Planar and Electrostatic

For other uses, see Planar graph.

For the corporation, see Planar Systems.

Something is called planar if it is made up of flat planes, or pertaining to planes. A graph is called planar if it can be drawn in the plane without any edge intersections; see planar graph.

In the context of computer graphics, Planar is method of representing pixel information with several bitplanes. There are also cases where byteplanes have been used. Each individual bit in a bitplane is related to a single pixel on the screen. Unlike Chunky, Highcolour or Truecolour graphics, the data for an individual pixel isn't in one specific location in RAM, but spread across the bitplanes that make up the display.

For example, on a Chunky display, each byte will represent one pixel. So, if colour zero is black, colour one is blue, and colour two is green, a byte of chunky pixel data would look like this:

00000000 = Black pixel
00000001 = Blue pixel
00000010 = Green pixel

Whereas planar data would look like this:

Plane 0, Byte 0: 00000000 = 8 black pixels
Plane 1, Byte 0: 00000000

Plane 0, Byte 0: 10000000 = 6 black pixels, one blue pixel, one green pixel
Plane 1, Byte 0: 00010000

Planar graphics were used a lot in the 80s and early 90s because displays tended to only be able to show fewer than 256 colours. Chunky displays always represent one pixel within a contigous grouping of bits. And usually have 1 byte or more per pixel, even with a colour depth not a multiple 8 bits (sometimes going as far as storing a 24 bit image in 32 bit chunks). This wastes RAM in cases where fewer bits are needed than are provided. If you only need to display 8 colours, you can use 3 bitplanes, and each pixel only has 3 bits assigned to it instead of 8 (reducing memory and bandwidth requirements by 62.5%).

Electrostatics is the branch of physics that deals with the forces exerted by a static (i.e. unchanging) electric field upon charged objects.

Overview

In electrostatics conditions of charge need not be 'static' and unchanging. Instead 'static' implies that the dynamic portion is being ignored, and we analyze frozen snapshots of the situation. In electrostatics we study e-fields, voltage, and charge but ignore any currents and magnetism which may also be present. Because of its relationship and interaction with magnetism, the two fields are often combined as electromagnetism.

The electrostatic approximation

The validity of the electrostatic approximation rests on the assumption that the electric field is irrotational:

From Faraday's law, this assumption implies the absence or near-absence of time-varying magnetic fields:

In other words, electrostatics does not require the absence of magnetic fields or electric currents. Rather, if magnetic fields or electric currents do exist, they must not change with time, or in the worst-case, they must change with time only very slowly.

Electrostatic potential

Because the electric field is irrotational, it is possible to express the electric field as the gradient of a scalar function, called the electrostatic potential (also known as the voltage). Thus, the electrostatic potential Φ is related to the electric field E by the equation:

Fundamental concepts

Coulomb's law

The fundamental equation of electrostatics is Coulomb's law, which describes the force between two point charges:

The Electric field

The electric field (in units of volts per meter) is defined as the force (in newtons) per unit charge (in coulombs). From this definition and Coulomb's law, it follows that the magnitude of the electric field E created by a single point charge Q is:

Gauss's law

Gauss' law states that "the total electric flux through a closed surface is proportional to the total electric charge enclosed within the surface." The constant of proportionality is the permittivity of free space.

Mathematically, Gauss's law takes the form of an integral equation:

Alternatively, in differential form, the equation becomes

Poisson's equation

The definition of electrostatic potential, combined with the differential form of Guass's law (above), provides a relationship between the potential Φ and the charge density ρ:

This relationship is a form of Poisson's equation.

Laplace's equation

In the absence of unpaired electric charge, the equation becomes

which is Laplace's equation.

Static Charge generation

Charge separation by contact

The presence of surface charge imbalance means that the objects will exhibit attractive or repulsive forces. This surface charge imbalance, which leads to static electricity, can be generated by touching two differing surfaces together and then separating them due to the phenomena of contact electrification and the triboelectric effect. Rubbing two non-conductive objects generates a great amount of static electricity. This is not just the result of friction; two non-conductive surfaces can become charged by just being placed one on top of the other. Since most surfaces have a rough texture, it takes longer to achieve charging through contact than through rubbing. Rubbing objects together increases amount of adhesive contact between the two surfaces. Usually insulators, i.e., substances that do not conduct electricity, are good at both generating, and holding, a surface charge. Some examples of these substances are rubber, plastic, glass, and pith. Conductive objects only rarely generate charge imbalance except, for example, when a metal surface is impacted by solid or liquid nonconductors. The charge that is transferred during contact electrification is stored on the surface of each object. Static electric generators, devices which produce very high voltage at very low current (such as the Van de Graaf generator or Wimshurst machine) and used for classroom physics demonstrations, rely on this effect. Note that the presence of electric current does not detract from the electrostatic forces nor from the sparking, from the corona discharge, or other phenomena. Both phenomena can exist simultaneously in the same system.

Triboelectric series

Main article: triboelectric effect

The triboelectric effect is a type of contact electrification in which certain materials become electrically charged when coming into contact with another, different, material, and are then separated. The polarity and strength of the charges produced differ according to the materials, surface roughness, temperature, strain, and other properties. It is therefore not very predictable, and only broad generalizations can be made. Amber, for example, can acquire an electric charge by friction with a material like wool. This property, first recorded by Thales of Miletus, suggested the word "electricity", from the Greek word for amber, ēlektron. Other examples of materials that can acquire a significant charge when rubbed together include glass rubbed with silk, and hard rubber rubbed with fur.

Electrostatic generators

Main article: Electrostatic generator

The presence of surface charge imbalance means that the objects will exhibit attractive or repulsive forces. This surface charge imbalance, which leads to static electricity, can be generated by touching two differing surfaces together and then separating them due to the phenomena of contact electrification and the triboelectric effect. Rubbing two non-conductive objects generates a great amount of static electricity. This is not just the result of friction; two non-conductive surfaces can become charged by just being placed one on top of the other. Since most surfaces have a rough texture, it takes longer to achieve charging through contact than through rubbing. Rubbing objects together increases amount of adhesive contact between the two surfaces. Usually insulators, e.g., substances that do not conduct electricity, are good at both generating, and holding, a surface charge. Some examples of these substances are rubber, plastic, glass, and pith. Conductive objects only rarely generate charge imbalance except, for example, when a metal surface is impacted by solid or liquid nonconductors. The charge that is transferred during contact electrification is stored on the surface of each object. Static electric generators, devices which produce very high voltage at very low current and used for classroom physics demonstrations, rely on this effect.

Note that the presence of electric current does not detract from the electrostatic forces nor from the sparking, from the corona discharge, or other phenomena. Both phenomena can exist simultaneously in the same system.

See also: Friction machines, Wimshurst machine, and Van de Graaf generators.

Charge neutralisation

Natural electrostatic phenomena are most familiar as an occasional annoyance in seasons of low humidity, but can be destructive and harmful in some situations (e.g. electronics manufacturing.) When working in direct contact with integrated circuit electronics (especially delicate MOSFETs), or in the presence of flammable gas, care must be taken to avoid accumulating and discharging a static charge.

'Static' electricity

Static can be a serious nuisance in the processing of analog recording media, because it can attract dust to sensitive materials. In the case of photography, dust accumulating on lenses and photographic plates degrades the resulting picture. Dust also permanently damages vinyl records because it can be embedded into the grooves as the stylus passes over. In both cases, several approaches exist to combat such dust deposition. Some brushes, particularly those with carbon fiber bristles, are advertised as possessing anti-static properties. Also available are handheld static guns which shoot streams of ions to discharge static on records and lenses. Static electricity is a class of phenomena involving objects with a net charge; typically referring to charged objects with voltages of sufficient magnitude to produce visible attraction, repulsion, and sparks.

Natural electrostatic phenomena are most familiar as an occasional annoyance in seasons of low humidity, but can be destructive and harmful in some situations (e.g. electronics manufacturing.) When working in direct contact with integrated circuit electronics (especially delicate MOSFETs), or in the presence of flammable gas, care must be taken to avoid accumulating and discharging a static charge (see electrostatic discharge).

Note that the presence of electric current does not detract from the electrostatic forces nor from the sparking, from the corona discharge, or other phenomena. Both phenomena can exist simultaneously in the same system.

Static electricity is an important element in the biological process of pollination by bees, since the charge on a bee's body helps to hold pollens to it.

See also

General

• Electromagnetism
• Electrostatic force
• Ionic bond

Electronics

• Electroscope
• Wimshurst machine
• Van de Graaff generator
• First photoconductive copy
• List of electronics topics

Natural

• Triboelectric effect
• Bioelectricity
• Pith
• Cumulonimbus clouds (and Relative humidity)
• Lightning
• Chemical Solutions
• Examples of electrical phenomena

Historical

• Luigi Galvani
• Pseudodoxia Epidemica

Other

• Static

References

• Halliday, David; Robert Resnick; Kenneth S. Krane (1992). Physics, New York: John Wiley & Sons. ISBN 0-471-80457-6.
• Griffiths, David J. (1999). Introduction to Electrodynamics, Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-805326-X.
• Hermann A. Haus and James R. Melcher (1989). Electromagnetic Fields and Energy, Englewood Cliffs, NJ: Prentice-Hall. ISBN 0-13-249020-X.

External links and further reading

General

• RMCybernetics - High Voltage Physics Homemade projects & experiments.
• "Man's static jacket sparks alert". BBC News, 16 September 2005.
• "Static electricity cause effects and solutions" ElectroStatics, Inc.

Essays and books

• William J. Beaty, "Humans and sparks; The Cause, Stopping the Pain, and 'Electric People'". 1997.
• Dampier, William Cecil, "The theory of experimental electricity". Cambridge [Eng.] University press, 1905 (Cambridge physical series). xi, 334 p. illus., diagrs. 23 cm. LCCN 05040419 //r33