Re: Is charge always conserved?
At 10:58 PM 12/8/4, Stephen A. Lawrence wrote: The basic formula for A at a particular point, from Rindler, 2nd edition, p. 111, or Griffiths, 3rd edition, p. 423 is just A = (1/4pi)integral([J]dV/r) where the integral is taken over all space, [J] is the retarded value of the 4-current density, and r is the distance from the point where one is evaluating A. Since J is time invariant in this case, [J] = J. Each component of J is integrated separately, which means phi = (1/4pi) integral(rho dV/r) where phi = electric potential and rho = charge density. To look at it yet one more way, if you're looking at a case where the current is not varying, then you're in the domain of magnetostatics and you don't need anything beyond simple EM to analyze it. Fancier approaches, such as the pancaking model, must agree with a simple analysis in simple cases. I have such uneasy feelings about the vector magnetic potential A, especially in the context of relativity, due to my lack of understanding I assume. Please excuse this momentary lapse into humor. Humor shield on. If the vector magnetic potetnial were real in any sense, then it seems to me we should build a National Vector Magnetic Field Facility (VMFF). Using wire made of twisted pair superconductors, there is no limit other than financial to the intensity of the VMF that can be created by a coil of such, due to the lack of force when A is not changing. The VMF shows up in a real way quantum phenomena, so maybe unusual things would happen at the center of the coil. The facility would also have political advantages for the operators. Unlike operators of future great tokamaks that happen to not break even, the VMFF operators would have a handy excuse. Someone changed the guage, so we dont know where the VMF went. 8^) Humor shield off. If it is true that the definition: @f/@t = lim dt-0 ( f(x,y,z,t+dt) - f(x,y,z,t) )/dt holds in a vector point field, for f a vector at point (x,y,x,t), then in an FEA simulation one can simply approximate: @A/@t = (1/dt) ( A(x,y,z,t+dt) - A(x,y,z,t) ) where (1/dt is now a finite scalar and ( A(x,y,z,t+dt) - A(x,y,z,t) ) is a vector subtraction. We thus use a finite number of values for x,y,z,t to simulate the results, based on starting conditions at time 0. SIDE NOTE: To compute A(x,y,x,t), given the set of current filaments comprising the torus, we can use: A = line integral of [(mu I dL)/(4 Pi R)] where R is the distance from the current element to the point at which the vector magnetic potential is is being calculated. This sets the guage, by assuming div A = 0, but the guage is arbitrary. Consider now a toroidal coil (or just torus) carrying constant current moving in space along its major axis, which is also the x axis, toward an electron at point (x,0,0). Since the current is constant we should be able to assume both B and E outside the torus is zero. - O Torus cross section (x,y,z) (e-)... Main axis of torus - O Torus in motion Now, since the coil approaches (x,y,z)==(x,0,0) for some fixed x, the magnitude of the magnetic vector potential A(x,0,0,t+dt) is larger than the magnitude of A(x,0,0,t). Using the definition of @A/@t above would imply that the electric field E = @A/@t imposed at (x,0,0) by the moving torus is non-zero. Now, consider a toroidal coil carrying constant current located at the origin with its major axis the x axis. An electron at point (x,0,0) has initial velocity v towards the origin. Since the current is constant we can assume E outside the torus is zero. O Torus cross section (x,y,z) (e-).X Target X at origin O Since the electron at (x,y,z)==(x,0,0) approaches the origin, i.e. dx/dt = v, then x diminishes with time, and the magnitude of the magnetic vector potential A(x+v*dt,0,0,t+dt) is larger than the magnitude of A(x,0,0,t). In other words dA/dt is non-zero for the electron, even for a fixed current toroidal coil. We can not assume @A/@t is non-zero because dA/dt is non-zero? Using the definition of @A/@t = dA/dt here implies that the electric field E = @A/@t imposed at (x,0,0) by the stationary fixed current torus at the origin upon a moving charge is non-zero. Yet we see that A(x,0,0,t) = A(x,0,0,t+dt), and A(x+v*dt,0,0,t) = A(x+v*dt,0,0,t+dt), so @A/@t at (x,0,0,t) = 0, and @A/@t at (X+v*dt,0,0,t+dt) = 0. At no time should there be an E = @A/@t experienced by the electron. Yet, as we saw above, if we change reference frames to that of the electron, both dA/dt and @A/@t are non-zero. This seems to indicate that the E experienced depends on velocity relative to the source of the A. If it is true that E depends on relative velocity with respect to the source of A, then we merely aim an electron beam at target X and it
Re: Is charge always conserved?
Stephen A. Lawrence writes Horace Heffner wrote: There are various concepts in which charge might not be conserved. [snip] Since the ring is uniform, the 4-current density is not varying in time, and we can forget about the retarded part. The motion of the ring affects the spacelike parts of the integral but not the timelike part. So, the timelike part of the 4-vector potential will be identical to the timelike part of the 4-vector potential for a STATIONARY ring of charge. This may be adding too much complexity, but... Thinking (out loud) about conservation of charge and capacitive coupling in the context of RTSC (room temperature superconductivity) raises a nonreciprocality issue. Does the capacitive coupling from a superconductor to a normal conductor always obey all the energy conservation laws? The knee-jerk reaction is yes, why not?... but have all the 4-vector potentials you mention been accounted for with RTSC as one component ? There seems to be some avenue for nonreciprocality in that instance, but it sounds like you are very much up-to-speed on these issues and may recognize why this would not work. Vortexians seem to be always looking for something new which fits into the idea of nonreciprocality : such that a source of potential energy (i.e. magnet or static field) + efficient means of modulating potential energy + nonreciprocal element = OU The information provided by any Maxwell's Demon type-device, of course, provides one generalized notable feature: the characteristic of classical nonreciprocality and asymmetry. Other devices like gyroscopes, Hall effect devices, Faraday effect devices, and microwave isolators are examples of classical nonreciprocality, but it has been difficult to fashion an energy device out of them, so many experimenters are thinking about the possibility of layering of two nonreciprocal devices. Using the magnetic vector potential may end up being one of the most inviting instance of classical nonreciprocality for the clever researcher - as it can be nonzero in regions of zero magnetic field. It may be possible to scale up this effect to a usable level by combining it with flux modulation (or flux-gating, for lack of a better term) or modulation of the capacitive coupling situation. At first glance one would say that an air coil surrounding a RTSC toroid coil which surrounds a PM magnetic core will have little interaction with either but there is such a delicate balance there that if capacitive coupling was not conserved, then any slight movement in the coil could be multiplied in two nonreciprocal ways. Either way alone might not be OU (in the sense of overcoming the parasitic losses of moving the coil (ultrasonics?), but the combination of the two might be OU (right). ...but he beauty of the A-B effect in part of any device is that it does not depend on EM radiation, but might be able to modulate it ... or not. Jones
Re: Is charge always conserved?
At 10:00 AM 12/8/4, Stephen A. Lawrence wrote: I had three comments on this analysis (which I snipped -- hope that's OK). Not only OK, but such snipping is mandated (or at least strongly encouraged) by the vortex rules. IMHO, the list could use more good snippers like you! 8^) First, watch out for Shadowitz -- I've seen an instance where he messed up an analysis by using the motion of the EM field relative to a particle, which has no role in relativistic EM. Rindler, Jackson, and Griffiths seem more reliable, to name some I'm aware of. I don't know any reason to doubt Shadowitz's formula for pancaking, but you should definitely double check any general assertions he makes about how fields transform. I've seen it various other places too. No refs handy at the moment. Second, pancaking of the field for a point charge is derived from evaluating the 4-vector potential for the charge using the retarded integral. Pancaking isn't really fundamental; the representation in terms of retarded integrals is. So, to see what's really going on in a complex situation involving accelerated charges, it's probably safer to use the retarded integrals directly. Yes, I was wondering what effect acceleration might have. The approach I used for that I even felt was bogus at the time. Finally, let's do just that. For simplicity, assume a rotating ring of uniform negative charge density, with a fixed positive charge in the middle of the ring. Let's look at the axial field. Since the ring is uniform, the 4-current density is not varying in time, and we can forget about the retarded part. This analysis bothers me. It says the whole is not the sum of the parts. I showed that if pancaking is valid for an individual particle, then the sum of such individual pancaking effects does not cancel at all points. However, I must admit I had the nagging feeling I probably left other important effects out of my analysis, like abberation, which might negate field pancaking. I have the impression that aberration applies to photons though, and pancaking to fields. There should be a simple way to visualize this situation. (Beign a rank amateur, I don't consider tensor analysis simple.) [snip conclusions] This field is well understood and it's certainly conservative. I am curious as to just why it is thought the huge polar jets of material fly out of black holes and neutron stars. An analagous (and additional) polar gravitational field should develop in the vicinity of black holes, if the analysis is done according to the gravimagnetic isomorphism I proposed on this list anyway. It's got a nonzero dipole moment but the far field on axis goes rapidly to zero (1/r^3, I think?). Yes, and thus aligned dipoles have a mutual 1/r^4 force. Regards, Horace Heffner
Re: Is charge always conserved?
Horace Heffner wrote: At 10:00 AM 12/8/4, Stephen A. Lawrence wrote: I had three comments on this analysis... First, watch out for Shadowitz -- I've seen an instance where he messed up an analysis by using the motion of the EM field relative to a particle, which has no role in relativistic EM. Rindler, Jackson, and Griffiths seem more reliable, to name some I'm aware of. I don't know any reason to doubt Shadowitz's formula for pancaking, but you should definitely double check any general assertions he makes about how fields transform. I've seen it various other places too. No refs handy at the moment. Oh, the pancaking is fine. The caveat is with respect to Shadowitz -- I'm looking at a scan of p. 124 from his Electricity and Magnetism in which he concludes that, in a particular case, moving a magnet past a wire produces no EMF in the wire, while moving the wire past the magnet does produce such an EMF. Someplace in there he seems to have suffered a breakdown in intuition which goes pretty deep. After seeing this particular analysis I'd tend to avoid him in favor of other authors. (I don't know the edition and don't have the book, just a scan of a few pages someone sent me during a conversation about homopolar generators. I suppose it's even possible that the text wasn't actually by Shadowitz, but the person who sent it to me is generally pretty reliable.) [ ... ] Finally, let's do just that. For simplicity, assume a rotating ring of uniform negative charge density, with a fixed positive charge in the middle of the ring. Let's look at the axial field. Since the ring is uniform, the 4-current density is not varying in time, and we can forget about the retarded part. This analysis bothers me. It says the whole is not the sum of the parts. Well, if the parts are accelerating, then perhaps it's not. Rindler, in his misnamed Introduction to Special Relativity (if that's an introduction then I'm the Pope) goes through the derivation of the pancaking for a single charge in uniform motion, but I got bogged down at the start of that section and went off to study French. (Call me a dilettante, I won't object...) Just before that, he covers the retarded integrals used to obtain the 4-vector potential in the general case, and there were some very tricky bits in there for accelerating charges. Here's the same argument I already gave, in slightly more detail (I've left out the epsilons and mus on general principles). The basic formula for A at a particular point, from Rindler, 2nd edition, p. 111, or Griffiths, 3rd edition, p. 423 is just A = (1/4pi)integral([J]dV/r) where the integral is taken over all space, [J] is the retarded value of the 4-current density, and r is the distance from the point where one is evaluating A. Since J is time invariant in this case, [J] = J. Each component of J is integrated separately, which means phi = (1/4pi) integral(rho dV/r) where phi = electric potential and rho = charge density. To look at it yet one more way, if you're looking at a case where the current is not varying, then you're in the domain of magnetostatics and you don't need anything beyond simple EM to analyze it. Fancier approaches, such as the pancaking model, must agree with a simple analysis in simple cases. I showed that if pancaking is valid for an individual particle, then the sum of such individual pancaking effects does not cancel at all points. But again, the formula you started with was for a point charge in uniform motion. However, I must admit I had the nagging feeling I probably left other important effects out of my analysis, like abberation, which might negate field pancaking. I have the impression that aberration applies to photons though, and pancaking to fields. There should be a simple way to visualize this situation. (Beign a rank amateur, I don't consider tensor analysis simple.) Huh. I agree, there should. But I sure don't know what it is, either -- wish I did. Consider this: There are two charged rings, one positive and one negative, with equal total charge quantities, arbitrarily close together. In the lab frame one is spinning and the other isn't. Hence, in the lab frame, there is a magnetic field present, but the E field is negligible. (You can replace the two charged rings with a simple loop of wire carrying a current, if you prefer -- the point is that the net charge density is zero when averaged over any finite volume.) Now, look at it in a frame of reference which is rotating with the rotating ring. A moment's gedanken experimentation with a test charge moving tangentially to the rotating ring (which will feel a force due to the B field in the lab frame) should convince you that there's an E field in the rotating frame of reference. But charge is conserved -- just moving into a different frame of reference doesn't create or destroy it. So where's the E field in the rotating frame coming from? The divergence
Re: Is charge always conserved?
At 10:58 PM 12/8/4, Stephen A. Lawrence wrote: Horace Heffner wrote: [snip stuff for a bit] I showed that if pancaking is valid for an individual particle, then the sum of such individual pancaking effects does not cancel at all points. But again, the formula you started with was for a point charge in uniform motion. [snip] Interesting observation. True, my analysis was based on a moment in time, with an attempted (and probably wrong) instantaneous adjustment for acceleration. If the point charges were *not* to be accelerated on around the circle, but rather allowed to continue along straight line (tangential) paths, we might then expect the non-conservative field to at least momentarily exist. I have to wonder at this point if the subject non-conservative field could be produced momentarily by independent straight current segments. One thing field pancaking does show, however. The effective charge depends on the veloctiy *and* relative location of the observer. In that sense at least, charge is not always conserved. Regards, Horace Heffner
Re: Is charge always conserved?
Harry Veeder wrote: Since it is acceptable to question conservation laws on this forum, perhaps CF is possible because the charge on subatomic particles is not conserved in all contexts. Note: This is different from the concept of 'charge shielding'. Furthermore, consider the fusion process: d + d -- He + gamma When deuterium fuses in a vacuum the wavelength of resulting gamma radiation is relatively short. If deuterium is able fuse in a Pd matrix because it periodically experiences a charge reduction (not charge shielding) the wavelength of the radiation will be longer. If a CF cell produces longer wavelength emissions, it might be evidence that subatomic charge is variable (not conserved) in some contexts. Harry
Is charge always conserved?
Since it is acceptable to question conservation laws on this forum, perhaps CF is possible because the charge on subatomic particles is not conserved in all contexts. Note: This is different from the concept of 'charge shielding'. Harry Veeder
Re: Is charge always conserved?
At 3:05 AM 12/4/4, Harry Veeder wrote: Since it is acceptable to question conservation laws on this forum, perhaps CF is possible because the charge on subatomic particles is not conserved in all contexts. Note: This is different from the concept of 'charge shielding'. There are various concepts in which charge might not be conserved. Here is an example I posted here a while back that indicates apparent charge moving in a circle may vary depending the angle of observation. Planar Circular Currents BACKGROUND AND ASSUMPTIONS It is well known that special relativity predicts changes in the observed field of a particle due to the flattening of the field in the direction of motion. This flattening is due to application of the Lorentz contraction due to relative motion. This relativistic effect of flattening the apparent field is called the pancaking of the Coulombic field. It is the intent here to discuss the effects of pancaking with respect to planar circular direct currents. On p.492 of *The Electromagnetic Field*, Albert Shadowitz provides the equation for relativistic (Coulombic) field pancaking as: E = Q/(4 Pi e0 r^2) (1 - (v^2/c^2))/(1 - (v^2/c^2) sin^2 theta)^(3/2) If we let b = v^2/c^2 then we can interpret apparent charge Q' to be: Q' = Q (1 - b)/(1 - b sin^2 theta)^(3/2) which can be interpreted to mean apparent charge is reduced to observers in line with the charge velocity vector and increased as the viewing angle is increased. NOTE - it is not standard physics to interpret pancaking as a change in apparent charge (standard relativity assumes charge is invariant with velocity) but rather a change in observed field strength, but we should be able to interpret the pancaking equation for Q' either way. Consider the Bohr model of the atom where the electrons whiz around a nucleus. Specific electrons present some degree of pancaking from any angle viewed. In some directions apparent charge is increased and some directions decreased. In a non-magnetic medium, the polar orientation of atom orbitals is mixed in a uniform way due to the orientation of atoms being mixed in a uniform way. Upon integration over 3D polar coordinates, one finds that the average net charge change, according to the pancaking equation, for randomly oriented atoms and orbitals, is zero. However, the conditions examined here differ from those of an atom not in the presence of ambient electronmagnetic fields, as do the resulting forces. ANALYSIS OF THE RELATIVISTIC PANCAKING EFFECT If some set of orbitals are aligned, say by a magnetic field, or if we have the case of a planar circular current in a conductor, a neutral medium, then the average apparent charge (as viewed from a long enough distance to make the circle diameter insignificant) does not net out to zero, except at a specific viewing angle. As viewed within the plane, pancaking reduces the apparent charge of charges in motion, and increases the apparent charge of charges in circular motion as viewed from the poles of the circular motion. The net apparent charge of a charge moving in a small circle relative to the distance of the viewer comes from integrating to find the average value of: k(theta,v) = (1 - b)/(1 - b sin^2 theta)^(3/2) for theta = 0 to 2Pi, where b = v^2/c^2, and then subtracting the average value from one to obtain the net charge change factor K(v), because if v = 0 then the observed (apparent) charge Q' is the same as the charge Q: Q' = Q * 1 If the average value of k(theta,v) is non-zero, when integrated over all angles theta, for v not 0, then an average apparent net charge exists when v not 0. The average value f_avg of any function f(x) is given by: f_avg(x) = 1/(b - a) [integral from a to b][ f(x) dx ] so the value of net charge change factor K(v) = 1 - [average over theta of k(theta,v)] is given by: K(v) = 1 - 1/(2 Pi - 0) [integral from 0 to 2 Pi][ k(theta) d theta ] which requires solving an elliptic integral of the second kind, and yields a net charge: Q_net = K(v) Q where K(v) can be approximately based on the average speed of the electrons. Note that in the 3D situation the averaging integral equivalent to the above would be [Integral from 0 to Pi] [k(theta) sin(theta) d theta] because it is necessary to average over theta with a weight of sin(theta) to account for the surface area involved. This integral evaluates to one, thus K(v) evaluates to zero. However, in the planar version, K(v) does not average to zero. NUMERICAL APPROXIMATION OF THE PANCAKING EFFECT The average values k_avg(v) of k(theta,v) for random planar orientations as viewed from the plane were directly calculated by computer program, thus producing the incremental force factor: K(v) = 1 - k_avg(v) over a complete circle, for theta = 0 to 2 Pi. Results for various values of v/c are shown in Table 1: v/c K(v) .99 0.363371045179493
Re: Is charge always conserved?
At 3:05 AM 12/4/4, Harry Veeder wrote: Since it is acceptable to question conservation laws on this forum, perhaps CF is possible because the charge on subatomic particles is not conserved in all contexts. Here are some additional old posts you might find of interest on this subject, though more along the lines of magnetic charge. Gravity, Electromagnetism, Maxwell Horace Heffner - 4/16/97 The following are some (gravity related) personal opinions and a follow-up of discussion of an earlier thread regarding Maxwell's laws with Daniel T (the empiricist) and Robert Stirniman. Also, some experiment ideas at the end. Any protracted discussion of gravity is likely to be a discussion of electromagnetism (EM) and issues of free energy. This is because: 1. The understanding of fields and the mathematics of vector fields developed largely as a result of electromagnetic theory 2. Much of the effort to understand gravity is centered in developing a unified field theory, i.e. linking gravity to EM effects, and vice versa. To the degree that effort is successful, a study of gravity *is* a styudy of EM, and vice versa. Gravity is considered by some researchers to be, wholly or in part, a second or third order EM effect, thus the term electrogravity. 3. Our senses only operate with electromagnetism (e.g. touch, sight, hearing, smell, etc.), so our perceptions and direct measurements of the effects of gravity or any physical thing can only be derived through effects of that thing on electromagnetic entities. 4. Classical EM is totally embodied in and deriveable from the vector form of Maxwell's laws. EM fields conserve energy. Any mechanism that does not conserve energy in our EM world is likely to violate Maxwell's laws, as any process operating consistently with Maxwell's laws will not. 5. Much of the interest in gravity is really more an interest in antigravity and/or gravity sheilding (especially in this newslist.) Anitgraivity, if it exists in the forms typically envisioned, denies conservation of energy, and very possibly light speed limits to travel velocities. 6. A result of all the above is that it is reasonable to search for keys to antigravity in the arena of any data or EM theories which stand contrary to Maxwell's laws. This arena is surprisingly large, and growing. It is also confusing due in part to the arkane or non-conventional vocabulary and in part due to mathematical complexity. I have only touched the surface of the literature in this strange but fascinating and wildly speculative world. I can only speak from an amateur non-expert viewpoint, but initial impressions of EM outside of Maxwell are that there are probably a number of bogus theories, nonsensical theories, and unfathomable theories, maybe some good and workable theories, certainly a lot of mainstream rejected theories, and lots of very interesting experimental data. - - - - - - - - - - At 1:17 PM 4/3/97, I wrote under the thread name Planets; Elements; Magnetics: I think B dot dS = 0 is totally equivalent to the statement there is no monopole. Ignoring the question of whether this Maxwell's equation is indeed a law -- if it is a law, it is equivalent to the statement that there are no free monopoles. All this is a consequence of the postulates (assumptions) of Maxwell's laws, which of course would need to be revised in the face of the discovery of a monopole. The existence or not of such a particle is a fact of nature while the rest are assumptions. It does seem to me fitting that Maxwell's Laws be called such because the other EM principles can be derived from them, so although they were a culmination of a long search and a summation of many principles discovered by others, they seem to me to have a very fundamental compact distilled quality. Just opinion. About the monopoles, though, they could only exist in pairs and be consistent with B dot dS = 0 if they at all times occupied exacly the *same point* in space. Otherwise, you could always have a way to place the envelope S around one and exclude the other. However, this being the case that they are always co-centered, they would therefore then always represent a scalar field, unless acted upon by a charged particle or EM field in the viciniy. - - - - - - - - In regard to the above issues, Robert Stirniman brought to my attention Advanced Electromagnetism Foundations, Theories and Applications, edited by Terrence W. Barrett and Dale M. Grimes, World Scientific Publishing, 1995. Of particular interest is the article Six experiments with Magnetic Charge, V.F. Mikhailov, p. 593 ff., which discusses a modern look at the work of Felix Eherenhaft (1879-1952). Eherenhaft performed the magnetic equivalence of a Millikan's oil drop experiment in the hopes of isolating magnetic monopoles and measuring magnetic charge. Surprisingly, Eherenhaft had positive results, obtaining a value for magnetic charge in the range of 10^-9 to
Re: Is charge always conserved?
At 3:05 AM 12/4/4, Harry Veeder wrote: Since it is acceptable to question conservation laws on this forum, perhaps CF is possible because the charge on subatomic particles is not conserved in all contexts. Irreverance here, especially amateur irreverence, also sometimes extends to thermodynamics. Why not? Something might even be learned by just bungling around. Second Law Violating Nanochip (SLVN) GENERAL The purpose here is to discuss issues regarding the construction of a Second Law Violating Nanochip (SLVN). The goal is to design a device that demonstartes that the assumed Second law of Thermodynamics is invalid by showing that it is possible to extract heat from one of two equal temperature compartments to increase the temperature of the second compartment. That is to say, extract kinetic energy from matter in the first compartment, convert it to electrical energy, and heat the second compartment via a joule heater. THE PIEZO-KINETIC APPRAOCH Let us consider the possiblility of manufacturing a chip with very thin very small piezoelectric crystals on the surface connected to integrated fullwave diode bridges. The output of all the tiny bridges would be collected together, the chip placed into a havy noble gas. Suppose the chip is placed in a compartment adjacent to which is another compartment at the same temperature. The chip drives a joule heater in the second compartment. At some operating temperature the chip it might be possible to convert kinetic energy from one compartment to electrical energy, which is then transferred to the kinetic energy of the second compartment. The difficulty is making the chip so it will not be destroyed by the operating temperature and the piezoelectric crystals small enough in area compared to the size of the impinging gas molecule, so that the voltage generated by the piezo-compression is sufficient to make it through the diode bridge, i.e. overcoming the diode forward bias potential. The peizo must have a small surface area to prevent the charge being spread over a wide plate, thus reducing the voltage. Any required energy requirement can be met by utilizing a sufficient particle energy, or operating temperature. The main difficulties are achiving a small piezo area, a small integrated fulwave bridge in the same cross section, and low enough diode forward bias. For a rough first cut at this assume an operating temp of 300 K. Since 1 eV = 11,600 K, at 300 K the typical particle in a gas will have an energy of 300/11,600 eV = .026 eV = .026 * (1.602 x 10^-19 J/eV) = 4.166 x 10^-21 J. Let's assume we want to charge a capacitor to .3 V. Since E = .5(C)V^2 we get C = 2E/V^2 = 2*(4.166 x 10^-21 J)/.09 F = 9.76 x 10^-20 F. Now C = Ke (A/w) (8.85 x 10^-12 F) where Ke is the dielectric constant, A is the plate area in m, and w is the thickness of the capacitor in m. For the sake of simplicity and to get scale, let's assume A = w^2, and Ke = 4, so C = 3.54 x 10^-11 F/m * w. So now w = (9.76 x 10^-20 F)/(3.54 x 10^-11 F/m) = 2.76 x 10^-9 m. The structure size for the device should be in the range of about 27.6 Angstroms. The atomic radii of Si, O, and Au are 1.46 A, .65 A, and 1.79 A respectively. So 27 A represents a structure about 7-10 atoms across. However, this assumes a perfectly non-elastic collision every time (estimate optimistic), yet the kinetic energy of a gas is a distribution, so many collisions will be more energetic, some much more so (estimate pessimistic). So, what does this say? The design is infeasible. The structures are too small to be practical or functional. The difficulty centers about the need to focus on a small enough area a sufficient amount of energy to overcome the forward bias of the diode. The forward bias sets a minimumn voltage level, which sets a maximum surface area over which the generated charge is to be distributed. If the forward bias of the diode were zero then there would be no upper limit to the size of the energy trapping structure, but like with browian motion, smaller gives more of a result. What about power? If such a device can be built that works at all, then there is a very good potential for significant energy production. This is because, assuming some of the generated energy is returned to stir the gas, a very large percentage of the molecules will connect with the sides of the container per second. This means a significant portion of the specific heat of the gas could be drained off per second. One problem with the chip might be maintaining balance, not cooling the compartment so much the energy is not transferred and yet not overheating the chip. But those are much easier problems. THE CHARGE-TRANSPORT APPROACH Having seen some of the difficulties of extracting energy from neutral gas particles, it is now easier to appreciate the advantages of extracting energy from an electrolyte. Here, the idea is to use local charge fluctuations, thus indirectly heat, in an electrolyte to
Re: Is charge always conserved?
Speaking of obtaining energy from the Zero Point Field (ZPF), the Atomic Expansion Hypothesis (AEH) might be applied to obtain free energy from the vaccum by doing electrolysis using a metal coated piezo-kinetic SLVN (described in prior post in this thread) for a cathode. I will post the Atomic Expansion Hypothesis separately now. As the H3O+ hydronium molecules are electronated at the cathode, as the proton tunnels through the interface to the cathode, the atomic expansion fueled entirely by ZPE provides mechanical free energy, which can readily be convered to electrical form by a piezo-kinetic SLVN. Alternatively, the sudden local presence of the tunneling proton charge might be used to obtain free energy directly by use of an EEP coated with an insulating layer and then cathode layer. Regards, Horace Heffner
