Research website of Vyacheslav Gorchilin
2019-07-21
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Electrostatic condenser
Still the name of the condenser has only been applied in games like "World of Warcraft" to refer to the armor high level players, though more would he have approached a branch of physics — Electrostatics. In this article we will return to it "former glory", define its properties, and even calculate it generator. We will focus on the electrostatic condenser, which is a mixture of regular and private capacity. A Tesla capacitor was called a condenser in the schemes meant for special.
All we know about the capacitor?
At the intersection of different branches of physics there are a number of phenomena that cannot be explained separately. Electrostatic condenser just appears at this junction: electrostatics and electrodynamics. In the case of direct currents, its parameters can be explained by electrostatics, but if such a capacitor is included in the dynamic chain, its new properties will fail to be interpreted only by electrodynamics.
Look at a typical docholliday capacitor (Fig. 1a). Ideally, it has two conductive plates and dielectric between them. Educated thus the capacity \(Cs\) we consider as the nominal value of the capacitor and take it to calculate electrical circuits. But really, any condenser, in the most General form, is a collection of classic electric and a minimum of two solitary vessels (Fig. 1b). Such a generalized capacity we will call the electrostatic capacitor (ESC).
Fig.1. The difference between conventional and electrostatic condenser. Their types.
In this figure, \(C_1\) and \(C_2\) are solitary capacity, which form two capacitor between the plates is \(Cs\) and Ground. Only from here we can assume that in the actual circuit design should be considered two reference systems: relative, which is studied in electronic Universities and semi-absolute in which the conditional absolute is the capacity and charge of our planet.

A solitary container in the most General terms, should be regarded as dooblydoo, the second lining which represents the totality of all the surrounding planets and galaxies. In this sense, the Earth itself is an isolated capacity. But if secluded capacity of the first electrode is small compared to an isolated capacity of the entire planet, with sufficient accuracy can be considered a second electrode grounded, the resistance of which tends to zero.

Figure (1c) presents a special case of ESCOs in the form of two folded into each other spheres. This same drawing is also suitable for another variant of ESK — nested into each other tubes in the form of coax. Figure 1d is more simple for the execution of the HSC in the form of several plates. By the way, in a similar way, Tesla was portrayed condensers on their schemes.
Algorithm of inclusion of ESK
We will further consider only such of ESK, where \(C_1\) and \(C_2\) are comparable in order with \(Cs\) (Fig. 1b). In this case, it is necessary to consider how the electrodynamic and electrostatic effects. Electrodynamic — boil down to the fact that due to the bias currents, the capacitor is \(Cs\) holds through the current with a certain time delay. This process is fairly well understood in TBE [1] and in this work he will also participate in this point of view. Electrostatic same class of effects is somewhat broader. The first thing that becomes immediately obvious: \(C_1\) and \(C_2\) are also involved in the processes of charge-discharge than can significantly affect the parameters of the entire scheme. Second, and most important effect, which is also involved in the overall process, called electrostatic induction method of targeting charges. Clearly it is shown in [2,3], and we only see some details.
Fig.2. The algorithm incorporating the electrostatic condenser.
Suppose we have a DC voltage source U, two keys SW1 and SW2, ESK and load resistance r2. Figure (2) presents an algorithm for inclusion of ESK, divided into 4 cycles. The first stroke (Fig. 1a) the switch SW1 is open and no processes occurs. In the second (Fig. 1b) — this switch is closed, and the left on the diagram plate ESK serves some potential from the DC voltage source U. Here occurs from two processes: through the bias currents of the resistance r2 is fed portion of the energy from this source (current I2) and the charged electrode ESCs due to the presence of solitary vessels \(C_1\) and \(C_2\). Moreover, the positive part of the charge on the right electrode ESK flows into the load, together with I2, and negative — remains on its inner side. In the third step (Fig. 1c) the switch SW1 is opened and SW2 connects r2 to the left side of ESK, than creates the current through the load. At the same time, remaining on the right side a negative charge spreads across the surface. This charge we also let through the load in the fourth stroke (Fig. 1d). Thus, once charging plate, we double remove from their charge.
Part of the energy that enters the load in the second cycle, well described in theoretical electrical engineering [1], we next consider the electrostatic phenomenon of a quasi-absolute reference system. Rate the electric charge remaining on the plates. Obviously it will be equal to the supply voltage multiplied by the magnitude of the secluded capacity \(C_1\): \[q_1 = C_1\,U \qquad (1.1)\] the same charge and will be on the second plate in the third beat, but because the solitary receptacle of the second plate may vary, the voltage on it proportional to change: \[U_2 = q_1 / C_2 = U \frac{C_1}{C_2} \qquad (1.2)\] This formula is useful to us in the future. At this stage it becomes clear that to achieve maximum energy efficiency, the difference between \(C_1\) and \(C_2\) must be small. But this formula shows only the ratio of voltages on the module. We must not forget that \(U_2\) is shifted relative to \(U\) at 90 degrees: when \(U\) a maximum positive charge, then \(U_2\) is zero when \(U\) is zero, then \(U_2\) is a negative minimum. This important moment, we also need in the calculation of more realistic schemes.
It can be shown that to increase the efficiency of the second kind the scheme (Fig. 2) cardinal will not work, despite the fact that the charge here is used twice. Visitors can see the calculations in the Appendix to MathCAD, where it is assumed that the energy supplied by the ESC, and then removed from all tanks by the algorithm (Fig. 2). The same result gives a circuit with a stationary process. The conclusion that can definitely be done from a mathematical and from a physical point of view is this: for more efficient use of ESCs in the scheme of its inclusion requires the use of inductors, which could accumulate charge, and then give it to this same circuit with a certain delay. In this scheme we are going to do in the second part of this work.
 
The materials used
  1. Wikipedia. Theoretical foundations of electrical engineering.
  2. YouTube. Physics. Experiments on electrostatics.
  3. YouTube. NRNU MEPHI. Electrostatic induction.