Scientific Teaching, Analysis and Research
If you need to brush up on this area of physics then any high school physic book will do. Just study the chapter that talks about the motion of a charged particle through an electric field. The science and the math are simple.
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One last thought. You have to wonder why this kind of research hasn't been done in more detail in the past. The potential results are staggering. (It's like reducing the price of a new automobile to 20 dollars.) The people at NASA and like places are not dummies. The idea of "field manipulation" for flight has been around for a long time. It seems that if it were possible to do it that someone would have done it by now. But how many people knew that the Earth had it's own natural electric field? I wasn't taught that in school. I suspect that very few (if any) people were.
If this is an area of overlooked science, then the opportunity for a new Thomas Edison or set of Wright Brothers exists. The idea of powered flight had been around for a long time before the Wright Brothers. All it took for them was to invent the idea of the right airfoil (when every scientist knew that it was impossible). They had the idea, and the math ... With simple methods and skills they made it work.
The capacitor will fly. All that is needed to make it pratical is the right dielectric.
Incidently, if the thought has crossed your mind, "to steal this information and file for your own patent" then let me save you some time, efford and money. This information is unpatentable for at least two reasons. First, it is a work that has already been published to the public. Second, the capacitor has already been invented. For example, one company discovered a previously unknown property of an alloy that had already been invented. The patent was rejected because the origonal alloy already had the property (resistance to corrosion) albeit unknown. Another example, someone invented "a pencil shaped device" for cleaning finger nails. The patent was rejected because the pencil had already been invented. Although it was never intended for that use, that use was one of it's properties. See for yourself.
I wish to you, good science (keep notes), good skill, good safety and good luck.