant entity, giving our first formula : 45)====================== The number of free unit charged particles are K = Ns/s ; N = ds.K constant distributed over ========================= the conductor length The free charge bearing particles (the electrons) in this segment generates a static electric field, which in a point outside the conductor is determined by : 46)============================= from the fromula 16) 2 re qr = q.Kt.Ka/Kv.--2--.N r ================================ and the corresponding electric field strenght in this point then is equal to : 47)==================== from formula 22) _ _ E = qr.c ; qr = E/c ======================= Now, in aim to get an understanding of the nature of the magnetic field, we will study the figure 5) above. In the chosen point outside the conductor, field mass is streaming in and out from the electrons in the chosen segment of the conductor. The mass streaming in is faster (see 14) than the corresponding mass streaming out, having only the velocity of light, c. The effect of that when the electrons move, will be a torsional effect in this space point, creating two separate field vectors with an angle, a, between them. In accord with the "sinusial theoreme" then the following relation is valid : 48)===================================== sina sin B ------ = ------- ; sin B = (v/c).sina c.dt v.dt ========================================= We define the magnetic field strenght, B' , as the product of the electric field strenght in this point and the sin(B) factor, giving the following relations : 49a)================== Our definition of magnetic _' flux density B = qr.sin(B) 49b)------------------ Using 48) and 49a) _' _ B = qr.(v/c).sin(a) 49c)---------------------- Using common definition of a _ _ ! ! ! ! vector cross product A x B =!A! . !B! .sin(a) ! ! ! ! 49d)---------------------- From 47) _ _ E = qr. c ; qr= E'/c 49e)----------------------------------------- Combining 49b),49c) _ _ _ _ _ 49d) B' = (E'/c).(v/c).sin(a) = (E/c) x (v/c) ============================================== Hence, the relation between the electric field and the current velocity in the conductor is defined by : 50)======================== The magnetic field strength _ _ 2 as defined by out theory B' = E' x v/c =========================== DERIVING BIOT-SAVART'S LAW OF THE MAGNETIC FIELD STRENGTH Biot-Savart's law of the magnetic field strenght outside a conductor is a law of similar importance as Coulomb's law of the electric field. Our aim is here to derive this law with start from now achieved results. We start by repeating the deinition of electric current, using 1e) and 37) : 51a)===================== _ _ i = Q/dt.n 51b)--------------------- ds = v.dt ; dt =d/v 51c)--------------------- The medium velocity of _ _ current in the conductor v = (ds/Q).i ========================= Inserting these parameters in 50) and using earlier achieved results from 19) and 21) gives : 52)============================= _ _ ds _ dB' = E' x ---2-. i Q.c _ _ ds _ dB' = qr.c x ----2--.i = Q.c 2 _ re _ ds .i 2 q.Kt.Kav. ---2--.N. c x ------------------------2-.(1/c )= r 2.Kt.sqrt(Ka.Kav.Pi).re.c _ q r _ 4.Pi.Kt.Kav ------2- . --3- x i.ds . ---------------------- = 4.Pi.c r 2.Kt.sqrt(Ka.Kav.Pi) _ 1 r _ ---------2 . --3- x i.ds . 2.sqrt(pi/Kv) 4.Pi.Eo.c r ============================================================ By integrating in respect to ds, the Biot-Savart's law is achieved: 53)================================================ _ _ 1 s r _ B' = --------- 2 . I --3- x i .ds .2.sqrt(pi/Kv) 4.Pi.Eo.c r ==================================================== 1 The factor -----2- is usually replaced by the symbole, uo , Eo.c giving the well known relation between the electric and the magnetic constants : 54)================== Relations between electric and 1 magnetic constants uo = -----2-- Eo.c ===================== _ The relationship between the common calculated value of B and our calculated value will be : 55)====================== The relation between the common _ _ calculated value of B and our B/B' = 1/2.sqrt(Kv/pi) calculated value ========================= -------------------- HOW AN ELECTROMOTORIC FORCE IS GENERATED BY INDUCTION IN A MAGNETIC FIELD When a metallic conductor move in a magnetic field, an electromangetic force is generated, represented by a flowing current or a voltage over it. The effect will arise mainly by two reasons 1) if the magnetic field density is changed in accord with time or 2) if the conductor accelerate or retard in the B-field. There are several reasons to change of the B field, for instance the current in the conductor is changed or a wire is moved in a homogeneous B field. The source for the electromotoric force generated, mainly emanates from the two terms in Newton's second law. Based on earlier achieved results the voltage generated when changing the B field will be : 56a)============================ F = dm/dt.v + m.dv/dt F = dm/dt.v ; (dm/dV) F/dV = ------.v dt F.dt.ds ------- = (dB/dt).v.dt.ds dV for F.dt.ds/dv = U, v=c and dt=dr/c : U = (dB/dt).dr.ds = (dB/dt).dA ------------------------------------ For the other term in Newton's law give the result: 56b)================================ F = m.dv/dt F/dV = (m/dV).dv/dt = B.dv/dt F.dt.ds ------- = B.(dv/dt).dt.ds dV For F.dr.ds/dV = U, dt = dr/c gives : U = B.(dv/dt).dr.ds = B.(dv/dt).dA --------------------------------------- and if these two effects are present at the same time : 57)================================= ! ! U = ! dB/dt + (B/c).dv/dt !.dA ! ! ==================================== In common theory only the first term is present. The reason for that may be that the second term will be relative small. Hence, a voltage is generated if the B field is changed in accord with time, or, if the the B field is constant, the velocity of a conductor in this constant field is accelerated. If the conductor move with constant velcocity, there will be no electromotoric voltage generated. ------------------------ MAGNETIC FLUX AND THE INDUCTANCE CONCEPT Magnetic flux is defined as the product of the B field and this area which the field encloses. Then the definition of magnetic flux is : 58)====================== fi = B.dA ========================= giving that the formula 57) can be rewritten to : 59)================================== Electric voltage / ! induced by change U = ! d(fi)/dt + (fi/c).dv/dt ! of B flux or by acceleration ! / of a conductor in a constant ===================================== B field ----------- THE INDUCTANCE CONCEPT In the same way as for the electric capacitor, there is a need of describing the ability of a conductor of storing magnetic energy in it, in terms of the conductors geometrical properties. We completeness, we perform a calcualtion of the inducatance factor for a simple case of a single wire loop : 60a)======================================================== U = dB/dt.dA _ uo s _ 3 _ uo s _ 3 _ B = --- . I ( r/r) x i.ds = ----.I(r/r)xi.D.da 4.Pi 4.Pi _ r = D.cosa.i + D.sina.j + z.k ; 2 2 r = SQRT(D +z ) _ i = -i.sina.i + i.cosa.j = i.(-sina.i + cosa.j) _ _ r x n = -z-cosa.i + z.sina.j + D.k _ uo a,z,A -z-cosa.i + z.sina.j + D.k B =(di/dt).----. I --------2---2-3/2------------.D.da.DA 4.Pi (D + z ) By performing integration of this expression gives: a= 0 --> 2.Pi, z= -z ---> +z, A= 0 -->A 60b)==================================== The induced voltage 2 in a coil as function uo.A.N of the current change U = (di/dt).-------2--2-- as function of time sqrt(D +z ) ======================================== where A is the area of the enclosed wire loop, N is the total number of turns in the coil and z is the length of the coil. Hence, the inductance factor is : 60c)======================== The inductance factor of uo.A 2 the coil L = ------2--2-.N sqrt(D +z) ============================ -------------------------- THE FORCE EFFECT ON A CONDUCTOR SITUATED IN A CONSTANT B FIELD. The B field represents a mass field with density B. This mass field give rise to an inflow of matter to a charged particle (the electron in a metal for instance) and this matter is absorbed and thrown out by effect of the particle's spin rotation, creating a counter reaction force. Using this idea on how a force is generated on a conductor moving in a B field gives: 61a)==================== The common flow formula Min = q.A.t.v 61b)-------------------- q is here substituted by the magnetic flux density B and v, the mean velocity Min = B.Ao.ds.N of the current flow, substituted by v= ds/dt 61c)-------------------- 2 2 min.c B.(Ao.N.to.c).c.ds.t dF = ------ = ------------------------- = re re.t t= re/c : 2 2 B.(Ka.re.c.N.Kt.re).c/c.ds .re/c ----------------------------------- = re.t 2 B.(2.Kt.Ka.sqrt(Pi/Kv).re.c.N).ds ------------------------------------- = t.2.sqrt(pi/Kv) B.(Q/te).ds. Kt/sqrt(Pi/Kv) = B.i.ds . 1/(2*sqrt(pi/Kv) ) 61d)====================== If Kv = 4.Pi s F = I B.i.ds ========================== --------------------------------- THE ENERGY STORED IN A MAGNETIC FIELD We have now calculated the magnetic field strength, B , in a magnetic field outside a conductor. Obviously, this B field represents an energy stored in the same way as for the electric field in a capacitor. The magnetic energy stored is a form of mechanical energy in the same way as for energy in the electric field. The movement of mass in the field, moving slowly in relation to the limit velocity of matter, c, then is the base for calculation of this energy stored. Newton's ordinary formula for "non relativistic velocities" then can be used, givning : 62a)=================== Newton's ordinary law for 2 kinetic energy W = (1/2).m.v ======================= The mass, m , is here represented by the mass in a small volume element in the common space field of denisty, q, as calculated before in 14). The velocity, v , is the momentary velocity of this mass, hence not equivalent with the current flow veleocity in the conductor. As calculated before, the formula 49) of the magnetic flux density B=qr.sina, the quantity of B.c represents a mass impulse density in the volume element, dV , in the way it has been generated of the movement of the electric current and the associated electric field. When this impulse hit the universal mass field in space with density, q, this impulse is re-transformed to the q field which get the velocity of vf. From that the following equality is achieved : _ 62b)================== The B field impulse of velocity, c, _ _ is transformed to the q field with B.c = q.v velocity, vf. __ _ vf = (B/q).c ====================== We also calcualte the field mass enclosed into the volume element, dV, in the space point to : 62c)================ The space mass enclosed in the space point of volume m = dV.q dV and density, q. =================== Instering these partial results in our energy formula 64a), gives: 62d)=============================== 2 2 2 W'= (1/2).(dV.q).B.c/q 2 2 W'/dV = (1/2).B.c /q 62e)-------------------------------- The energy stored 2 in a magnetic field W' = (1/2).B/uo per volume unit. ==================================== DETERMINING PARTICLE PARAMETERS Ka,Kv,Kt ----------------------------------- From 19g) 2 2.Kt.Ka.sqrt(pi/Kv) = eo/(re.c) ----------------------------------- From 19h) 2 2 3 Ka.Kt.re -------- = Eo me.Kv ----------------------------------- From 19c),19h) 2 2 eo/Eo = 4.Pi.re.me.c eo = 1.60217733E-19; re = 2.8179409238E-15; Eo = 8.854187817E-12; me = 9.109389754E-31; c = 2.99792458E8; 2 eo/Eo = 2.899161E-27 2 4.Pi.re.me.c = 2.899161E-27; ----------------------------------- From 22b) 1 = (1/2).sqrt(Kv/pi) ----------------------------------- From 30b) 2 Ka -------- =1 4.Pi.Kv ----------------------------------- From 35c) 2.SQRT(Pi/Kv) = 1 ----------------------------------- From 42) SQRT(Pi.Kv) ------------- = 1 Kt ---------------------------------- From 44) 2 16.Pi ----2--- =1 Ka ----------------------------- 22b) Kv=4.Pi, 30b) Ka= 4.Pi, 42) Kt = 2.Pi 44) Ka=4.Pi, 30b) Kv= 4.Pi , 42) Kt = 2.Pi 35c) Kv=4.Pi, 30b) Ka=4.Pi, 42) Kt= 2.Pi The model agree best with Ka=4.Pi, Kt=2.Pi, Kv = 4.Pi Kt must be slightly adjusted to 0.85238*2*Pi for exact agreement for 19g,h For torus, Kv = 2.Pi*Pi = 19.7392 For exact agreement : Kv = 4*pi = 12.5663 For exactness of 19b Kv= 2.Pi.Pi (as for torus) ********************************************************* It seems as the electron is a cavity, hence not comletely filled with matter !!!! ********************************************************* ============================================================ Hence : Ka = 4.Pi = 12.5663 Kt = 2.Pi*0.85238 = 5.35566 (for exactness of 19g,h Kv = 4.Pi = 12.5663 ============================================================ MAXWELL'S EQUATIONS OF THE ELECTROMAGNETIC FIELD James Clerk Maxwell published his electromagnetic field theory in 1873 "Treatise on Electricity and Magnetism", one of the most gigantic scientific work of a single scientist ever. An important result of his theory was that he found a close relationship between the electric field and the magnetic field, being two sides of the same thing and from the same source. Another interpretation of the theory was that electromagnetic energy was propagating in free space with a finite speed, c , equivalent with the light velocity in vacuum space. The nucleus of this theory was a mathematical inter- pretation of the electromagnetic phenomena summarized in a couple of formulae named "Maxwell's equations" of the electric and magnetic field as propagating in free space and in media. Maxwell's theory was built on the assumption of existence of a mechanical aether carrying light and "electromagnetic waves". This assumption was later on faded out and today only a shell of mathematical formalism remains. In spite of great successes, the theory has not escaped from criticism. One point is, although the theory is assumed to give a correct description of electromagnetism, it does not explain anything about electromangnetism, only describe it. Other criticism is that the equations not are symmetric in respect to Lorentz transform in the theory of relativity. But the most serious remark is the idea that electromagnetic energy is assumed to propagate like waves or disturbances in an aether sea, this aether which never was detected experimentally. Maxwell come to this conclusion by comparing the common, or general, wave equation with results from his electromagnetic theory because of symmetry in these equations. Inspired by Maxwell's theory Maichelson and Morley 1887 performed an experiment amimed to detect the light aether. The attempt was failed, hence denying the Maxwellian aether wave hypothesis. That gave rise to an exhalted debate of the nature of light during the subsequent part of the nineteenth century, a debate which declined by the birth of the theory of relativity 1905. But the problems still remain unsolved. Our ambition are not to discuss and penetrate everything in Maxwell's work, not either to dig our way through all these formuale contained in this work. Our main interest is to see if appr. the same results can be achieved from our theory and to try understand his way of thinking. We begin by making a brief list over some of the most common used equations which is enclosed in his theory, with name of "Maxwell's equiation of the electromagnetic field" : 63a)========================= Qf i the total amount of A _ _ "charge" enclosed within Qf = I D.dA the closed area A. _ 63b)------------------------- D is defined as a velocity _ _ vector of the electric field D = Eo.E 63c)------------------------- qf is the charge density in __ _ case of a non polarized field !/ D = qf 63d)------------------------- Valid at poliarization __ _ !/ E = qf/Eo ----------------------------- The next set of formulae are perhaps the best known of Maxwell's electromagnetical theory. They are valid for electric and dipole sources : 63e)------------------------- At free radiation from a __ _ point formed electric source !/ E = 0 63f)------------------------- At free radiation from a point formed magnetic source __ _ !/ B = 0 63g)------------------------- Relationships between the __ _ _ electric and the magnetic !/ x E = - dB/dt field (d = the partial derivative) 63h)------------------------- Relationships between the electric and the magnetic __ _ 2 _ field (d= the partical derivative) !/ x B =(1/c ).dE/dt ----------------------------- DERIVING THE EQUATION 63a We will now derive these Maxwell's equations with start from our own electromagnetic theory. We start with the equation 63a, where the total amount of charge enclosed in a charged point is calcualted. 64a)============================= From 22) _ 2 2 _ E = q.Kt.Ka/Kv.re.c.(1/r).n 64b)---------------------------- From 19f) Eo = 1/q 64c)--------------------------------- Combining 64a),64b) _ _ 2 2 _ gives 63b) D = E.Eo = Kt.Ka/Kv.re.c.(1/r).n ------------------------------------- _ __ 2 We intergrate the D flow over a vector area dA = 4.Pi.r, giving : 0 _ __ 2 X = I D.da = Kt.Ka/Kv.re.c . 4.Pi. According to 19c) the charge 2 is equal to eo = 2.Kt.Ka.sqrt(Pi/Kv).re.c. Hence, X will be equal to charge if : 64d)--------------------------------- 2.Kt.Ka.sqrt(Pi/Kv) = 4.Pi.Kt.Ka/Kv Kv = 4.Pi 64e)--------------------------------- Gives 63a) a _ __ Q = I D.dA (if Kv = 4.Pi) ===================================== DERIVING EQUATION 63c _ _ _ We start defining the vector field D, where D = Eo.E (see 63b). We_ select a small volume element within this vector field D with sides /!x./!y./!z (see figure below). _ D constitutes a field vector where each term Dx, Dy,Dz contain a quantity of charge expressed in varibles of _ x,y and z. We denote the field vector D as : _ 65a)======================== The D vector expressed as _ a field vector by components D = Dx.i + Dy.j + Dz.k Dx,Dy,Dz ============================ Dy y ! Dz ! ! / ! __ _ / ! /___/! ! / ! !! ---> Dx ! / !____!/ x---------------!--------------------- / ! / ! z ! ! Figure 7 In addition, with start from the equation 66), we denote the partial charge streaming out from one of the unit surfaces limited by the edges /!!x,/!y,/!z by : 65b)=========================================== dQ1 = (dDx/dx)./!x.(/!y./!dz) dQ2 = (dDy/dy)./!y.(/!x./!z) dQ3 = (dDz/dz)./!z.(/!x./!y) dQ = dV.(dDx/dx) + dV.(dDy/dy) + dV.(dDz/dz) __ _ dQ/dV = !/ D or _ 65c)---------------------- The D field divergence is equal to the charge __ _ density in a field point !/ D = qf ========================== As we will see, and as a remark to Maxwell's equations, is to say that it contains not much of information of the real source and nature of electromagnetism, mostly being mathematical manipulations of already known facts. DERIVING THE EQUATION 63h We intend to derive Maxwell's most famous equations as defined in 63e-h and start with the formula as defined by 63h). From 50) we have : 66a)================== From equation 50) _ _ _ 2 B = E x v/c ====================== We calculate the cross product of both sides of this equation, giving for the LEFT SIDE : 66b)=================== __ _ LEFT SIDE = !/ x B ======================= and for the right side : 66c)================================== __ _ _ 2 RIGT SIDE = !/ x (E x v/c ) ====================================== Performing some vector analytic manipulations of the right side, gives the result : 66d)======================================= RIGT SIDE __ __ __ __ (v.!/)E - v.(!/.E) - (E.!/).v + E.(!/.v) !--1--/ !--2---/ !--3---/ !--4---/ -------------------------------------------- We analyses each part of this relation and study the physical content in it, giving : RIGHT SIDE, part 1--------------------------------------- Part 1 _ __ _ (v.!/)E = (v1.d&dx +v2.d/dy + v3.d/dz).(E1.i+E2.j+E3.k) = v1.dE1/dx.i + v2.dE2/dy.j + v3.dE3/dz.k = dE1/(dx/dv1).i + dE2/(dy/dv2).j + dE3/(dz/dv3).k = dE/dt RIGHT SIDE, part 2 and 4--------------------------------- __ _ __ _ _ _ !/ E = k.!/.v ; E = k.v ( see equation 22) _ __ _ _ __ _ !-v(!/ E) + E.(!/.v ) = _ __ _ _ __ _ -v(k.!/.v) + k.v.(!/.v) = 0 RIGHT SIDE, part 3 -------------------------------------- _ __ _ -(E.!/).v = -(E1.d/dx + E2.d/dy + E3.d/dz).(v1.i+v2+j+v3.k) = -(E1.v1.dv1/dt.i -E2.v2.dv2/dt.j - E3.v3.dv3/dt.k = 0 at no acceleration of the source. ---------------------------------------------------------- Hence, at no acceleration of the source we get the results: 66h)======================== Relations between B,E and time __ _ _ at no acceleration of the E !/ x B = dE/dt source. ============================ DERIVING THE EQUATION 63g The equation 63g is achieved when changing the B field as function of time. There is many reasons for change of the B field. One reason may be change in the current flow in the conductor or when the conductor moves in an inhomogeneous magnetic field. We limit our investigation for the first mentioned case. Once again we start from our base equation 50) and derive both sides of it in respect to time, giving : 67a)==================== The relation between the B _ _ and the E field produced _ E x v by a conductor with current B = ---2-- velocity v. c 67b)------------------------ _ _ _ E x v dB/dt = d/dt ( ----2-- ) = c __ _ 2 _ _ !/ v/c.(E x v ) = _ _ 2 _ __ 2 2 __ _ (v.v/c.(E x !/) = - v/c.(!/ x E ) 67c)========================= _ 2 2 __ _ dB/dt = -v/c.(!/ x E ) ============================= Hence, only in case of a free wave where v=c the result correspond with Maxwell's result. We may guess that Maxwell did this assumption to achieve the result of equation 63g). LIGHT AND ELECTROMAGNETIC WAVES Maxwell's theory was from beginning a pure aether theory, or a mechanical theory of electromagnetism, where electromagnetical waves where thought to travel in space in a similar way as for sound in air, for instance. That conclusion was achieved by comparing results from his electromagnetical theory by the general wave theory, giving an illusion of physical equivalence between propagation of electric and magnetic energy as energy in a medium. This conceptual mistake has never been cleared up and has never been confessed by science. It is therefore still an unsolved problem. The manipulations with his eqiations are as follows: 68a)============================================ __ _ _ !/ x E = dB/dt (63g) __ _ 2 _ !/ x B = 1/c .d/dt.E (63h) __ __ _ __ 2_ __ __ _ __2_ !/x(!/ x E ) = - !/ E + !/(!/.E) = -!/ E __ _ ( !/ E is equal to zero for a non accelerated point source, see equation 24) ). __ __ _ __ _ __ _ !/ x (!/ x E ) = !/(dB/dt) = d/dt (!/ x B) = 2 2 2 2 _ d/dt(1/c .d/dt.E) = 1/c .d/dt .E 68b)====================== __2_ 2 2 2_ -!/ E = 1/c .d/dt E ========================== We perform a similar manipulation with start from the B field : 69a)=============================== __ _ _ !/ x E = dB/dt (63g) __ _ 2 _ !/ x B = 1/c .d/dt.E (63h) __ __ _ __2_ __ __ _ __2 _ !/ x (!/ x B ) = - !/ B + !/(!/ B) = - !/ .B __ _ (!/ B is equal to zero for a non accelerated point formed source in the same way as for the E field, see equation 24)). __ __ _ __ 2 _ !/x(!/ x B ) = !/(1/c .d/dt E ) = 2 __ _ 2 2 2 _ 1/c .d/dt(!/ x E ) = 1/c .d /dt .B 69b)-------------------------------- __ 2_ 2 2 2 _ -!/ B = 1/c .d /dt .B ==================================== These results were compared with the general wave equation, having the following mathematical structure : 70)================================ __2_ 2 2 2 _ !/ Y = 1/v .d /dt .Y =================================== where we easily can see that the mathematical structure of these results 70b,71b,72 are the same. The only thing these equations says is to describe how energy is distributed out from a point formed source point, giving not much information about the nature of electromagnetism. The equations are true both for a wave source and a particle source, hence do not support light or electromagnetism as a aether wave phenomenon. ----------------------- DIMENSIONAL ANALYSIS OF ELECTROMAGNETIC CONSTANTS AND UNITS Established electromagnetic theory cannot tell us what electric charge is, not either what an electric or magnetic field is. As we have seen here, all these phenomena can be described in pure mechanical terms in accord with Newton's basic laws, hence valid both on macrocosmical as well as microcosmical level of matter. That give us an unique possibility to express all physical units and entities in terms of basic units like mass, time and length. For summarizing, we end the session here by a brief dimensional analysis of the most important and common physical entities, collected in the table below: -------------------------------------------------------- PHYSICAL ENTITY FORMULA, SYMBOLE DIMENSION OR UNIT M L T -------------------------------------------------------- MASS M,m kg 1 0 0 -------------------------------------------------------- LENGTH L,l m 0 1 0 -------------------------------------------------------- TIME T,t s 0 0 1 -------------------------------------------------------- VELOCITY v=ds/dt m/s 0 1 -1 -------------------------------------------------------- ACCELERATION a=dv/dt m/s*s 0 1 -2 -------------------------------------------------------- AREA A = X x Y m*m 0 2 0 -------------------------------------------------------- VOLUME V = XxYxZ m*m*m 0 3 0 -------------------------------------------------------- WAVELENGTH w = v/f m 0 1 1 -------------------------------------------------------- MASS DENSITY q = M/V kg/(m*m*m) 1 -3 0 -------------------------------------------------------- MASS IMPULSE I = m.v kg.m/s 1 1 -1 -------------------------------------------------------- MASS MOMENTUM M=m.v.r kg.m*m/s 1 2 -1 -------------------------------------------------------- FORCE F= m.v.v/r N 1 1 -2 -------------------------------------------------------- FORCE MOMENTUM M= F.r Nm 1 2 -2 -------------------------------------------------------- ENERGY E=mc.c. J 1 2 -2 -------------------------------------------------------- POWER P=E/t J/s 1 2 -3 -------------------------------------------------------- PRESSURE p=F/A N/(m*m) 1 -1 -2 -------------------------------------------------------- ELECTRIC CHARGE Q=k.r*r.v As 0 3 -1 -------------------------------------------------------- ELECTRIC CURRENT i=Q/t A 0 3 -2 -------------------------------------------------------- PERMIT. CONSTANT Eo=1/q F/m -1 3 0 -------------------------------------------------------- PERMEAB.CONST uo=1/(c*c*Eo) N/A 1 -5 2 -------------------------------------------------------- ELECTRIC VOLTAGE U=Q.D/(Eo.A) V 1 -1 -1 -------------------------------------------------------- ELECTRIC IMPEDANCE Z,R =U/i Ohm 1 -4 1 -------------------------------------------------------- EL. CAPACITANCE C=A.Eo/D F -1 4 0 -------------------------------------------------------- EL. INDUCTANCE L=uo.A/D 1 -4 2 -------------------------------------------------------- EL.FIELD STRENGTH E=q.v V/m 1 -2 -1 ------------------------------3------------------------- MAGN. FIELD STR. B=uo.i.A/r Wb/(m*m) 1 -3 0 -------------------------------------------------------- MAGNETIC FLUX O= B.A Wb/(m*m) 1 -1 0 -------------------------------------------------------- PLANCK CONSTANT h=k.me.re.c 1 2 -1 -------------------------------------------------------- GRAVITY CONSTANT G=F.D*D/(M*M) -1 3 -2 -------------------------------------------------------- HUBBLE CONSTANT H=1/t 0 0 -1 -------------------------------------------------------- AT. FINE STR. CONST a = h/(me.re.c) 0 0 0 ------------------------------3------------------------- RYDBERG CONSTANT R=K.re.a-1 0 -1 0 -------------------------------------------------------- The table may be read in the following way, an example: Force = mass x velocity squared divieded by a radius. That gives : 2 F = M.v.v/r = M.(L/T).(L/T)/L = M.L.L/(T.T.L) = M.L/T Then M = 1, L =1 anf T = -2. -------------------------------------------------- SOME CONCLUSIONS Our analysis of electromagnetism shows that these phenomena of nature are of mechanical art on which Newtonian mechanical laws can be applied. All well known and tested physical laws can be derived from this starting point. Furthermore, we see that Maxwell's equations not give much contribution to an understanding of electromagnetism. This theory mainly seems to be of pure mathematical and formal interest. -------------------------------- SOME DEFINITION OF SYMBOLES q mass density of a a quasi material vacuum space qp mass density of electron or proton qr electric mass field density on distance r from a source point c the velocity of matter inside a point particle, equal to the standard velocity of light as leaving a source pint in rest relative an observer in rest. C the effective velocity of the vacuum matter (even used as symbole form electric capacitance) me the electron rest mass Mp the proton rest mass or the mass of any point like elementary charged particle Vp volume of a point particle (electron or proton) Ap effective interacting area of a point particle in relation to space Rp radius of a point particle re radius of the electron in rest (the classical radius) tp mass converting time of a point particle Ka,v,av, se definitions above Q electric charge of an arbitrary particle or a collection of particles eo electron unit charge of an electron N the number of unit charges in a charged point of charge Q _ _ n a unit vector entity = r/r for a point source W energy stored in an electric or magnetic field in accord with common theory W' energy stored in an electric or magnetic field in accord with our theory _ B magnetic field strenght in accord with common theory _ B' magnetic field strenght in accord with our theory L the inductance factor of a conductor L' the same for our theory C the capacitance factor for a capacitor in accord with common theory C' the same for our theory i electric current in accord with common definition I electric current as defined as the number of unit charges passing a cross area per time unit uo the permittivity of vacuum constant uo' the same for our theory Eo the permeability of vacuum constant Eo' the same for our theory _ E electric field density in common theory _ E' the same in our theory U electric voltage U' electric voltage in accord with our theory Z electric impedance in common theory Z' the same as in our theory Zo zero impedance of vacuum space Zo' the same in our theory --------------------------------------------- REFERENCES : As support for writing this article common available litterature has been used, mainly including scientific dictionaries and student litterature treating this subject in a well established and general way. (First published 1981 in "A NEW WAY TO PHYSICS") This original dated 11/20-1991) (Selected parts published in Galilean Electrodynamic 1993) (Reworked/developed/improved 16/4-1994) (end)