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# Understanding fields, capacitance and potential

```I'm writing this to help clarify the understanding of some coiler's who ask
questions like:

"Will two stacked torroids have more capacitance than seperated ones?"
"Will an aluminum torroid have more capacitance than a copper one?" and
"How can a single isolated terminal have capacitance?"

I have wondered the same things because I often read about practical parts
from vendors, for the purpose of building projects, years before studying
the theory behind them in school.

First understand empty space (vacuum) has the ability to be stressed by an
electric potential or voltage, in a positive or negative direction. A
2-dimensional metaphor is a rubber sheet, warped into a pit or peak by a
heavy mass above or an upward force from below.

The fundamental property that warps space electricaly is charge. Electrons
and protons have charge. It takes more charge to electricaly warp a larger
space to a given voltage, than a smaller one. The more charge in a smaller
area, the higher the voltage or potential, and the more energy density.

Charge = capacitance * voltage, or Q=CV.
Energy = 1/2 capacitance * voltage^2 (voltage^2 means voltage squared).

Think about the amount of force it takes to warp the sheet, with different
shaped tools. The distance the sheet is warped is analagous to voltage. The
area of the tool used on the sheet determines how the force is applied and
how much energy is stored in the sheet's strain. A large area tool will
require more effort (work or energy) to displace the sheet than a small one.
Analagously, it has more capacitance.

If two tools, or an irregularly shaped tool is used to warp the sheet, the
impression by the tools in the sheet will blur as distance from the sheet
increases. Capacitance is charge storage capacity (like a compressed air
bottle or spring) and surface area does not directly correlate to
capacitance or stored charge.

Field mapping can be used to plot the direction of the electric field and
the amount of strain. Imagine grid lines on the rubber sheet. Poke the sheet
with a tool, and watch the sheet, and its grid, warp. The direction the
lines now take plot the electric field's voltage gradient (slope). The
seperation of the lines determine the energy storage for a given area.
Knowing the shape of a terminal, tells you the nature of the field it
produces, and averaging the strains over the whole surface (inegrating) can
give you capacitance.

It doesn't matter what the tool is made of: aluminum, brass, iron. But it
does matter what the "space" is made of. If you increase the thickness or
stiffness of the rubber sheet in the mechanical analog, it will take more
average force or energy to move it to the same potential as a thinner or
looser rubber sheet.

Since molecules are made of charged particles, they, depending on molecular
structure, will be more 'springy' than empty space. In fact if you take a
material such as aluminum, electro-chemicaly treat it to increase its
surface area, and form an insulating dielectric, it can have 1000's of times
more capacitance than empty space.
A wonderfull tutorial about this is on the net. Do a web search for
"Faraday-net" and electrolytic capacitors.

Hopefully, this has been instructive, and will motivate those lurking Tesla
God's to answer my lame queries in the future, which seldom elicit a
responce. If I have mistated facts, or you can explain this topic more
succinctly, please correct me and do it!

```