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ISOTROPIC CAPACITY

 

Richard Hull
 

  If we take two metal spheres, one larger than the other and contain the smaller within the larger, we have a formal capacitor with the dielectric medium being the intervening air or a vacuum.  Now let them be charged from a source of electrical energy.  Imaginary electric field lines now supposedly exist between the two spheres.  Due to the regularity of their surfaces and one of those qualitative laws of electrostatics mentioned earlier, the lines of electric charge distribute themselves uniformly over the entire surfaces of both spheres.  Now the energy within the capacitor is fixed.  Due to laws of geometry, for a given number of total lines, the number per unit area on the small, inner sphere will be much higher than on the larger, outer sphere.  If we now expand the outer sphere to a much larger diameter, the number of lines per unit area on the now larger outer sphere decreases dramatically, but the number of lines per unit area on the inner sphere remains, effectively, the same.  This argument can be expanded until the outer sphere recedes to infinity.  From this it can be seen that charge can be separated in space and one sign of it can be effectively placed on an isolated sphere!  Whereas this charge's other sign is assumed to be at infinity, actually, it can be lurking in the vicinity and distributed over many other material surfaces.  Nonetheless, the effective appearance to us is that the single sphere is charged and can be discharged with relation to other matter.  In short, we have what appears to be a single plate capacitor!  This is where many people run astray.  The separated charge is never on the small sphere, but in the space around it!  We just see one sign of the total charge appear concentrated around the interfacial boundary of the sphere and the dielectric medium in contact with it!  In general, any conductive body removed by ten times its major axis length from the presence of other bodies may be considered, electrostatically, isotropic.

This is no thought experiment, but a verified reality.  Therefore, to store charge in space we only require one conductive object, and a dielectric.  The assumed second conductive object is all the rest of the material bodies in the universe out to infinity.  This occurs on a Van de Graff generator where the large spheroid terminal is charged by the moving belt.  Oops!  The space surrounding the sphere is charged by the moving belt.  (Old habits and thought processes die hard.) The sphere is just one terminal of an imaginary capacitor capable of supplying only one sign of that charge to a closed conductive circuit.  In fact, due to the small size of most Van de Graff generators, there is a complex mixture of two plate capacitance and isotropic capacitance involved.  On earth and in electronic systems, it is difficult to develop 100% of any body's isotropic capacitance.  Certainly, however, 99% or better should be possible with good engineering.  This is where Tesla's magnifier and construction engineering paid off.  I will come back to this later on.

These concepts are at the core of much current scientific discussion and must not be assumed to be entirely factual.  They are intended as aids for explaining charge storage in terms which allow a modicum of understanding of how to proceed to higher levels of understanding.  As such, many scientists and educators tend to take these ad hoc and interim concepts as established truths.  Certainly, at the high school or even college engineering level, these explanations will serve to introduce higher conceptualizations without undue trauma of needing to know more details.  Physicists, however, are much concerned with the intimate details!


What is Charge?

We still have little actual idea of what charge is and just how it is stored, especially in the vacuum of space.  Such ethereal concepts are difficult to visualize by we 'touchy-feely' humans.  The whole concept of the contact action of the field is due to this innate human desire to touch and feel and see a 'push' result in delayed, time-ordered reaction.  More importantly, to see a mechanical linkage between cause and effect.

Tesla seems to have never had any doubts about the nature of electrostatic charge, especially as relates to isotropic capacitance.  For our purposes, it is enough to finally see how electrical energy can be stored in space, and to view an isolated sphere surrounded by that space as a real world capacitor capable of recovering this stored spatial energy.

In Tesla's day, before the particulate theory of matter, electricity was viewed as a kind of fluid.  It was noted that the 'fluidics' electricity could be placed into or brought out of insulated items by friction, that is to say, rubbing them with another insulator.  An example of this, triboelectrification, is when a teflon rod is rubbed with wool.  It was also noted that no amount of rubbing would charge a conductive ball or a piece of metal.  The generative nature of charge seemed to be totally locked within relatively good insulators.  It was further discovered that a charge, once generated on an insulator could seemingly be transferred to a metal sphere (isotropic capacity, remember?).  It was actually determined that the metal itself contained no charge, but created an interfacial charge region with the space around it.  The opposite charge was assumed to be off at infinity or concentrated about nearby objects.  The charge could be moved about the interfacial area of the sphere by the approach of other objects based on Dufay's and Coulomb's laws.

Irregularly shaped, conductive charged objects can have concentrations of charge based on the radius of curvature of the object.  A sphere of fine smoothness will have a perfectly distributed charge spread over its entire surface.  The thrust of this paragraph is that if one has an object with sharp points on it, then the electrical charge will be almost totally concentrated in those areas and the rest of the object might, locally, exhibit little or no charge.  This further causes large concentrations of charge potential to perhaps bleed away from the object if the tension is so great that the coulomb forces are strong enough to ionize the surrounding air dielectric.  The resulting conductive path away from the interface drains energy as work is done by the charge potential on the surrounding air molecules and atoms.

As it is understood today, charge is strictly the absence or presence of more or less electrons.  The electron is a negative particle.  While the proton is a positive particle, it cannot be considered in the conduction scheme as it is not free to move about.  In order to free protons, tremendous nuclear energies are required and are never encountered in any day-to-day conduction processes on earth.

Electrons can be freed from their conductor atoms relatively easily.  Just a few volts of potential can shear off an electron.  Electrons quickly recombine with the ionized atom to seek a neutral state of lower energy.  Conduction itself is a process, not of moving electrons, but of the 'effect' of charge separated electron differentials between points of a separated charge.  In a conductor, there are lots of linked electrons in metal lattices.  The effect of the presence of a surplus or deficit of electrons at one end of the conductor will be almost instantaneously felt at the other end where the opposite condition exists and the 'ripple through' energy is what is felt and not a genuine flow of electrons.  As these charge effects attempt to cancel one another, current flow is manifested within the conductor and load, and work is done.  The number of electrons present or absent at a point is measured in coulombs (1 coulomb = ~ 1019 electrons).  This value is computed from Robert Milikan's original oil drop experiment and is based on Coulomb's law and the mass of the electron.  In electrostatics the volt is literally related to the number of coulombs or electron charges separated within a given unit of capacitance, E=q/C, i.e., if 10 million electron charge separations, or 10-12 coulombs, occur within a 1 picofarad capacitor, the terminals will be at a potential of about 10-12/1012 = 1 volt.  It must be appreciated that this volt has nothing to do with current but is a static, scalar potential.  This potential represents the work done in separating charge.  It is merely a quantity of free electrons, ionized atoms or separated charge units contained within a controlled volume of space.  The charge units all have the unit charge of the electron only, whether they are positive ions or actual free electrons.

Tesla and his contemporaries viewed space and insulators as the domain of electric potentials, charges and forces.  They saw electrical fluids in motion and metallic conductors as conduits to provide a pathway for stored charge to reach loads and perform work.

In more modern times, we are supposedly better informed, having discovered the electron and accepting its charge as the smallest unit of charge associated with electrical activity.  Now all charge is derived from within matter alone.  There can be no disembodied electric fluid.  Metals and matter are the source of electrons and, ultimately, charge.  Space is just an empty place in today's relativistic world.

Some grave problems occurred due to this particulate revolution.  Relativity, quantum mechanics, and more recently Feynman's quantum electrodynamics (QED) were required to stabilize our supposed understanding of electricity, charge and the like.  Is it any wonder that Tesla and, later, Einstein rebelled at this grander complication and increasing fuzziness of the universe? True or not, the new material is not very elegant, almost totally non-intuitive, and is virtually immaterial to the normal function and design of standard macroscopic structures and appliances.

What Was Tesla Trying to Accomplish?

Based on Tesla's diagrams and the few public discussions of his systems, it appears that Tesla's plan for the communications portion of the World System involved electrostatic potential swings.  The swings would use a tremendous movement of powerful electrical currents coupled to the earth through an extensive subterranean ground connection, and resonant electric waves coupled to the earth via a large isotropic capacity.  The system was to be a simple series capacitive circuit where a micro capacitance--the giant Wardenclyffe tower dome--would be forced to swing through tens of millions of volts in order to induce the earth's massive natural capacitance to swing through a few volts over its entire surface.  In this scenario, grounding was the key element, providing physical linkage between the two systems.  The isotropic capacitive linkage was the return path.

Source: Tesla Coil Builder’s Guide to the CSN, Richard Hull