Levitation and propulsion in a electrostatic field

[Virtual Presenter] Good morning everyone. Today we will be discussing Earnshaw's Theorem. This theorem was formulated in 1842 by British mathematician Samuel Earnshaw and states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This theorem has important implications for areas such as levitation and propulsion. We'll be exploring this theorem and its applications in further detail throughout this presentation..

[Audio] Earnshaw's Theorem declares that a group of point charges cannot be held in a secure balanced arrangement just through the electrostatic collaboration of the charges. In spite of this this system constitutes an exemption to this theorem. Its exceptional capacity to self-control without the need of a P-I-D loop or some other feedback system is based on its utilization of ionization as a controlling force. This system is able of operation and maintain a stable equilibrium configuration only in ambient surroundings..

[Audio] Earnshaw's Theorem states that a collection of point charges can not achieve a stationary equilibrium configuration solely through electrostatic interaction forces. This theorem has inspired levitators which are able to fly without aerodynamics or visual propulsion. In addition to maintaining stability levitators can easily accelerate self-level and self-propel. At a lower voltage they can wobble and jump like an animal: I refer to the four ionizers as horses and the one ionizer as a chicken. With a higher voltage the levitator acts like a Russian soldier marching in a parade..

[Audio] Earnshaw's Theorem has had profound effects on many scientific disciplines particularly in the engineering of basic classic levitators. These levitators use the theorem to suspend an object in a state of balance utilizing electromagnetic fields. By creating fields of equal force to the object's the object can be kept afloat without any additional external forces..

[Audio] Earnshaw's theorem proposed in 1842 states that it is not feasible to have an arrangement of charges which remains in a stable equilibrium only due to the interaction of those charges. In order to challenge this theorem experts have invented a machine known as a levitator. This device is 14 microns thick and made of either aluminum or non-conductive material. By adjusting the positive and negative charges near it the levitator can maintain neutrality. When placed between two charged plates it has a negative charge which is partly compensated by an ionizer which prevents it from being pulled up to the upper plate. This serves to demonstrate that Earnshaw's theorem can be defied granting us with fresh insights into physics..

Forces on the Levitator. The electrostatic attraction force is up. The gravitational force is downwards. The ionic wind is up, or depended on the direction of the pointer(s)..

[Audio] Earnshaw's Theorem first proven in 1842 by British mathematician Samuel Earnshaw is a significant principle for comprehension the electrostatic interaction of point charges. The theorem states that a set of point charges cannot be held in a stationary steady equilibrium arrangement only by the electrostatic interaction of the charges. To comprehend this concept measurements must be taken. For a given trajectory the measurements should include a height of between 100-110 millimeters and a width of 60 millimeters. These measurements are crucial to recognizing Earnshaw's Theorem and how it is related to point charges..

[Audio] Earnshaw's Theorem states that it is not possible to maintain a stable equilibrium configuration of point charges solely with electrostatic interaction. To illustrate this one can look at the phenomenon of corona and ionization. Generally the light from the upper corona is brighter than the light from the lower ionizer and is more easily affected by the electrostatic interaction of the point charges which is used to demonstrate Earnshaw's Theorem..

[Audio] Earnshaw's Theorem was an important breakthrough in the history of mathematics as it was the first to prove that a collection of point charges cannot be sustained in a stationary equilibrium. This theorem has had a profound effect on modern technology specifically in the field of propulsion. In particular the ion thruster uses Earnshaw's theorem to achieve thrust. The same levitator that houses and holds the ions also tilt them at an angle of 22.5 degrees which causes them to be ejected from the side. This creates a sideways force that translates into a forward thrust propelling the levitator forward..

[Audio] Earnshaw's Theorem is an important result in electrostatics and has been used to understand how ions can be used to lift an object. Specifically it is necessary to place a counterweight on the same side of the direction of intended motion in order to achieve a net sideways displacement. This counterweight provides the necessary balancing force to keep the levitator in balance..

[Audio] To create a 'Chicken Levitator' a sample consisting of a chocolate paper with an aluminum foil coating and weight made out of Low-Density Polyethylene (L-D-P-E-) foam will be used. This levitator will be based on Earnshaw's Theorem which was proved in 1842 and states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges..

[Audio] Earnshaw conducted an experiment in 1842 using a single balsa wood levitator with a neon bulb affixed to it. This experiment helped him to prove his theorem which states that it is impossible for a collection of point charges to remain in a stable stationary equilibrium configuration solely through the electrostatic interaction of the charges..

[Audio] Earnshaw's Theorem first proven in 1842 by British mathematician Samuel Earnshaw states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. To maintain an object in equilibrium one of the solutions is the use of multi-collector and ionizers. An example of this is the Horse Levitator a 120 millimeters static levitator with multi-collector and ionizers. This device combines levitation and electrostatic forces as well as an array of magnets to achieve equilibrium of its subject..

[Audio] Samuel Earnshaw's theorem which was proven in 1842 states that a collection of point charges cannot be kept in a stable equilibrium configuration only through electrostatic interaction. This slide displays the power utilization concerning humidity for a 65 millimeters levitator that is seen on the lower part of the graph. Inputting 8.62 grams of power requires between 1.2 and 1.6 watts for every gram to bring about levitation. A 120 millimeters levitator on the contrary necessitates double the power at 2.62 grams. The graph indicates that between 48 and 53 percent humidity power consumption is at its minimum. Outside this range power consumption is not steady..

[Audio] Humidity can significantly impact electrical engineering as it can alter the behavior of electrical components. In a dry environment the air has a higher dielectric strength which allows high voltages to be applied without an electric discharge. On the contrary humidity lowers the air's dielectric strength leading to a lesser high voltage threshold..

[Audio] Earnshaw's theorem has a multitude of practical applications one of which is the utilization of levitation systems to lift items of considerable weight. By utilizing a number of levitators the system is able to generate more prominent lifting forces. Thus it is feasible to move and manage heavier objects than would be attainable without its use..

[Audio] Earnshaw's Theorem is an important concept in basic levitator design particularly when it comes to Weight to Power comparing. This table shows the Weight in Kg of the basic levitators on the left and the Power in Watts on the right as well as the Amount. As you can see the more the Weight the higher the Power must be. This table is a useful tool for levitation design..

[Audio] British mathematician Samuel Earnshaw proved Earnshaw's Theorem in 1842 which is an important principle in physics and engineering. This theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. With regards to design the system is designed with protections against shock and fire and has the lowest cost for levitation and propulsion when compared with other systems. It's power requirements are low making it ideal for battery operation. In terms of education Earnshaw's Theorem can be used to enhance learning of physics and to create interesting games or activities such as war games or speed racing. In terms of medical use the system may be able to treat psoriasis allergies and eliminate viruses and bacteria. It can also help with environmental improvement as its components can help filter and clean the air..

[Audio] Earnshaw's Theorem demonstrated by Samuel Earnshaw in 1842 is an important breakthrough in electromagnetic theory which states that a configuration of point charges cannot remain at rest or in a stable equilibrium if it is solely dependent on the electrostatic interaction of the charges. It has implications on levitation technology which has been tested to reach heights of 500 millimeters speeds of 4m/s and weights of 6 grams. Additionally it has even worked without a grounding plate when used on water or a wooden table though one may be necessary in some cases..

[Audio] Earnshaw's Theorem was created by British mathematician Samuel Earnshaw in 1842 and it states that a group of electric charges cannot stay in a stationary equilibrium through electrostatic interaction. To build a levitator one needs a high voltage power supply a mini digital scale with a resolution of 0.01 gram a humidity meter aluminum foil 0.5 millimeters nylon or .35 millimeters P-L-A LDPE packing materials contact glue and a 3D printed template for the levitator. These are the minimum requirements to get started..

[Audio] Exploring Earnshaw's Theorem and its applications for understanding electrostatic levitation and propulsion this presentation has provided a general overview on the concept. Hopefully this has enabled you to further your understanding in more detail. Thanks for listening..