www.lsmsa.edu teacher Robert Dalling's Physics Lectures (see also www.ushumans.net)
The Electrical Charge and Force
There are two types of electrical charge, and they occur in discrete packets that are multiples of the charges found on protons and electrons. In the year 1747, Ben Franklin used the terms positive and negative to describe these two charge types: a proton has a positive charge while electrons carry negative charge. (For biographical information about Franklin, see PBS or here and here, which includes a video of lightning striking his kite.) Charge quantities are measured in Coulombs, in honor of Charles Coulomb. In the year 1785, he found that the force between two charges is described by the equation F = kq1q2/r2. This is known as Coulomb’s Law, where the constant k = 9x109 Nm2/C2. Protons and electrons carry the same amount of charge, denoted by e = 1.6x10-19 Coulomb, but their charges are given opposite arithmetic signs. About 6x1018 electrons have a combined charge of one Coulomb. We all remember from grade school that like charges repel and unlike charges attract. In the coming chapters, we will see that charge is never created or destroyed: its total is conserved in any process.
We have all experienced slight electrical shocks when petting a cat or touching metal objects on a dry day. Static electricity accumulates during the frictional scraping of two objects past each other. When you move a comb through your hair, the comb scrapes negatively charged electrons from your hair which is then left with an excess positive charge. This scraping process sometimes occurs on the prairie as electrically charged sand is blown by the wind across the long wires of a fence, giving a shock to unsuspecting animals who later touch them. Wind-blown snow can also become charged through frictional scraping. Thunderclouds may become charged through the frictional rubbing of ice and water within turbulent currents. Charge separation occurs during the splashing of water that generates both large and small drops, each of which become oppositely charged in an incompletely understood process. Moving sugar, flour, grain, paper, yarn, plastic, or any other product through long pipes or past metal can cause sufficient static build up to cause an explosion. Static electricity provides the cling in clear plastic food wrap, makes balloons and metal bottle-caps stick to walls, and makes clothes stick together as they are taken out of the dryer. (The student might want to identify the scraping process in each of these situations.) Near the toll booth on the highway, metal bands have been placed in the road to collect static charge from vehicles. In an electrostatic spray gun, paint particles are given an electrical charge and then propelled toward an oppositely charged target, resulting in less paint lost to the surroundings. Paint particles are also electrically attracted to the back side of the target that is facing away from the sprayer. Water and salts are electrostatically removed from crude oil before it is refined.
Since frictional rubbing occurs as air and water moves past a boat, boats can become electrically charged. In recent centuries, sailors experienced a particularly impressive version of static electricity as the so-called St. Elmo’s fire was emitted from the tips of the ship’s wooden masts. What do you suppose a sixteenth-century sailor would imagine to be the cause of lighting being emitted from masts while sailing in a particular location for a particular reason? The build up of static charge has caused explosions on oil tankers. Airplanes become charged when moving through dust, sleet, snow, or charged clouds.
An electrical charge can be “induced” in an object by placing it near or touching it with charged object. When a neutrally charged block is undisturbed, it consists of little packets–its atoms–of equal amounts of positive and negative charge. When an exterior positive charge is held near the block, the block's positive charges are slightly repelled while its negative charges are slightly attracted toward that exterior charge. This makes a slight separation between the positive and negative charges within the block. The near side of the block is then slightly negative, while the far side is slightly positive. The result is that the neutrally charged block is slightly attracted toward the exterior charge, as shown here.
Demonstration:
There are a variety of static electricity demonstrations. Static electricity is shown in videos and animations by WFU, NCSU (scroll down until you see numbers in the 50s on the left), FAU, UMN, Phet, John Travoltage, Rutgers, Judson Wagner, the Physical Universe, Rochester, and the Physics Classroom 2 3. Here is an electrostatic chime.
Demonstration:
Have someone hold a charging Van de Graf generator to acquire enough static electricity to make his or her hair stand on end.
Student:
The Exploratorium has some electrostatic experiments to try using objects available at home.
Beginning in the seventeenth century, scientists began accumulating and storing static electricity in devices like Leyden jars (see here and here). Ben Franklin made a large Leyden jar whose static discharge once knocked him unconscious and might “kill a large turkey.” At the time, dangerous “circle shocks” were in fashion in which a group of persons held hands, touched a Leyden jar, and transmitted an electric spark from person to person.
Static electricity is used in hundreds of machines today, including xerox machines, ink-jet printers, and electrostatic precipitators that collect pollution within smokestacks. The difference in electrical force on the components of a mixture enables the electrostatic separation of wheat from chaff, rodent waist from rice, and salt from pepper–as can be seen if you first move your comb through your hair and then wave the comb over a mixed pile of salt and pepper. For more information, you might like to read Electrostatics, Scientific American March 1972.
Static charge can be dangerous when putting gasoline into your car. The trouble might happen if the driver begins filling and then collects a static charge while getting back into and then out of the car while the pump is going. When the driver once again returns to touch the pump handle, a spark sometimes occurs that ignites gasoline vapor. Throughout the nation, this happens only a few times a year. For our safety, gasoline stations could use grounding straps and automobile manufacturers could use anti-static materials in car seats; historically, car manufacturers have shown more interest in removing one dollar from the cost of cars. You might avoid getting into and out of the car while the pump is running, and you might make a habit of first touching a grounded metal pole or other object to discharge before touching the pump handle. The tiny spark that might result does less harm when it occurs far away from the gas tank.
Static electricity is the buildup of excess charge. The electrical forces causes these charges to move whenever a path occurs. This force holds atoms together, causes rubber bands and springs to rebound, and keeps you from falling through the floor. It will also push a collection of charges through a wire. Electricity is the flow of charges.
Tension is transmitted along the length of a stretched string by the electrical interaction of each neighboring pair of atoms.
Our bone growth is electrically controlled through a pressure sensitive, piezoelectric effect in which pressure on a solid substance releases electric charge. To promote bone repair, some therapies transmit a pressure wave, which is sound, through damaged bone. The same sort of therapy is used to repair cracked teeth.
Electricity consists of moving charges and is found in nerves, muscles, eyes, brains, hearts, eels, lightning, and in the electronic machines that we use every day. Electricity is the flow of charge. Lightning is an example of the flow of electrical charge.
Lightning (images at www.lightningsafety.noaa.gov/photos.htm and Lightling_Kane_Quinnell-1.jpg at http://205.243.100.155/frames/longarc.htm#Pos-Lightning1. The Lightning process is described at http://apollo.lsc.vsc.edu/classes/met130/notes/Chapter15/stroke3.html, with video clip) may be the most thrilling example of the flow of electrical current. Small lightning bolts and hair-raising displays (video) can be made using a Tesla (bio at http://ntesla.org, biography at www.teslascience.org, see copyrighted image in lightning lab at www.teslascience.org/archive/descriptions/picture15.htm and copyright free image at http://en.wikipedia.org/wiki/Tesla) coil (video clip), while 50-foot tall Van de Graf generators are used to make lightning in the lab (video). A student might like to construct a Tesla coil for the school, see http://www.eskimo.com/~billb/tesla/tesla.html. In a modern version of Ben Franklin’s (image) famous kite experiment (video of lightning striking kite at www.mos.org/sln/toe/kite.html, see also www.pbs.org/benfranklin/exp_shocking.html), researchers (Langmuir Lab in Socorro, NM at www.lightning.nmt.edu/~langmuir, and the
University of Florida lab at www.lightning.ece.ufl.edu and the PBS NOVA video Lightning!) attach ground-bolted wires to rockets fired into thunderstorms, inducing lightning to flow down the wire where it impacts a test object such as an airplane frame (seen in the PBS video Lightning!). Many persons consider lightning (image) to be art, as is the fulgurite (http://plaza.ufl.edu/rakov/Gas.html and www.usfcam.usf.edu/allan.html) that results from the branching path taken by lightning as it passes through sand or is generated during the electrical breakdown of materials (http://teslamania.delete.org/frames/lichtenbergs.html). Art at www.plasma-art.com
The electric force results from either an electric charge or from a changing magnetic force. The electric force is very strong. It depends on the system but typically, the electrical force is a zillion (1020 to 1045) times stronger than the gravitational force. This means that you would have to be able to measure 20 to 45 decimal digits before you could see the tiny, gravitationally produced change in motion for two objects that are also interacting electrically. All matter is composed of these electrical charges. Everyday objects have equal mixtures of positive and negative charge, making them electrically neutral.
Example:
Two particles separated by a distance r have equal mass m and charge e. For what value of m will the electric and gravitational force be equal? We have
FG = FE = Gm1m2/r2 = kq1q2/r2.
Putting m1 = m2 = m, q1 = q2 = e, and cancelling r gives
m = √(ke2/G) = 10-9 kg.
In this system, the two forces match no matter what distance separates the two particles. What sort of object has a microgram mass? This list shows that a small grain of sand has that mass, while the mass of a mosquito is 1,000 greater than this.
Example:
A group of 1030 electrons has a mass of 1 kg and a charge of 1.8 x 1011 coulombs. If two such groups are placed one meter apart, the electrical force between the two groups will be
FE = kq1q2/r2 = ( 9x109 Nm2/C2 )( 1 coulomb)2 / ( 1 m )2 = 3 x 1032 N.
The gravitational force between the two will be
FG = Gm1m2/r2 = (6.67 x 10-11 Nm2/kg2 )( 1 kg )2 / ( 1 m )2 = 6.67 x 10-11 N.
In this system, the ratio of the electrical to gravitational force is
FE / FG = 3 x 1032 N / 6.67 x 10-11 N = 4.5 x 1042.
All electronic circuits make use of the electrical force. A battery contains separated positive and negative charges. The negatively charged side of a battery produces a repulsive force on negatively charged electrons, forcing them to flow through the circuit toward the other, positively charged side of the battery that is attracting the electrons. The earliest usable batteries were made in 1800 by Alessandro Volta. In his honor, we rate battery strengths in "volts." The electric force pushes charges, causing them to flow through an engineer's circuits as a "current." One of the first persons to make measurements of electrical current was Andre Marie Ampere (1775-1836). Today, we measure the size of electrical current in units called "amperes" that are named after him.
It was soon found that each material has a characteristic resistance to the flow of electrical current. This was studied by in 1826 by Georg Simon Ohm. The unit of electrical resistance was named "ohms" in his honor. It took several years of research to find a way to cause an electrical current to flow through a material for distances of just a few yards (meters) and even more years to get electricity to flow through wires for distances of kilometers and miles. This research led to the development of the telegraph machine, which occurred in the year 1844. Telegraph lines were often placed along existing railroad lines because few roads existed at the time. The Trans-Atlantic cable (or here) was completed in 1857.
In 1864, James Clerk Maxwell wrote a set of four equations describing all electric and magnetic phenomena. These four equations, which are called "Maxwell's equations," describe a fundamental truth of nature and will be useful for all of us humans for the rest of time. They describe every electrical and magnetic machine that will ever be made including generators, streetlights, radio and television sets, motors, MRI and CAT medical imaging devices, the circuits of a computer, and toasters. Maxwell's equations also made it clear that the electric and magnetic forces are two different aspects of a single phenomenon of nature, called electromagnetism, and that light too, is an electromagnetic phenomenon.
It was found that whenever an electric charge is wiggled it sends out electromagnetic "light waves" that move away at the speed of light. Here is an animation of waves emanating from wiggling charges. In turn, those waves cause electrons to wiggle within the antenna of your radio receiver. The frequency with which the charge is wiggled determines the "color" of the light. Blue light has a higher frequency and more energy than does red light. (It also occurs that a hot object that glows with blue light is at a higher temperature than an object that glows with red light.) The electrical charges that make up matter are caused to wiggle whenever a light wave passes by, and this in turn causes them to emit light waves of their own. Light waves come in many colors, most of which are invisible to us. Some of these are called radio, microwave, infrared, ultraviolet, radar, x-ray, and gamma-ray. This means that the operation of lenses, mirrors, cameras, optical fibers, infrared remote control devices and nighttime viewers, radar detectors for the weather and the speed of automobiles, microwave ovens, medical x-rays, and other such devices are also described by Maxwell's equations because they involve electromagnetic waves. In addition, it has been found that each chemical element wiggles at uniquely different frequencies and that these characteristic frequencies increase as the temperature of the chemical increases; scientists have already measured millions of these frequencies. When astronomers look at the light coming from a star, they measure the received frequency and then know the chemical composition and temperature of that star.
We see the Sun because its wiggling charges emit light, and since these charges wiggle at many frequencies, the Sun emits many different colors of light. But because of its temperature, the Sun emits most of its light between the red and blue colors and much less beyond the infrared and ultraviolet colors. This is the reason our eyes are sensitive to the red through blue colors. It wouldn't help for Earthlings to see colors that our Sun doesn't produce. Since many other stars emit most of their light in colors not emitted by our own Sun, the eyes of creatures who might live around those stars would be more sensitive to those other colors, which might be infrared, ultraviolet, or even x-ray. The eyes of the nighttime creatures of the Earth–snakes, for example–are more sensitive to infrared light than are those of daytime creatures. Flowers are brightest in the ultraviolet colors because the eyes of their "partners," the bees, are most sensitive to these colors.
At the time of the publication of Maxwell's equations in 1864, it became clear that it was possible to generate electromagnetic "radio waves" using oscillating, electrical circuits in which current flows back and forth between capacitors and inductors (in many ways, this oscillatory motion is similar to that of the pendulum). It took about twenty years before Heinrich Hertz was first able to do so, and we have named the unit of frequency after him. We hear television and radio station frequencies given in terms of kilohertz, megahertz, and gigahertz. (My computer keyboard is operated at a speed of three nanohertz.) In 1888 Marconi was able to invent the machine we call a "radio-frequency detector" or "radio" by electrically producing an electromagnetic wave in one place and detecting it in another. The detector is nothing but another circuit containing the same capacitor-inductor combination. The frequency to which the circuit reacts is adjusted by altering the circuit components, which we are doing as we turn the radio knob. (The radio entertainment industry did not blossom until the 1920s.)
The first radio sets consisted of a number of vacuum tubes in which electrons are greatly accelerated before they are suddenly stopped by a collision with metal tube-components. Since the sudden stop is equivalent to a very high frequency wiggle, the stopping electrons emit high frequency light. In the year 1895, research involving the light emitted from vacuum tubes accidentally stumbled across the ability of certain frequencies to pass through body-sized pieces of matter. This was the discovery of x-rays by Wilhelm Roentgen.
It was claimed above that many seemingly unrelated phenomena are simply different aspects of a more fundamental law of nature. The above list of electrical machines and the following list of light-phenomena illustrates this point. Some examples of light phenomena described by Maxwell's electromagnetic equations include polarized sunglasses, the rainbow patterns seen on spilled oil sheets and soap bubbles, the highly reflective paint used on highway signs, telescopes, binoculars, a mirage on a hot day, the colors separated by water drops and the resulting rainbow, the halo that is sometimes seen around the Sun or the Moon, the blue sky, the red sunset, the color of every object, and the streaks of light you see when you squint your eyes while looking at a lightbulb. Each of these is simply a different aspect of electromagnetism. Each is described by Maxwell's equations and results from pushing on an object with the electromagnetic force. It is impressive that humans figured this out–in the year 1864, no less. There is no end to the usefulness of this understanding and its applications. In fact, humans are another example of this fundamental law of nature at work in that the atoms within our body are held together by the electrical force.
In the year 1864, nobody could imagine what sorts of machines would be made using the electromagnetic equations. In the same way, we cannot imagine the future machines that will result from today's scientific research. What sort of machines and medicines will be developed 150 years from today that are based on the just-completed human genome project or that are based on the quark research of today's elementary particle accelerator projects?
The electric force holds together atoms and molecules, including those within your body. (Remember that there are about one hundred different kinds of atoms, from hydrogen to uranium, and that a molecule is a collection of atoms.) In the same way that the gravitational force can pull two masses–the Earth and Moon, for example–into a circular orbit around each other, the electric force can pull two or more electrically charged atoms into a circular orbit around each other. This is similar to the way in which the force between two hand-holding skaters sort of orbit each other. Since the electrical force is sometimes attractive and sometimes repulsive, depending on whether the involved charges are alike or unlike, all molecules do not electrically attract all other molecules. This is in contrast to gravitational attraction, which is always attractive. If two molecules, or collections of atoms, electrically repel each other then they will not join together. Those molecules electrically attracting each other will join together–indeed, they must.
At room temperature, most molecules are electrically neutral, but the electrical charge of a large molecule is unevenly distributed about its three-dimensional shape. Just as a block having a zero net charge can be electrically attracted to a nearby, external charge, two neutrally-charged molecules can be electrically attracted to each other. When two multi-atom molecules face each other, a slightly positive charge of one side of the first molecule and a slightly negative charge of one side of the second molecule can result in an electrical force that holds the two molecules together. Within our bodies, the electrical builds large molecules containing thousands to billions of atoms.
The electrical interaction is the physical basis of the multi-atom molecules of biology and life. Living creatures consist of one to one-trillion cells, each of which contains one trillion interacting atoms. The operation of each creature occurs through thousands to millions of chemical reactions, each of which involves the electrical forces among the charges of the mixing atoms. The electrical force makes proteins fold, stretches DNA molecules when needed, and pushes and flips water molecules as they pass through channels. Here is a simulation of the electrostatic forces among one-million atoms comprising a tobacco virus.
The ease with which two approaching molecules can electrically interact depends on their shapes and charge distributions and also on their relative orientations and speeds while near each other. Each type of molecule has a specific shape. Biological molecules contain thousands to millions of atoms and have convoluted shapes. Their outer surfaces have numerous bumps, indentations, and projections. Some of these features or regions have an overall positive electrical charge, others have a net negative charge, and yet others are neutral. Two molecules can become bound either by sharing electrons between adjacent atoms or molecules or through the mutual attraction of oppositely charged regions of their outer surfaces. Often, there is no relative orientation in which the molecules attract each other. You might imagine what would happen if you similarly attempt to join two handfuls of magnets. Depending on their orientations, some might fly away while others join. As two different types of molecules drift past each other, those molecules that can merge, will; in fact, they must. Those that cannot merge will not do so.
The one hundred types of atoms found in nature can be placed side by side two at a time, three at a time, and so on, into countless sequences of increasing numbers of atoms. But few types of atoms simply placed next to each other will be able to electrically hold on to each other. Of the zillions of possible combinations, most do not produce an electrically stable molecule and so do not occur in nature. (In the last century or two, chemists have found many rules that help to predict which combinations can form stable molecules.) Any combination that is stable will occur whenever its components are mixed together.
Out of the one hundred types of atoms, we have seen that carbon atoms are the most suited to be joined together into rings and long chains containing hundreds or thousands of atoms. Much of biology involves the organic chemistry of carbon. For example, proteins are large molecules formed by combining several types of atoms and lots of carbon rings. The largest biological molecules contain billions of atoms.
Four families of organic compounds form the building blocks of life: twenty amino acids, carbohydrates such as sugar and glucose, lipids or fatty acids that do not dissolve in water and so form cell walls and store energy within fat, and the five nucleotides that comprise DNA and RNA. The molecules of each of these four organic compounds consist of about twenty carbon, oxygen, nitrogen, and hydrogen atoms (97.5% of the atoms within our bodies consist of these four elements, while calcium comprises 2%, phosphorus 0.2%, sulfur 0.1%, and all others 0.2%). Though hundreds of amino acids have been synthesized in the lab, only twenty different amino acids appear in living systems. These four types of compounds form the building blocks of larger structures– just as a home is built of individual bricks, doors, and windows (see Trefil and Hazen)–in that our bodies consist of, and operate using these four things. In particular, the twenty amino acids form the proteins used in the operation of our bodies. For more about the role of the electrical force in the molecules of life, see here.
The electric field of point charges
Here is the electric field of a positive charge, of two positive charges, and an eel that generates an electric field around its body and detects disturbances in that field due to nearby objects.
field lines emerge from positive charges or from infinity and end on negative charges or at infinity. The field is more intense where they are more dense. The field lines act like rubber bands in that if the charges are released, the charges will move in the direction that those rubber bands would propel them.
The electric field of a wire
(orbiting a wire http://www.ac.wwu.edu/~vawter/PhysicsNet/QTMovies/ElecPotential/Part-LineChargeOrb.mov )
The electric dipole
http://230nsc1.phy-astr.gsu.edu/hbase/electric/dipole.html#c3
orbiting a dipole
http://www.ac.wwu.edu/~vawter/PhysicsNet/QTMovies/ElecPotential/TwoPointChargesOrbital.mov
The electric field of continuous charge distributions
http://230nsc1.phy-astr.gsu.edu/hbase/electric/elelin.html
http://rt210.sl.psu.edu/phys_anim/EM/indexer_EM.html
http://planetphysics.org/encyclopedia/ElectricFieldOfALineOfCharge.html
http://scitec.uwichill.edu.bb/cmp/online/P10D/Hunte/Electric%20fields.htm
http://scitec.uwichill.edu.bb/cmp/online/p10d/sodha/lecture2/lect2.htm
http://www.physics.upenn.edu/courses/gladney/phys151/lectures/lecture_jan_31_2003.shtml
Electrical potential:
Gauss’s Law
http://scitec.uwichill.edu.bb/cmp/online/p10d/sodha/lecture4/lect4.htm
http://scitec.uwichill.edu.bb/cmp/online/p10d/sodha/lecture5/lect5.htm
In the chapter on Energy, we saw that the chemical energy of peas is about 1 Calories = 4,186 Joules per gram and that the energy contained in about 6 grams of peas enables a person to run and pole vault. A pair of 1-coulomb charges separated by 2.1 x 106 meters has a potential energy of 4,186 Joules. The electrical energy contained within N ??? cellular atoms provides sufficient mechanical energy for a 65-kg person to run. “Each ATP molecule represents the capture of 7.3 kcal/mole of energy.” “The breakdown of one glucose molecule results in a maximum of 36 to 38 ATP molecules.”
“Efficiency is 263 (kcal/mole)/686 (kcal/mole) or 39% of available energy in glucose is transferred to ATP”
http://www.cst.cmich.edu/users/baile1re/bio101fall/enzphoto/enzphoto/enzymes/enzynote.htm “Also, recall that the energy available in the ATP molecule is provided by the bond between the 2nd and 3rd phosphate groups, and amounts to about 7,000 calories of energy. [NOTE: a CALORIE is defined as the amount of energy required to raise the temperature of one (1) cubic centimeter (cc) of water one (1) degree Centigrade]”
http://micro.magnet.fsu.edu/electromag/java/ has RC time constants, charging a capacitor...
Electricity is the flow of electrical charges.
Electricity consists of moving charges and is found in nerves, muscles, eyes, brains, hearts, and eels. Our bone growth is electrically controlled through a pressure sensitive, piezoelectric effect . The electrical force binds together the atoms forming the molecules of life. Not only does the electrical force drive the chemical operations of our bodies, it is also the force driving the machines of our homes, factories, and civilization. Every few minutes, you reach for a machine consisting of electrical circuits, including toasters, dryers, TVs, phones, radios, computers. Medical CAT scan and MRI devices are electrical machines. In addition light (module) is an electromagnetic phenomenon.
We have all seen water and its current flow but electrical flow is more mysterious because we can not see with our own eyes the microscopic electrons moving within the wires. We can take advantage of our experience with water and its flow to make an analogy between the flow of electrons with that of water. When water flows in a current or river, it is moving from a highly elevated region to one that is lower in elevation. It moves from a region of high gravitational potential energy (glossary and modules) to a region of low gravitational potential energy. The separation between elevated and lower-lying regions makes water flow in a current. Similarly, when electrical current flows, the charges are always flowing “downhill” from high to low regions of electrical potential energy . This electrical potential difference can be setup by arranging that a region of negative charge concentration is connected by a wire to a region of positive charge concentration. Negative charges “flow downhill” by moving from the region of negative charge concentration to the region of positive charge concentration. The electric force between the separated charges makes the electrons move in a current.
Figure 1: Drawing of a water-filled pipe section through which a person is pushing a piston.
In the drawing (figure 1) is seen a water-filled pipe section through which you are pushing a piston. It takes a bit of pressure , which is the force of your push divided by the area of the piston, to cause the water to flow through the pipe. Imagine that you are the person in the drawing, and feel your own muscles doing this work. The water resists your attempt to make it flow through the pipe. The water flow is measured in mass per second (kg/s). The harder you push against the piston, the greater the resulting water pressure (animation of person pushing against piston, raising the needle in a pressure gauge. Or place a weight-scale against the wall and push to raise the scale reading.). The greater the pressure, the greater will be the resulting flow, which is measured in kg/s
Figure 2: Drawing of a water-filled pipe section through which a person is pushing a piston, causing a water-flow that spins a wood-cutting saw. This time, the person has to lean into the push. (In the drawing, the person might stand within the pipe.)
In Figure two, a propeller is placed in the flow and attached by a rod to an external saw. The rod passes through a hole drilled in the pipe wall. The propeller spins as water is made to flow past it. The saw cuts wood as it is made to spin, but it spins only when you push on the piston. As soon as you stop pushing, the saw stops spinning. Not only does the water resist being made to flow through the pipe, but the saw also resists being made to spin and cut the wood. You may have past experience with the muscle force needed to saw wood.
Figure 3: Circuit diagram of pressure source and resisting device
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To avoid leaks, let’s form the pipe into a closed loop, and to save your muscles, let’s have a pump do the work. In the circuit diagram shown in Figure 3, the circle represents the pump and the jagged line represents the saw teeth. The larger the pump, the more pressure it develops in the line, and the greater will be the resulting flow of water (kg/s) within the pipe.
Figure 4 (similar to Figure 1):
Drawing of a pipe section through which a charged piston is pushing like-charged ions, causing a flow of charges
Figure 4 is similar to Figure 1 except that the water has been replaced with a gas of ionized hydrogen atoms having a positive electrical charge . We remember that like charges repel, so that placing additional positive charges on the piston that is again shoved through the pipe will cause the hydrogen atoms or ions to move away from it, resulting in a flow of ions which is measured in coulombs per second (c/s). This time, you do not have to move the piston because the electric field generated by the charges on the piston will force the ions to move. (But you will still have to do work to force the mutually-repelling charges onto the piston.) Again to avoid leaks, let’s form the pipe into a closed loop and place an electrical saw into the circuit. In addition, let’s place negative charges on a second piston that is separated slightly from the first piston. The positively-charged ions will be pushed away from the positive piston and pulled toward the negative piston. The pair of pistons act just like a battery. The more charges placed on the pistons, or generated by the battery, the stronger will be the resulting electric field, measured in volts, that pushes the ions through the pipe. The electric field generates the electrical “pressure” that forces the ions to move. The ion flow or current is measured in charges/sec or amperes . A current of one ampere means that one coulomb of charge is moving past a point each second (one coulomb is defined to be the electrical charge found on 1.6x10^19 electrons). The ions resist the attempt to make them flow through the pipe. The moving ions are the flow of electricity in this pipe. The resulting circuit is diagrammed exactly as in the water circuit of Figure 3. This time the jagged line represents the electrical resistance of the saw or toaster or any other electrical device, and the circle represents the battery, which is an electrical pump. The stronger the battery, the higher will be the voltage it generates (causing an electrical “pressure” analogous to water pressure), and the greater will be the resulting electrical current , which is measured in charges/second.
The hollow pipe can be replaced by a solid metal wire. A tiny voltage is enough to push an outer electron away from each atom within that wire. These electrons comprise the electrical current pushed by the battery’s voltage . In a current-carrying wire, this is summarized by Ohm’s (image and biography) law : Voltage equals current times resistance, or in symbols, V=IR.
The electrons do not travel through the wire as freely as the ions moved through the hollow pipe. Instead, they ricochet off atoms much the same as falling balls bounce off a pin-filled pegboard that is tilted, as seen in Figure 5 (video at www.cs.utah.edu/~jrsnow/cs5610/demos). Increasing the tilt of the pegboard effectively increases the downward gravitational pull and increases the downward flow measured in kg/s. Within the wire, each electron moves a short distance before colliding with an atom . Some of these collisions cause the electron to bounce backwards, momentarily moving against the flow until its upstream speed is reduced to zero and reversed by the battery’s electric field . A series of collisions send each electron on a series of upstream, downstream, and sideways paths. On the average, the electron is moving downstream at a speed of just a few millimeters per second.
The electric field is generated as the battery uses chemical energy to separate charges. The electric field moves through the wire at the speed of light, while the charges move at an average downstream speed of a just a few millimeters per second.
Consider for a moment a line of many persons. There are two ways to get those people to move forward. One might push the person at the very back, who then collides with the adjacent person, in turn causing that person to collide with the next individual, and so on down the line. This is the way sound waves travel (see wave module and its video of a longitudinal wave on a slinky). Another way to get those persons moving is for all of them to begin walking when you shout “go,” see Figure 6 (omit this figure) as is effectively done within a wire by the electric field . Before the voltage , which is the electric field per unit charge, is established in the circuit, electrons are spread throughout the wire. When established, the force of the electric field causes the electrons to begin moving, wherever they are.
Test Questions:
1) The pump supplies a) water b) pressure c) resistance
2) The battery supplies a) charges b) pressure c) resistance
3) Which of the following is true? a) Voltage and current flow at the same speed. b) Voltage has no speed. c) Current has no speed. d) Current flows through the circuit at a higher speed than does the voltage. e) Voltage flows through the circuit at a higher speed than does the current.
4) If the magnitude of the pump or battery is increased, the a)
Kirchoff’s (copyright-free image and bio at http://en.wikipedia.org/wiki/Gustav_Kirchoff) loop rules are statements of the conservation of charge and of energy (glossary and module)
Figure 7: Circuit diagram of two pressure sources and resisting devices
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Figure 7 shows a circuit containing two water pumps or batteries and two saws. Notice that a piece of water or electrical charge can take first the upper loop, then the lower loop, and then the outer loop. The piece of water or electrical charge gains energy going through a pump or battery and looses energy when making one of the saws turn. The conservation of energy (glossary-module) requires that in any closed loop, the energy (glossary-module) gains must equal the energy (glossary-module) losses. The conservation of water mass or electrical charge requires that the water or electrical charge flowing into a junction must equal that flowing out.
Kirchoff’s (image) two loop rules are statements of the cons of charge and energy (glossary-module) in an electrical circuit:
1) The current flowing into a junction also flows out
2) Around any closed loop, the combined energy (glossary-module) gains must equal their losses
problem solving procedure for circuits:
draw circuit, label components, guess the direction of current flow in each loop and show it in the circuit, list knowns and unknowns, we need an equation for each unknown, first get an equation by applying conservation of charge at each junction, then write enough conservation of energy (glossary-module) loop equations to accumulate the same number of equations as are unknowns, in the circuit diagram show and number each loop used, if a loop goes in the direction of assumed current flow then batteries cause energy gain (glossary-module) and resisters cause energy (glossary-module) loss, otherwise the opposite is true
Some steps in the history of electrical knowledge and technology:
A voltage source or battery can be made by poking two unlike metals into a lemon (experiment) or by alternating metals in a stack of acid-soaked cloth, as done in the earliest usable batteries made by Volta (copyright-free image and bio at http://en.wikipedia.org/wiki/Alessandro_Volta) in 1800. Such voltage sources enabled the flow of electrical current to be studied. In 1826 Georg Simon Ohm (copyright-free image and bio at http://en.wikipedia.org/wiki/Georg_Ohm) found that each material has a characteristic resistance to the flow of electrical current. It took several years of research to find a way to cause an electrical current to flow through a material for distances of just a few meters and even more years to get electricity to flow through wires for distances of kilometers, leading to the development of telegraph in the year 1844 and the completion of the trans-Atlantic cable in 1856. Electric streetlights were another early use. In 1864, Maxwell (copyright-free image and bio at http://en.wikipedia.org/wiki/James_Clerk_Maxwell) explained that wiggling charges emit light and that the color of the light is determined by the frequency with which the charges are wiggled (see light module).
In previous centuries, people laughed at the mad scientists enthralled with little rocks that push and pull each other. Amber = electric. iron, magnetic rocks push and pull. ancient Greece
In the year 1828, nobody could imagine what sorts of machines would be made using electric current. (reference books full of circuits,) In the same way, we cannot imagine the future machines that will result from today's scientific research. What sort of machines and medicines will be developed 150 years from today that are based on the just-completed human genome project (www.genome.gov other modules) or that are based on the quark research of today's elementary particle accelerator projects (www.fnal.gov Fermi lab website).
Science and society connections:
You might like to list the electrical devices you use during one day, or try to describe what everyday life was like before the development of today’s electrical devices. How has electricity made your life different from that of your grandparent’s when they were young?
Describe the function of some interesting circuits listed in one of the following collections: list a few books that each contain 1,000 circuits functioning as anything from dimmer switches to motion detectors.
Each year in the U.S., electricity causes between 300 and 1000 accidental deaths per year (see www.cdc.gov/nchs/data/nvsr/nvsr53_05acc.pdf) and as many as 10,000 worlwide. How do we make electricity safer? Should we continue to use electricity?
Somewhere in the world, about once per month an electrical sub-station fails, explodes, and burns (video clip XfrmBlast1.mpg from http://205.243.100.155/frames/mpg/XfrmBlast1.mpg), sometimes injuring people. A web search for “substation fire” will return TV station news coverage of these events (www.wndu.com/news/052004/news_35042.asp). Call your local electric utility office and discuss their maintenance procedures and safety record.
We like our electrical machinery, but about half of all greenhouse gases emitted in the U.S. come from the electrical power generating plants that burn fossil fuels. Fossil-fuel-burning cars emit another quarter of the total (see www.eia.doe.gov/cneaf/nuclear/page/analysis/ghg.pdf) Notice that this pollution still occurs when burning fossil fuels to generate the electricity needed to run electrically-powered cars. (For zero-emission cars, see www.pbs.org/now/science/caautoemissions2.html) Dams are pollution free but upset the ecology of rivers. How should we generate electricity? Should we stop using electricity?
For more information and video clips about Tesla (image) coils, high voltage, and lightning visit:
http://205.243.100.155/frames/mpg/500kV_Switch.mpg
See www.teslamania.com for the text associated with this video clip. See www.pbs.org/tesla for the documentary Tesla - Master of Lightning.
The website http://hot-streamer.com lists many tesla coil websites. An interested student might like to build one for the school.
The Tesla (image) coil stunts at www.hvfx.co.uk/stunts.php include a woman's Van de Graf hair movie vdg.mpg, Lightning-Man (lightningman.mpg), and stuntsuit-man (stuntsuit.mpg).
For an eye witness description of ball lightning, see www.amasci.com/weird/unusual/bold.html.
Visit the turn of the century, electro-therapy museum website at www.electrotherapymuseum.com
For explanations of static electricity, electrical current, and Ohm’s Law, visit: www.iit.edu/~smile/ph8902.html
http://en.wikipedia.org/wiki/Electrical_current
www.glenbrook.k12.il.us/gbssci/phys/Class/estatics/u8lia.html
www.ndt-ed.org/EducationResources/CommunityCollege/EddyCurrents/Physics/CurrentFlow.htm
A historical review of electrical and magnetic developments tells us something about science and the accumulation of knowledge and techniques.
Marina Milner-Bolotin of the University of TX at Austin has a reproduction of “A history of great discoveries in electricity,” which is from Safe and Simple Electrical Experiments, by Rudolf F. Graf, 1964.
http://www.ph.utexas.edu/~ps304/History%20of%20electricity.htm
Magnet
http://wps.aw.com/aw_knight_physics_1/17/4389/1123703.cw/nav_and_content/index.html
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