### Static Electricity

Electricity has a very long history.  The Greek philosopher Thales of Miletus (640 - 546 B.C.) is sometimes credited with being the first person to notice that amber will pick up bits of dry grass or straw if it is rubbed with a cloth.  (Amber is a honey-colored mineral which is actually fossilized tree sap.)  Most of what we know about Thales was written down by Aristotle hundreds of years after Thale's death, so the story of his discovery is essentially hearsay.  Nonetheless, it proves that Greek philosophers were aware of the attractive properties of rubbed amber by at least 600 B.C.

Electrostatics in Daily Life

Static electricity is simply an excess (or deficit) of electrons.  When you say that something is "charged" with static electricity, all you are saying is that the number of electrons it contains does not equal the number of protons.  Electrons have a negative charge and normally "orbit" the positively-charged nuclei in atoms.  The positive charge in the nuclei cancels the negative charges of the electrons, and the material is electrically neutral.  Normally, materials remain electrically neutral since it takes energy to pull electrons away from an atom.  But for some materials, the action of rubbing them together can lead to a very small number of electrons jumping from one of the materials to the other.  The precise physics of how this happens is astonishingly complex - it involves intimidating quantum mechanical mathematics way outside the scope of this discussion - so suffice to say that it does happen.  Materials that can lose (or gain) electrons in this way are called triboelectric.

When triboelectric materials are rubbed together, the material which the electrons are jumping from ends up with too few electrons and therefore a positive charge, and the material the electrons are jumping to ends up with too many electrons and therefore a negative charge.  This is what we call "static electricity", and the attraction between the positive and negative charges is exactly what causes static cling in a clothes dryer.  Unless you live in a place where the weather is extremely humid the year round, static electricity is much more familiar to you than it was to the ancients.  Greek philosophers had to search for exotic materials like fossilized tree sap to generate static electricity, but all you have to do is walk across the carpet.  This is because complex organic materials such as plastics, nylon, rubber, and paper tend to gain and hold static electric electricity rather easily, and our homes are filled with these, unlike the homes of the ancient Greeks.

The excess electrons that create static electricity are not bound to any particular atomic nucleus.  Rather, they cling to the material's surface somewhat like an oil film on a piston.  These excess electrons have a tendency to stay put once they're in place, which is where we get the term static (i.e., unchanging) electricity.  Static electricity is not really static, however.  If you bring a positively charged object close to a negatively charged one, the electrons will begin streaming to the positively charged object, neutralizing the static charge.  Streams of such electrons are essentially microscopic lightning bolts, and they give off light and noise just like their larger cousins.  (Pull apart some crackly, static-clinging socks in a dark closet, and you'll be amazed at the light that comes off.)

Static electricity is "static" in different ways for insulators and conductors.  Insulators are materials such as rubber, cloth, glass, plastic, or wood which do not allow electrons to move freely through them.  Conductors, which are virtually always metals, are materials that do allow electrons to move freely.  The English scientist Stephen Gray (1695 - 1736) is thought to be the first person to notice this distinction.  Gray concluded that insulators were materials such as silk or glass that could hold a static electric charge but could not conduct it from place to place, whereas conductors were materials such as metal or water which could not hold a static charge, but did conduct it.

Gray was partly correct, but he had made a subtle mistake.  He was correct in noticing that insulating objects such as a glass ball can hold a static charge if they are simply touched by something charged (because the electrons cannot move across the glass surface once they are put on it), whereas a conducting metal ball setting on a table will instantly lose its charge.  But he was incorrect in assuming that conductors cannot hold a charge at all.  If you want to place a static charge on a conductor, the conductor must first be separated from the rest of the world by an insulator, such as a rubber pad.  Otherwise, any excess electrons you put on the conductor will instantly run through it and into the Earth, analogous to water running through a sieve.  Charles Du Fay (1698 - 1739), working in Paris in 1734, was the first person to correctly point this out.

On an isolated conductor, where the electrons of a static charge are cut off from the Earth but can still freely move, the electrons instantly rush all over the conductor's surface, evenly coating it as they try to move as far apart as possible.  Then they become static.  There is nothing mysterious about this:  like charges repel, so the electrons repel each other.  They only come to rest after they have completely filled the space available to them.

We humans are mostly water, so we are fairly good conductors of electricity.  However, we often wear shoes that are very good insulators, and this puts an electric barrier between us and the Earth.  It is fairly easy for us to acquire a static electric charge, exactly like a conducting ball placed on an insulating stand, as we walk about and rub against chairs, carpets, and the like.  And since we are conductors, the charge on us is free to move if we touch another conductor that is "grounded" (i.e., connected to the Earth), and thus all the static electricity we have on us can zip away in a single burst, producing a spark that can be downright painful.

Such sparks can be dangerous.  Static electricity is one of the leading causes of accidental explosions in fireworks factories and other places where there are large quantities of highly flammable materials.  The entrances to such factories are normally equipped with grounded copper plates that all personnel must touch before they enter.  This ensures that they are free of any static electricity which might cause an explosion.

Electrostatics on a Large Scale

Beginning in the mid-1600's, inventors began constructing electrostatic machines that could generate and hold far larger charges than can be produced by rubbing a piece of amber, or tossing around socks in a dryer.  The first electrostatic machine we know of was built in 1660 in Magdeburg, Germany, by Otto von Guericke, the same gentleman who proved that teams of horses cannot put apart an evacuated sphere.  Early electrostatic machines had various designs, but they all worked on the same principle.  A rotating wheel or cylinder made of glass, sulfur, or some other insulating material was electrified by continuous friction with an agent such as cloth or fur.  Using these machines, electrostatic sparks several centimeters long could be generated.

An important development occurred in 1745, in Leyden, Holland, when Pieter van Musschenbroch invented what came to be known as the Leyden jar.  A Leyden jar is a glass jar partly coated inside and out with metal foil, an arrangement which allows it to hold onto a large static electric charge.  By connecting two Leyden jars to an electrostatic machine (one to hold the negative charge and one to hold the positive), one can build up a very substantial amount of static electricity - to the point where it can be dangerous.  My high-school physics teacher once placed the contacts for two Leyden jars that were part of a hand-cranked electrostatic machine a bit too far apart, and when the 15-cm spark finally jumped from one of the Leyden jars, it jumped to his hand rather than to the other Leyden jar.  It was nearly twenty minutes before he could move his arm again.

Building ever-more-massive electrostatic machines to see how big a spark you could make became something of a fad in the mid-18th century.  In America, Benjamin Franklin amused himself by electrocuting turkeys bound for his dinner table rather than throttling them.  In 1750, French physicist Abbe Nollet arranged a demonstration for the King of Paris in which more than one thousand Carthusian monks were told to hold hands in a circle 900 feet across.  When a massive Leyden jar was discharged into the monks, Nollet noted that all the monks jumped into the air at the same time, thus proving that the speed of an electric discharge is instantaneous, or at least extremely high.

Nollet himself did not participate in the experiment.

The marked similarity between the white-hot, cracking sparks of the electrostatic machine on the one hand, and lightning bolts on the other, did not escape notice.  In June of 1752, the American diplomat, publisher, and scientist Benjamin Franklin decided to directly test whether or not lightning was a giant electric spark.  During a thunderstorm, Franklin and his son sent a kite aloft and used the string to the kite to charge up a Leyden jar.  This extremely dangerous experiment proved that the thundercloud was electrically charged, and therefore that lightning was an electric discharge.  Franklin proposed that buildings could be protected from lightning strikes by placing tall metal rods on the tops of the buildings, then connecting the rods to the ground.  Such an arrangement would harmlessly conduct any lightning past the building.  This idea - which worked beautifully - came during the full flower of the French Enlightenment, and was hailed in Europe as the epitome of rational man triumphing over nature.

Franklin performed many electrostatic experiments, but it is his theoretical ideas about electricity which have turned out to have the most lasting influence.  It is to Franklin that we owe the designations "positive" and "negative" for electric charge, and it was Franklin who first performed experiments demonstrating that the amount of negative charge accumulated on a rubbed object is exactly equal to the positive charge accumulated on the rubbing object.  In other words, it was Franklin who first began to glimpse the concept of conservation of charge.  Conservation of charge is an easy concept to grasp if you believe in indivisible particles carrying irreducible units of mass, charge, and other quantities.  In Franklin's time, however - when everything from electric charge to heat was thought to consist of mysterious fluids and atoms were not even an accepted idea - the concept that the positive and negative charges generated by an electrostatic machine must always be equal represented a major advance.

In 1753 Franklin was awarded the Copley Medal, England's greatest scientific prize, by the Royal Society of London.  Years later, during the American Revolution, it was Franklin's considerable fame as a scientist which opened diplomatic doors to him that would otherwise have been closed to an unofficial ambassador from an unimportant country far from Europe.

Lightning

Lightning and thunder are created by the same physical processes that make your laundry crackle.  It is only the scale of the electrical discharge which distinguishes a lightning bolt from garden-variety static electricity.  In a thunderstorm, circulating air currents replace the rotating wheels of the electrostatic machine, and tiny droplets of ice and water replace the Leyden jar.  Water droplets (and water vapor) have a marked tendency to acquire electric charge, which is why static electricity is much less noticeable in a humid climate:  the water vapor conducts it away.  During a thunderstorm, the water droplets and ice crystals on the bottom side of a thunder cloud steadily become more negatively charged as the air circulates, and this leaves the ground immediately below very positively charged.

Air is a very poor conductor of electricity, so for some time the gathering charge just continues to accumulate in the clouds.  But sooner or later the attractive force becomes too great, and an invisible, charged column of electrons begins to force its way downward through the air, seeking the shortest path to the ground.  As the column approaches the ground, the intense build-up of static electric charge in the immediate vicinity can cause any people standing there to sense "prickliness" or "electricity in the air".  If the charge becomes great enough, people's hair can stand on end, because each strand has become identically charged and therefore is being repelled from the others.

Eventually, the charged column of electrons descends enough to make contact with the highest point in the vicinity - and the result is an electrical dam bursting.  In one titanic stroke, all the accumulated electric charge comes roaring down the column, and a lightning bolt strikes the ground.  The lightning bolt simply follows the path of least resistance, which means that it will strike high objects before it strikes low ones, and will move through good conductors (such as metals or something soaked with water) if it can.

Lightning Safety

If you should be outside during a storm, and find your hair standing on end, you must move immediately to safety.  The human body is a fairly good conductor and can attract lightning strokes; even more unfortunately, the part of the human body which conducts electricity best is the nervous system.  Even a nearby lightning strike that does not result in death for a human can cause permanent paralysis or other neurological damage, due to electricity running through the nervous system.

To find a spot safe from lightning, the first rule is, get inside if you possibly can.  A person inside a metal object such as a car is perfectly safe from the effects of a lightning bolt, because electricity can only run down the outside of a conductor.  The same repulsive force that makes static electric charge on a conductor spread out as far as possible also insures that a current of electrons is always forced away from the center of any conducting object.

The second rule of lightning safety is, stay away from tall objects.  A tragic number of lightning-relating injuries occur every year on golf courses, when people who have been caught out in the rain try to escape it by standing beneath trees.  This is a very bad idea.  A rain-soaked, isolated tree standing in the middle of a flat space such as a golf course is little more than a lightning rod with leaves.  It is far better to get wet than to stand under a tree in a thunder storm.

The dazzling flash of a lightning bolt is created by the high-energy electron stream as it collides with atoms in the atmosphere.  Since we have already said that air is a good insulator - which means that it will not conduct electrons - you may well wonder how it is that a stream of electrons can move through the air at all.

The answer is that air, like all insulators, can only stop the motion of electrons up to a point.  If the electric force across an insulator becomes great enough, then it can exceed the force which binds the electrons to their respective molecules, and the molecules are literally ripped apart as their nuclei go one direction and some of their electrons go another.  This is known as insulator break-down, and it happens whenever a stream of electrons rips a conducting path through an insulator.  It is easy to see the disruptive effect of an electric discharge on an insulator if you have electrostatic machine.  Just hold a piece of paper between the electrodes while you generate a few sparks, then hold the paper up to the light.  You will see that it is now perforated by tiny pinholes - one for each spark.

The intense burst of light created by lightning is caused as the electrons and disrupted molecules of the air repeatedly separate and recombine.  (Why this creates light will be dealt with later in the course.)  Super-heated air, rushing outward from the inner, white-hot zone of the lightning, creates the rumbling of the thunder - or, on a smaller scale, the crackle in your laundry.

Coulomb's Law

The first quantitative study of electrostatic force was carried out in 1785 by Charles Coulomb (1726 - 1806) in Paris, France.  Coulomb invented a torsion balance in which the essential feature was a thin rod, carrying equal masses at either end, that was balanced from a delicate wire.  If the slightest rotational force was placed on the rod, it would rotate until the torsion in the twisting wire just balanced the rotational force.  By measuring the angle of rotation, Coulomb could then accurately measure the rotational force.  Coulomb placed his torsion balance in a glass chamber to ward off air currents, and also placed a stationary ball in the chamber.  By putting electric charges on the stationary ball and a ball on the balance rod, then measuring how far the balance rod had twisted, Coulomb was able to demonstrate that electric charges obey the force law:

F  =  k q1 q2 / r 2        (Coulomb's Law)

where:  k (electrostatic constant)  =  8.99 X 109 N m2 / C2,   q1 and q2 are the two charges,   r  =  distance between the charges.

Charge in the metric system is measured in coulombs, and has the abbreviation C -- not to be confused with °C for degrees centigrade!  A coulomb of charge is related to the charge of the electron (or the proton) by the formula:  e (charge of the electron)  =  1.60 X 10-19 coulomb, which means 1 coulomb = the charge on 6.24 X 1018 electrons (or protons).

The similarity between Coulomb's Law and Newton's Law of Gravitation is obvious.  Both decrease with distance as r2, and both depend directly on the charge (or mass) of the two objects exerting force on each other.  The gravitational constant G is just replaced by the electrostatic constant k.  This similarity is partly because the same geometric arguments as given on the Isaac Newton page for gravity also apply to Coulomb's Law.  That is, one can think of electric force as "radiating" from a point charge in much the same way as light radiates from a light bulb.

Charge Excess On A Piece Of Paper

The electrostatic force between electrons and protons is enormously greater than the gravitational force between them.  This means that it takes surprisingly little excess charge to create static electricity, or to put it more mathematically, the relative number of electrons that move between electrostatically charged objects is extremely small compared to the total number of electrons they contain.  We can see this by estimating how much excess charge has to be transferred to a 1-gram bit of paper from a plastic comb, in order for the comb to lift the paper electrostatically.

The gravitational force pulling on the paper is just:  F = mg = (0.001 kg)(9.8 m/s2) = 9.8 X 10-3 N.

The electrostatic force between the comb and the bit of paper must at least equal the gravitational force, so:

F = mg = 9.8 X 10-3 N = k q1q2 / r2, where k = 9 X 109 N m2/C2

From conservation of charge, we know that the negative charge transferred to the paper must equal the positive charge left on the comb, so we know q1 = q2 which means q1q2 = q2, where q is the unknown charge we're looking for.

Strictly speaking, the distance r in the electrostatic formula is only valid if the charges are point charges.  However, for an estimate, we can approximate r by assuming it to be the distance between the centers of the two objects.  In this case, assuming r = 1 cm will be adequate for our purposes.

Substituting in the numbers, we have:  9.8 X 10-3 N = (9 X 109 N m2/C2) q2 / (0.01 m)2,
or q = [(0.01 m)2 X (9.8 X 10-3 N) / (9 X 109 N m2/C2)]1/2 = 1 X 10-8 C

The charge on a single electron is 1.6 X 10-19 C, so the total number of electrons transferred is:  (1 X 10-8 C) / (1.6 X 10-19 C) = 6.3 X 1010 electrons transferred.

This may seem like an enormous number, but consider how many electrons there are in a 1-gm bit of paper.  Roughly speaking, ordinary matter consists of ½ protons and ½ neutrons.  (We can neglect the mass of the electrons.)  So, the total number of protons in a 1-gm bit of paper is roughly:

# of protons = ½ (0.001 kg)/(mass of proton) = (5 X 10-4 kg)/(1.7 X 10-27 kg) = 3 X 1023

The number of electrons in electrically neutral matter must be equal to the number of protons, so the fractional number of electrons which have been transferred to our bit of paper as static electricity is:  6.3 X 1010 / 3 X 1023 = 2 X 10-13.

This fraction is incredibly small.  It is about the same as comparing one dollar to the entire U.S.  economy.  And yet, this insignificant fraction of excess electric charge is more than enough to lift the bit of paper against the gravitational pull of the entire Earth.

Voltage and Amperage

An electric current is simply a flow of electrons, and an electric spark is simply a very brief (often rather unsteady) electric current.  The power of an electric current is characterized by two quantities you may already be familiar with:  voltage and amperage.  Visualizing an electric current as a (very swiftly moving) flow of electrons is a good way to see that it is similar to water flowing in a pipe.  Voltage is analogous to the water pressure, and amperage is analogous to how much water is flowing.  To give you an idea of typical values for these quantities, household current in the U.S.  runs at 120 volts, and a fairly heavy-duty appliance such as a space heater may draw up to 15 amps.  The power of an electric current is given by the simple formula:  electric power = volts X amps, or P = VI.  (Physicists always use I for electric current.)  So, a space heater drawing 15 amps at 120 volts is consuming (120 volts) X (15 amps) = 1800 watts.

It takes an astonishing 30,000 volts of electric "pressure" for a spark to traverse one centimeter of air -- this is a measure of how much force it takes to disrupt the air molecules so that they will conduct electricity.  Thus, you can see that even the modest sparks from an electrostatic machine can easily exceed 100,000 volts.  Such sparks have extremely low amperage, however, so although they may be painful if they should zap your finger, they are not especially dangerous because their power is very low.

A lightning bolt, on the other hand, may carry up to 20,000 amps at a billion volts.  It is the enormous voltage of lightning which gives it the ability to split trees, fuse sand into glass, and shatter stone.  It is only the fact that lightning bolts are very brief (and therefore do not transfer their terrific power for very long) that makes it possible for people to sometimes survive direct hits.

We can easily connect the macroscopic units of amps and volts to the microscopic world of moving charges.  One ampere of current is defined as an electron flow of one coulomb per second, i.e., one amp is equal to 6.24 X 1018 electrons moving past a point per second.  From the formula P = VI, we see that a volt is equal to a watt/amp, or:  1 volt = (joule/sec) / (coulomb/sec) = J/C = 1.6 X 10-19 J / electron.

In other words, voltage is a measure of the average kinetic energy per electron in a current.  (In this sense, voltage plays somewhat the same role for electrons that temperature plays for the atoms in a perfect gas.)  As a simple example, if we take ordinary household current operating at 120 volts, then the kinetic energy of an electron in the current is just:

120 volts X one electron = 120 X (1.6 X 10-19 J / e) X one electron = 1.92 X 10-17 joule

The quantity of energy 1.6 X 10-19 J is called an electron-volt by physicists (abbreviated eV), because it is equal to the kinetic energy of one electron which has been accelerated by a one-volt electric field.  This tiny unit of energy is not so useful to us now, but it will become very useful when we begin to examine the physics of the atom.

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