^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

The asymmetric capacitor’s lift force formula can be obtained on the basis of literature review, which can almost cover all practical forms of asymmetric capacity forms. But there are still some problems we should solve. The first and foremost one is whether the formulas are correct and can they be verified in engineering practices? On the contrary, the parameter

How can we solve lift force produced by a lifter formed of an asymmetric capacitor? Based on some hypothetical conditions, a formula was obtained through three methods in an ideal scenario [

In former papers [

An unknown variable

Nevertheless, the analysis of hypothetical predetermined conditions verifies that the capacitance

Regarding the reason why the experimental result is more precise than expected, the analysis of the unique characteristics of the asymmetric capacitor has presented several objective reasons: (1) the distance

Under the initial condition, we begin to deduce capacitance of the asymmetric capacitor [

For

Equations (

where

Because the distance

For a thin wire small plate capacitor, we can take

where

Because

referring to equation (

Mainly considering the electric field variation beside the thin wire, we have

Considering the effective fan-shaped part, we have

Integrating both sides of equation (

So we get the capacitance

For a spherical small plate capacitor, we can take

Combining equation (

Referring to equation (

Integrating both sides, we obtain

For the distance

So we get the capacitance

We can calculate the electric lift force of asymmetric capacitor loaded by high voltage with the capacitance

For thin wire small plate capacitor, using equation (

This is the lift force formula about a normal lifter in thin wire asymmetric capacitor form under high voltage loaded.

For spherical small plate capacitor, using equation (

Considering the condition

If simplifying calculation as a spherical plate, the surface area of plate 1

This is the concised formula that finally turned out, from which we can tell the maximum lift force produced by spherical asymmetric capacitor under high voltage loaded.

The formulas are exerted on two applications to test their validity. They are, respectively, lift force estimation of a electricity lifter [

When a lifter loads with high voltage (Figure

A lifter flying up loaded with high-voltage power.

An asymmetric capacitor in lifter form.

On the initial conditions, using equation (

That is to say, a lifter loaded with 30 kV voltage can produce a largest lift force of 11.7 gf.

As we know, when a high voltage loads on human body, our hair may be lifted up by the static electricity [

Voltage loaded on the head

When the voltage is loaded on the hair under the above initial conditions, what is the maximum length of the hair (

In this case, the head and ground can be considered as the two plates of asymmetric, where the head may be regarded as a small plate and its area of sphere surface is

The sum of the electrostatic lift force acted on the hair is

The surface area of the head is

The intensity of pressure supported by electrostatic force is

The average transverse area of a hair is

Head surface area occupied by a hair can support a mass by the electrostatic force:

The mass is converted into length of a hair:

Therefore, the final result is obtained: when human being’s hair is loaded by high-voltage static electricity of DC 100 kV through a conducting metallic ball, approximately 29 cm length hair floats up into air.

Based on some assumptions with simplified calculation, we derived lift force formula produced by an asymmetric capacitor in different conditions, with which the assess in certain survey and qualitative research can be undertaken in spite of unsatisfying precision. The method also provides a convenient way to calculate static electricity lift capacity produced by an asymmetric capacitor or lift force of lifters. It also contributes to the parameter optimization in designing [

The data used to support the findings of this study are included within the article.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors gratefully acknowledge the support of the Thirteenth Five-Year Plan of Hefei Institute of Physical Science of Chinese Academy of Science (Grant no. Y86CT21051, “Electric and Magnetic Propulsion System”), Research Activity Funding of Postdoctoral Fellow of Anhui Province (Grant no. 2018B250, “High-Energy Ions Accelerated Thruster”), and Natural Science Research Project of Anhui Education Department (Grant no. KJ2018A0725, “The Uniformity Optimization and Software Development for MRI Magnets”). A portion of this work was supported by the High Magnetic Field Laboratory of Anhui Province.