ELECTROSTATICS NEWSLETTER
March/April 2001 No.155
PRESIDENT’S MESSAGE
If you are a member of the ESD Association, you may have been following an ongoing discussion concerning the proper unit for surface resistivity (see, e.g., “Ohms per Square What?” by Gene Chase, January/February Threshold.) Two camps – the ohms and ohms-per-square aficionados, appear to have emerged on either side of this issue. Although I understand the arguments on both sides, I would like to plant myself squarely in the “ohms-per-square” camp. If the ultimate objective is to improve understanding in the field, one can make the case that the unit ohms-per-square for surface resistivity leads to less to far less confusion than does the simple unit of ohms. Other opinions on this issue are welcome, but here is mine.
The most fundamental unit that describes ohmic materials is volume resistivity r, measured in ohm-m. Although this unit contains a dimension (meters), it is really a continuum quantity (i.e., defined at a point) that stems from the vector constitutive law for ohmic materials:
J = E/r
where J is the current density and E the electric field. It's only when we package a resistive material inside geometric boundaries that J, E, and r translate into the familiar units of amperes, volts, and ohms contained within Ohm's law V = IR. Suppose, for example, that wire terminals are allowed to make contact with a rectangular slab of ohmic material of length l, width w, and depth d. The connection is made in such a way that the end faces of dimension w ´ d are completely contacted by a conducting interface. In this case, the voltage V becomes (roughly) El, the current I becomes Jwd, and the terminal resistance that would be measured by an ohmmeter connected to the two wires becomes
R = r l/wd
This lumped-element resistance has the units of ohms and consists of the volume resistivity r modified by geometrical parameters.
When we speak of “surface resistivity”, the implication is that we are talking about a layer of ohmic material of intrinsic volume resistivity r that is very thin in one direction (e.g., in depth). In such a case, the depth d reduces to a film thickness t. If we revisit the example of the rectangular slab of ohmic material, the slab instead becomes a rectangular surface film of thickness t. If we make a connection to two opposite edges of this "two-dimensional" slab in the same way as was done for the slab of larger thickness, its terminal resistance still can be described by the same formula but with t substituted for d:
R = r l/wt
Because one dimension of the film -- its thickness t -- is known, we can characterize the film by the quantity rs = r/t, which indeed has the fundamental physical units of "ohms". If we connect an ohmmeter to the contacting wires, the terminal resistance of this thin slab again has the units of ohms. But is the measured terminal resistance equal to the intrinsic surface resistivity rs? The surface resistivity will be equivalent to the measured, lumped element terminal resistance only if the surface film has the shape of a square. Attempting to apply the concept to films of other shapes, e.g. rectangles, circles, or triangles, produces a terminal resistance that can be quite different from the intrinsic surface resistivity of the material. Assigning the unit of ohms to surface resistivity without acknowledging that it is an intrinsic material property can lead to considerable confusion. Many an engineer or technician has been tempted to erroneously equate a simple, two-probe ohmmeter reading with surface resistivity. For example, if I probe a surface film at two points with a common ohmmeter, I will not (unless I'm very lucky) obtain an “ohms” reading on the meter that corresponds to the film's surface resistivity. Similarly, if I change the spacing between the probes, my resistance reading will change while the intrinsic surface resistivity will not. In contrast, if I probe the film with a calibrated four-point probe in which the probe tips are arranged in a square, I will obtain an appropriate reading independent of the size of the probe. Similarly, if I happen to measure the terminal resistance of a square of surface film using the edge contact method described for the rectangular slab, then my ohmmeter reading will yield the same ohms value as the intrinsic surface resistivity rs = r/t.
Assigning the units ohms-per-square to rs reminds us that it's a special quantity reserved for surface resistivity and that it is in intrinsic material property. It's not to be confused with the lumped element, terminal value of resistance, for which we should reserve the simple units "ohms". Adopting the surface resistivity unit "ohms-per-square" doesn't mean that we must apply it only to squares. In the same way, using the fundamental unit of volume resistivity r, which has the units of ohm-m, does not imply that it can only be used to describe centimeter-long pieces of material.
I'm in favor of propagating the use of ohms-per-square. Appending the “per-square” designation reminds us that the quantity "ohms" is reserved for lumped-element terminal resistance such as one would measure with a simple ohmmeter, and that intrinsic material quantities such as volume and surface resistivity must be modified by the appropriate geometrical parameters before we translate them into terminal resistance. In some cases -- circular geometry in particular -- accounting for the geometry may involve some algebra or integral calculus, but the intrinsic surface resistivity of the material, specified in the ohmic value that a square of material would have, will remain the same regardless of the shape of the film.
For the Friendly Society,
Mark N. Horenstein
ESA President
CONCERNING THE LEAF ELECTROSCOPE
When Mark Horenstein wrote about the leaf electroscope in the last ESA Newsletter, he provoked in me some thinking about the operational principles of this ancient and venerable electrostatic instrument. During school days, many of us used a leaf electroscope in science class, and some of us may have built working models from a glass jar, a paper clip, and some thin aluminum foil liberated from a chewing gum wrapper. But despite such familiarity, most of us probably have never given the instrument so much as a moment's critical thought.
Mark's explanation of how the device operates awoke me from mental lethargy. He suggested that it is not the repulsive force of like charges that causes the two, closely spaced, hanging leaves of the device to spread apart, but rather the attractive force between the leaves and opposite charges located somewhere. He argued that,
because the two leaves have like charge and are at the same electrostatic potential, the field between the leaves is very small, so that any repulsive Lorenz force term qE must be very small. I found this explanation intriguing, but something bothered me about it as well.
Faced with a scientific dilemma like this, it seemed like a good time to go back to basics. Coulomb's Law describes the repulsive and attractive action at a distance between like and unlike charges, respectively. Reduced to essentials, it may be stated:
F ~ (Q1 Q2)/r2 (1)
where Q1 and Q2 are point charges separated by distance r. It is important to notice that Couloub's Law does not invoke such notions as the electric field, voltage, or electrostatic potential. There is nothing more to Coulomb's Law than what is expressed in Eq. (1) and, as long as we use it with care, it will always gives us the correct answer. A problem in the correct application of Coulomb's Law occurs when electrical conductors are present; however, there is a way around this problem. It involves locating ALL net free charges, and only then doing the accounting work of adding up the vectors forces. If we apply Coulomb's Law to the leaf electroscope, one sees that we do not need any opposite-sign charge to predict that the leaves will separate when charge is applied. The like-sign charges located within the two leaves simply repel each other. The only effect of the conductivity of the electrically charged leaves is to dictate certain details of the way the charge is distributed.
The qE representation also works fine, but one must be careful not to count the portion of the total field created by the charges in one leaf as being capable of acting upon that same leaf. In other words, a body can not exert a force upon itself. To use qE unambiguously, one may think of the electric field created by one of the leaves acting on the charge in the other leaf. This approach leads to the same conclusion reached before that mutual repulsion pushes the leaves apart; and again, opposite-sign charge need play no part in this effect. In fact, the presence of any nearby, opposite-sign charge might interfere with electrometer operation, reducing measurement precision.
Below follows an independent argument that supports the conclusions reached above. For the sake of simplicity, assume the universe is net neutral with respect to charge. The implication of this assumption for our leaf electroscope is that any charge on the leaves must be exactly balanced by charges on the external walls or structure of the electrometer. Now, leaving the dimensions of the leaves alone, make the size of the electrometer's enclosure larger and larger, so that this opposite-sign charge, which remains finite, move toward infinity. The electric field between the charges on the leaves and the opposite-sign charge on the walls must then go to zero, and so, according to the hypothesis that the attractive force between the leaves and the walls is responsible for the operation of the electroscope, the instrument should cease working. But such a result suggests an extraordinarily strong (1/r2) dependence of the electrometer's response upon the geometry and size of the externals. If any such strong dependence existed, electrometers would not be the precision instruments they are known to be.
Tom Jones
WHO INVENTED THE LEYDEN JAR?
I read your (Mark Horenstein’s) message in Electrostatics Newsletter No. 154, and noted you mentioned Cunaeus’ discovery of the Leyden Jar. It’s a bit more complicated than that - there were a number of people claiming priority on that invention.
Scientists of the day were still in the trial-and-error mode. It was not all that long - twenty years at most - since Stephen Grey had discovered the laws of electrical conduction, had tried various substances and classified them according to their conductivity, and found that the human body could be electrified and hold a rather impressive amount of electricity. People were still working with this’n’that putting electricity in and seeing what happened. They didn’t get right around to water (it was a liquid) but eventually some bright fellow (who may have been Andreas Cunaeus) put water in a jar, dipped a wire in, and used the wire to get electricity from the generator to the water.
Ellen R. Kuhfeld, PhD
Curator, The Bakken
ARE YOU TROUBLED BY PIXEL FLUTTER?
An article in the Economist, Dec 23,2000, might be of interest to our ESA members. It's entitled “The Fluttering of Tiny Pixels", and it describes yet another means of displaying images from an electronically generated pixel array, such as we see in our TV. Until now, the most ubiquitous form has been the cathode ray tube. Liquid crystal displays take second place, and LED's are in the race, too. And let’s not forget Charlie Kalt's electrostatic shutter method, which is continuing to gain ground.
The latest method reported is a fascinating example of inventing a way to control something mother nature invented long before we were born... interference colors. We see them when we look at a thin film of oil on water, and we also see them when we look at certain butterflies.
Iridigm Technology, in California, hopes to build display panels consisting of tiny paired, semi-reflecting mirrors for which the spacing between them can be adjusted electrostatically. They call their technology “I-mod" for interferometric modulator. The display works by fine-tuning the spacing between the mirrors to one of four settings. Three of the settings produce the primary colors red, green, or blue, while the fourth setting produces black, by reflecting no visible wavelengths.
The front semi-reflecting panel is rigid, and appropriate voltages are applied to the movable panels to apply electrostatic forces that “pull them together or push them apart". (We know from last month's ESA Newsletter, thanks to our President, Mark Horenstein, that like potential electroscope leaves do not repel each other, they are pulled apart by the lower voltage world around them.)
Iridigm claims pixels 30 microns by 40 microns area, giving 80,000 pixels per square centimeter. They haven't yet solved the problem of connecting voltages to them at such dimensions, but they hope to make practical demonstrations at 100 pixels per inch.
We have to ask, “How do we cope with the color shifts that result from changing the viewing angle?" If you ever looked closely at the ruby-throat hummingbird, you may have noticed that his ruby-red throat suddenly turns a dark green when he turns sideward to you. The viewing angle increases the effective distance between the semi-reflecting surfaces, and it can be found by dividing by the cosine of angle.
Maybe Charlie Kalt has the ultimate winning system after all. Time will tell...
Bob Gundlach
WHO GAVE US ELECTRICITY ?
By MARILYN TRUMPFR-SAMRA, News Special Writer, Ann Arbor News (11/25/2000)
Ignorance is to blame. Just plain old ignorance. And in some cases the hard-boiled politics of historians, who for reasons known only to them, continue to perpetuate the myth even when the error's been clearly pointed out.
It sticks like a burr under the saddle of John W. Wagner that in history classes throughout the United States, Thomas Alva Edison is generally celebrated as the inventor of electricity. The honor, he insists, goes to Nikola Tesla, an Austro-Hungarian immigrant who came to the U.S. in 1884 at the age of 27 with just four cents in his pocket and a book of poems he'd authored.
At his death in 1943, Tesla held all of the seminal patents on his worldwide system of polyphase alternating current - or AC power. The stuff of light bulbs, radios, TVS, washing machines and the mighty assembly line at Ford. Wagner, who's spent the past 17 years working to right the wrong, credits Tesla with powering the second industrial revolution, creating the AC current that freely traveled great distances, while Edison's adopted DC technology required a grid with transformers and was limited to use inside one square-mile. "In the 74 years between 1895 when people still rode horses to 1969 when the United States put a man on the moon - it was the impact of AC electricity which put the muscle into factories," said Wagner "Tesla was a genius." Wagner retired from teaching in 1993 after 42 years at the chalk-board, and today at age 72 volunteers three days a week at Summers-Knoll, a private elementary school on Ann Arbor's southeast side where he teaches composition and penmanship.
His passion for Tesla is contagious. For nearly two decades he's rallied his students behind the cause. They've written papers on the injustice, but it didn't stop there. When a student's father, Ron Sharp of Dexter, an attorney and artist, offered in 1988 to create a bust of Tesla if Wagner could fund the purchase of the costly materials, Wagner bit. His students began a letter campaign, soliciting funds from corporate CEOs. They designed a T-shirt with Tesla's portrait and artwork that read: "He invented tomorrow," and sold hundreds and hundreds over the Internet at $21 each. Funds began to roll in. Students raised the requisite funding for the bust, appraised at $6,000. It was cast in bronze and premium black granite for the base was ordered from India. The first nearly 2-foot-tall bust was donated to Harvard University in 1989.
In the ensuing years, new students of Wagner picked up the mantle and ran with it. Similar letter campaigns and T-shirt sales raised the necessary funding six more times. All total, bronze busts have been donated to Harvard University, Yale University, Princeton University, Massachusetts Institute of Technology, Cal Tech, the University of Michigan and the University of Wisconsin. Wagner offered to donate a bust the Smithsonian and the Henry Ford Museum in Dearborn, but both institutions declined. He credits their unflagging allegiance to Edison to be politically driven, anchored by costly existing displays, Ford's friendship with Ford's friendship with Edison, and hard-nosed historian who work to portray their version of history. In 1943 the U.S. Supreme Court in a landmark decision, awarded Tesla radio patents previously held by Marchese Guglielmo Marconi. "It was his genius that created the polyphase system marked by the millions of (high tension electrical) towers that dot the countryside throughout the world,” Wagner said, adding, "They are his monuments."
Brad Canale, the executive director of College Relations for the University of Michigan said the bust permanently installed there this past September is on display in the atrium of the Electrical Engineering and Computer Science Building. According to Canale, Time Magazine recently named Tesla as one of three people who should have received a Nobel Prize, and did not. "Dr. Wagner’s done significant research on the subject and he tells some fascinating stories, Canale said. "(Tesla) is obviously a historical figure in science and engineering." Wagner said he'll keep pushing ahead "until I drop," he said. "It inspires children to write, and, reading and writing are a very important part of going to school. Word on Tesla is filtering out. "I get thousands of e-mails on this, dozens a day, from all over the world," Wagner said.