# ELECTRICITY

Although electricity contains many parallels with motion, it involves a fundamentally different force. Electricity is the study of the motion and effect of charges just as mechanics is the study of the motion and effect of masses. The subject of electricity was placed on a firm quantitative basis by the Scottish mathematician and physicist, James Clerk Maxwell (1831-1879), whose four equations encompass all electromagnetic phenomena. When Einstein, a generation later, upset almost all of "classical physics," Maxwell's equations survived untouched. Electrical demonstrations, especially those involving very high voltages, constitute some of the most spectacular in the whole of physics.

## Electrical Safety Considerations

The use of electricity in demonstrations entails special hazards from electrical burns and electrocution[1]. The hazards of electricity (see Table 4.1) depend on the amount of electrical current, its frequency, its duration, its path through the body, and the physical condition of the person. Alternating current at 60 Hz is slightly more dangerous than direct current, but high frequency currents (greater than a few kHz) are safer because they tend to flow on the surface of the skin and away from the heart and lungs. The resistance of the body varies from about 300 ohms to about 100,000 ohms, and thus even very low voltages can produce lethal shocks. Fatalities have occurred at voltages as low as 24 volts. For currents that exceed the "let-go" current (10-20 mA)[2] the person becomes frozen to the circuit, and the current typically rises to a level of about 25 mA where muscular contractions onset. Then the person is either thrown clear of the circuit or the current continues to rise until ventricular fibrillation or cardiac arrest occurs (at 50-200 mA), assuming the path of the current is through the heart.

Pulsed currents such as one might encounter with the discharge of a Van de Graaff generator or other charged capacitance present special considerations. One can endure currents that would otherwise be lethal if the duration is short enough. For pulses of less than a few seconds duration, the relevant quantity is the square of the current integrated over the time of the pulse. Values of I2t greater than about 0.01 A2- sec can cause electrocution for a typical adult. For a reasonably low body resistance of 2000 ohms, this translates into an energy of about 10 joules. Severe shocks can occur at levels 10-100 times lower and can startle one into an accident, since it is natural to jerk away from such a shock.

The usual safety precautions entail some combination of the following: copious and redundant insulation, grounding of all exposed metal parts, interlocks, isolation transformers and ground fault interrupters. Good practice entails standing on an insulated surface and keeping one hand in a pocket or behind one's back while working around high voltage. In performing electrical demonstrations, one should ideally have a knowledgeable assistant trained in cardiopulmonary resuscitation (CPR) always present. The probability of resuscitating someone is good if CPR is begun within three minutes but becomes poor after about six minutes. CPR classes are offered by many groups such as the American Red Cross and the American Heart Association.

#### REFERENCES

1. E. A. Lacy, Handbook of Electronic Safety Procedures, Prentice- Hall: Englewood Cliffs, New Jersey (1977).

2. C. F. Dalziel and W. R. Lee, IEEE Spectrum Feb, 44 (1969).

## Average Effects of Continuous ac or dc Electrical Currents on Healthy Adults

```     Electrical Current       Biological Effect

1 mA           threshold for feeling

10-20 mA       voluntary let-go of circuit impossible

25 mA          onset of muscular contractions

50-200 mA      ventricular fibrillation or cardiac arrest```

## 4.1

An electrical discharge is illustrated by connecting a high voltage power supply to a pair of conducting bars close together at the bottom and farther apart at the top, between which a discharge strikes at the bottom and rises to the top and then restrikes at the bottom.

#### MATERIALS

• power supply, preferably >10 kV and >1 mA, current-limited
• 2 bars at least a meter long with insulated mounting base

#### PROCEDURE

A device with little practical use but which often appears as a prop in old science fiction movies is the Jacob's ladder[1],* named after the biblical character who had a dream of a ladder to heaven with angels ascending and descending on it.** It consists of two vertical conducting bars close together at the bottom and far apart at the top, like a pair of television rabbit-ear antennas. A high voltage is applied between the bars causing an electric arc to form at the bottom where the bars are closest together. The arc then slowly propagates up the bars until finally it extinguishes, whereupon it instantly restrikes at the bottom. The Jacob's ladder is sometimes called a "climbing arc."

*Available from Carolina Biological Supply Company, Edmund Scientific and Frey Scientific Company

**Genesis 28:12

To make a good Jacob's ladder, a voltage in excess of 10 kV and a current in excess of a few milliamperes is required. The voltage primarily determines the length of the arc, and the current determines its intensity. The device can be run with either ac or dc current. The voltage source must be such that it can be short-circuited indefinitely without harm. Transformers designed for neon signs are good because they have a large leakage inductance between their primary and secondary windings so as to limit the short-circuit current. With a normal transformer, one can place a suitable impedance (inductance preferred, but resistance or capacitance will do) so as to limit the output current to the rated value. For example, if one has a transformer with an output rated at 20 kV and 10 mA and if the input is 115 V, the desired impedance is 1152/.01/20000 = 66 ohms. This could be either a resistor with a power rating of >1152/66 = 200 watts, an inductor of 66/2(pi)f = 175 millihenries or a capacitor of 1/66×2(pi)f = 40 microfarads. The inductor must have enough iron so as not to saturate and a reasonable Q at f = 60 Hz (much less than 66 ohms of winding resistance). The capacitor must have a voltage rating greater than 115×2½ and not be electrolytic but must be designed for ac service. Motor starting capacitors are suitable.

#### DISCUSSION

When the device is turned on, the full voltage initially appears across the bars causing an arc to form at the closest point, where the electric field is highest. The voltage then drops to a low value because the impedance of the arc is low. The arc heats the air, and the hot air begins to rise because it is less dense than the surrounding air. As the arc rises, its impedance increases, and the voltage between the bars rises. Eventually the arc gets so long that the voltage is not sufficient to sustain it, and the arc goes out. Then the voltage rises to its full open-circuit value, and the arc restrikes at the bottom. There is also a magnetic force causing the arc to rise, but the dominant effect is the heating of the air as can be demonstrated by tilting the whole device on its side.

The Jacob's ladder illustrates electrical discharges and the variation of the density of air with temperature. The principle is used in the horn gap on power transmission lines and in transformer yards for dissipating the arc of disconnects. It could serve as an introduction to a discussion of the physics of plasmas (ionized gases) and electrical breakdown. If the Jacob's ladder is operated inside a closed tube, the tube fills with a red-brown oxide of nitrogen. The oxide may then be aspirated through water to form nitric acid, illustrating the fixation of atmospheric nitrogen by lightning. The Jacob's ladder also converts oxygen gas (O2) into ozone (O3), a pungent, highly reactive allotrope of oxygen.

#### HAZARDS

This demonstration is potentially very dangerous. If currents of more than a few milliamperes are used, the Jacob's ladder will severely shock anyone who comes too close to the bars while it is in operation. Some measure of safety is provided if the secondary is not grounded so that one would have to be close to both bars simultaneously to receive a shock. The safest arrangement would be with the whole apparatus enclosed in a transparent case which can also serve to support the bars at the top. The case also acts as a resonant acoustical cavity, enhancing the sound of the arc.

#### REFERENCE

1. H. Strand, Popular Science 184, 110 (1964).

## Van de Graaff Generator

A Van de Graaff generator is used to illustrate many principles of high voltage electrostatics, such as making a person's hair stand on end.

#### MATERIALS

• Van de Graaff generator*
• grounded conducting sphere
• grounded pointed needle
• insulated stool
• hand mirror or Polaroid camera (optional)
*Available from Central Scientific Company, Edmund Scientific, Fisher Scientific, Frey Scientific, Klinger Educational Products Corporation and Sargent-Welch Scientific Company

#### PROCEDURE

A standard physics demonstration is the Van de Graaff generator named after the American, Robert J. Van de Graaff (1901-1967), who developed it in the 1930's. A Van de Graaff generator can be made with a hollow metal dome, a belt to transfer charge to the dome and a motor, preferably with variable speed control[1-5]. More commonly, Van de Graaff generators are purchased from vendors of scientific demonstration apparatus. The limiting voltage is determined by the electrical breakdown of air (about 30 kV per centimeter at atmospheric pressure), and so a Van de Graaff generator with a 10-cm-radius dome is capable of producing up to about 300 kV. The voltage may be considerably less if the humidity is high or if sharply pointed, grounded conductors are nearby to allow corona[6] to discharge the dome. The dome and insulated supporting column should be carefully cleaned before use. Despite common belief, the electrical breakdown of air is only slightly affected by humidity, but surface leakage is greatly affected by moisture.

The standard demonstration involves having a volunteer stand on an insulated stool (of a height greater than the diameter of the dome to ensure adequate insulation) and place a hand on the dome while the Van de Graaff generator is turned on. After a few minutes, the volunteer's hair will begin to stand on end. A hand mirror is useful to allow the person to see what is happening (but don't hand it to someone charged to high voltage!). A Polaroid photograph also makes a good souvenir.

It is best to choose someone with medium length, fine, dry hair. Shaking the head helps make the hair stand up. The person should be well away from any grounded conductors and told to leave the hand on the dome at all times until told to remove it. When finished, the dome should be slowly discharged by bringing a grounded, pointed needle near the dome while the person is still in contact with it. The hair will drop back into place as corona from the needle discharges the dome, and the volunteer can then step down from the stool. The stool should be cleaned before use. If the stool is at all tipsy, the person should be given help up and down.

Afterwards, one could show the distance over which a spark can be made to jump by bringing a grounded sphere near the dome. The increased capacitance of the sphere makes the spark more intense and visible. If the grounded sphere is mounted on a flexible rod, the attractive force due to the induced charge in the sphere will make the support rod bend toward the dome. When a spark occurs, neutralizing the charge on the grounded sphere, the support rod will straighten, producing a mechanical vibration.

Other demonstrations can also be done with the Van de Graaff generator. Puffed rice placed on the dome will fly off in all directions when the generator is turned on. A pinwheel placed on the dome can be made to rotate from the corona given off the points. A fluffy cotton ball or silvered balloon[7-9] released near the generator will be attracted to the dome and then repelled after it touches the dome and becomes charged with the opposite polarity. Soap bubbles can be blown toward the dome by someone at ground potential or away from the dome by someone touching the dome[10,11]. Bits of fur can be tossed into the region between a charged and grounded dome and illuminated with a strong light to illustrate qualitatively the shape of the electric field[12].

#### DISCUSSION

The Van de Graaff generator demonstrates a number of principles foremost of which is the relationship between charge and voltage, Q = CV, where C is the capacitance of the dome. The capacitance of a sphere with respect to infinity is about 1.1 pF per centimeter of radius. The electrical energy stored in the Van de Graaff generator is CV2/2. Energies below about 10 joules (corresponding to a dome with a 27-cm radius) are relatively safe. Hair stands up because it acquires charges of like sign which tend to repel one another. The Van de Graaff generator was one of the earliest particle accelerators used for nuclear physics research. Modern Van de Graaff generators and other similar electrostatic accelerators are still used for that purpose and are capable of voltages in excess of 20 million volts[13].

#### HAZARDS

Small Van de Graaff generators (less than a few hundred thousand volts) are relatively safe since the charging current is typically only a few microamperes and the capacitance is too small to allow much of a charge buildup, provided additional capacitance is not added externally[14]. Even so, it is probably best not to let someone with a weak heart touch the dome. The greater danger is that a spark to the person will be startling and might prompt a recoil that could cause injury.

#### REFERENCES

1. R. J. Van de Graaff, et. al., Rep. Progr. Phys. 11, 1 (1946).

2. A. D. Moore, ed., Electrostatics and its Applications, John Wiley & Sons: New York (1973).

3. H. Walton, Popular Science 185, 142 (1964).

4. E. Francis, Popular Electronics 24, 57 (1966).

5. C. L. Strong, Scientific American 225, 106 (Aug 1971).

6. L. B. Loeb, Electrical Coronas, University of California Press: Berkeley, CA (1965).

7. P. Hood, Am. Journ. Phys. 14, 445 (1946).

8. A. V. Baez, Am. Journ. Phys. 25, 301 (1957).

9. M. D. Daybell and R. J. Liefeld, Am. Journ. Phys. 31, 135 (1963).

10. G. R. Gore, Science Teacher 39, 48 (1972).

11. R. Prigo, Am. Journ. Phys. 44, 606 (1976).

12. J. L. Smith, Phys. Teach. 27, 358 (1989).

13. P. H. Rose and A. B. Wittkower, Scientific American 223, 24 (Aug 1970).

14. A. D. Moore, Electrostatics: Exploring, Controlling & Using Static Electricity, Doubleday: New York (1968).

## Tesla Coil

A Tesla coil, because of its high frequency, provides a safe way to demonstrate very-high-voltage, high-current phenomena.

#### MATERIALS

• Tesla coil*
• fluorescent tube
• insulated platform
*Available from Carolina Biological Supply Company, Edmund Scientific, Fisher Scientific and Frey Scientific Company

#### PROCEDURE

The Tesla coil is a type of resonant transformer that is capable of producing high frequency voltages of upwards of a million volts. The Tesla coil was developed by Nikola Tesla (1856-1943), a contemporary and rival of Thomas Edison (1847-1931). Tesla's biography makes especially interesting reading[1-4]. In 1899 Tesla produced 135 foot long discharges, 200 feet above the earth with a 12 million volt coil at his Colorado Springs laboratory, and the overload on the power line set fire to the alternator of the Colorado Springs Electric Company. Tesla imagined using his invention not only for wireless communications around the world but also for the widespread dissemination of electric power without the use of wires.

Because of its high frequency, the Tesla coil provides a relatively safe way to demonstrate very high voltage phenomena. A large Tesla coil is probably the most spectacular of all electrical demonstrations. The Tesla coil also makes an excellent student project since there is much room to experiment and to optimize its performance. The followers of Tesla almost constitute a cult. There is an International Tesla Society** and a Tesla Coil Builders Association*** that publishes a journal containing much useful information. Old issues of electronic hobby magazines[5-10], scientific journals[11-14] and books[15-17] have construction details. A recent book that contains much practical design information is Modern Resonance Transformer Design Theory, by D. C. Cox.****

**International Tesla Society, 330-A West Uintah Street, Suite 215, Colorado Springs, CO 80905-1095 (303) 570-0875

***Tesla Coil Builder's Association, 3 Amy Lane, Queensbury, NY 12804 (518) 792-1003

****Available from Resonance Research, Corp. R1, Shadylane Rd., Box 320A, Baraboo, WI 53913 (608) 356-3647. This company also produces custom-made Tesla coils and other electrical demonstration apparatus.

There are many other possible uses for the Tesla coil aside from producing long and impressive sparks in the air surrounding the top of the coil. It should be possible to illuminate a fluorescent or gas-filled tube held in the hand some distance away. A hydrogen-filled balloon on the end of an insulated rod can be made to explode when brought near the top of the coil. It is possible to draw the current through one's body by bringing a long metal rod held in the hand near the top of the coil. With a large coil one should be able to light an incandescent bulb in series with the rod. One should use the highest voltage bulb possible to get the most light for a given current. If a sufficiently well-insulated platform is available, one should be able to stand with bare feet on a metal plate (or more impressively sit in a washtub full of water) connected by a wire to the top of the coil and light a discharge tube or clear incandescent light bulb held in the hands or draw sparks off the tips of the fingers. In doing this demonstration, the hair should be wetted and metal thimbles worn on the fingers to prevent burns.

The Tesla coil is essentially a radio transmitter without the antenna, and thus Tesla rightly deserves some of the credit for the invention of the radio, although his interest was more in the transmission of electric power than in communication. It is capable of producing severe radio interference and thus should be operated inside a shielded cage and only for brief intervals. A suitable detector, such as a large loop of wire with a pair of conducting balls on the ends between which sparks can jump, placed some distance from the coil, demonstrates the propagation of these radio waves. One can also point out that the discharge is a good example of a fractal.

#### DISCUSSION

The Tesla coil consists of primary and secondary resonant circuits tuned to the same frequency (f = 1/2(pi)(LC)½) of the order of 100 kHz to 1 MHz and designed to have the highest possible Q (lowest circuit loss). The secondary capacitance Cs is predominantly distributed capacitance due to the proximity of adjacent windings, and thus the secondary behaves much like an open circuit transmission line with a resonance whenever the electrical length is an odd multiple of a quarter wavelength. The Tesla coil is normally designed to operate at the lowest resonant frequency of the secondary to avoid a voltage maximum other that at the top of the secondary coil. If the coupling between the primary and secondary is adjusted to be near the critical value (kQ ~ 1), then the secondary voltage is given approximately by Vs = Vp(Ls/Lp)½ independent of the turns ratio. In practice one would normally construct the secondary coil and then adjust Cp, Lp and the coupling constant k to give the largest Vs for a given Vp. The Tesla coil will have to be retuned depending upon what is connected to the secondary. Taps on the primary are useful for this purpose.

The input voltage Vp can be produced in a number of ways. The usual way is to connect the input through a rotary spark gap to the secondary of a high voltage (several kV) transformer connected to the ac power line through a current-limiting inductor. The opening and closing of the rotary gap (typically a few hundred pulses per second) creates a ringing voltage waveform after each opening. The spark gap and transformer can also be inserted in series between Cp and Lp to create a ringing waveform after each closing of the switch. The acoustically noisy spark gap can be replaced with a thyratron or ignitron and triggered from a source that is phase-locked to the 60 Hz power line. The voltage Vp can also be derived from a high voltage, vacuum tube oscillator circuit.*****

*****See an old issue of The Radio Amateur's Handbook, published yearly by the American Radio Relay League: 225 Main Street, Newington, Connecticut 06111.

#### HAZARDS

With a Tesla coil, it is possible to touch the very high voltage secondary without being electrocuted because of the skin effect. The high frequency currents flow on the surface of the skin rather than through the body where damage to the heart could occur. Furthermore, the muscles of the body are less sensitive to high frequencies than they are to dc or low-frequency ac. Even so, it is probably best not to allow anyone with a weak heart to come into contact with the high voltage. In fact, with large Tesla coils, the use of volunteers is not recommended. In some Tesla coil designs the primary has 60 Hz voltages present, and these could be lethal. A more serious danger is the possibility of burns to the skin, especially if the discharge strikes the skin directly. For this reason, the discharge should only be drawn to the body through a metal object which makes a large area of contact with the skin. If the discharge strikes an unsuspecting person, the result would surely be startling, and the recoil could cause injury.

If the Tesla coil is used to light a fluorescent tube, care should be taken to avoid breaking the tube. The powder that lines the inner walls of such tubes as well as the mercury that they contain are highly poisonous.

#### REFERENCES

1. M. Cheney, Tesla: Man Out of Time, Prentice-Hall: Englewood Cliffs, New Jersey (1981).

2. I. Hunt and W. W. Draper, Lightning in his Hand: The Life Story of Nikola Tesla, Sage Books: Denver (1964).

3. T. C. Martin, The Inventions, Researches and Writings of Nikola Tesla, Omni Publications: Hawthorne, California (1977).

4. J. J. O'Neill, Prodigal Genius: The Life of Nikola Tesla, Neville Spearman: London (1944).

5. L. Reukema, Experimenter 4, 309 (1925).

6. R. C. Dennison and E. H. McClelland, Electrical Journal 28, 328 (1931).

7. K. Richardson, Popular Electronics 12, 72 (1960).

8. C. Caringella, Popular Electronics 21, 29 (1964).

9. E. Kaufman, Popular Electronics 21, 33 (1964).

10. V. Vollano, Popular Electronics 71, 29 (1989).

11. G. Breit and M. A. Tuve, Nature 121, 535 (1928).

12. G. Breit, M. A. Tuve, O. Dahl, Phys. Review 35, 51 (1930).

13. C. R. J. Hoffmann, Review of Scientific Instruments 46, 1 (1975).

14. I. Boscolo, G. Brautti, R. Coisson, M. Leo, A. Lunches, Review of Scientific Instruments 46, 1535 (1975).

15. H. S. Norris, Induction Coils - How to Make, Use, and Repair Them, Spon and Chamberlain (1909).

16. G. F. Haller and E. T. Cunningham, Tesla High Frequency Coil - Its Construction and Uses, D. Van Nostrand Co.: New York (1910).

17. A. D. Bulman, Models for Experiments in Physics, Crowell Co.: New York (1966).

## 4.4

A screen cage large enough for a person to enter is used with a Tesla coil or Van de Graaff generator to illustrate the fact that a closed conducting surface is an equipotential.

#### MATERIALS

• closed screen cage
• Tesla coil or Van de Graaff generator
• 2 fluorescent tubes (optional)
• metallic tinsel (optional)

#### PROCEDURE

The Faraday cage is simply a cage constructed of metal or screen so as to completely enclose the interior with an electrically conducting boundary. A Faraday cage large enough to put a person in allows even more dramatic demonstrations. In such a case, a door should be provided to allow the person to enter and leave. In 1837, Faraday performed an experiment in which he had someone enclose him with his field-measuring instruments in a large (12-foot) conducting cube charged to a high voltage until sparks flew from its corners, and proceeded to convince himself that he could not detect the fact that the cage was electrically charged. The Faraday cage is often used in conjunction with a Tesla coil or Van de Graaff generator.

The most spectacular demonstration is to put a person inside a grounded Faraday cage and turn on a large Tesla coil or Van de Graaff generator outside the cage. It is especially good to have a celebrity known to the audience enter the cage. The discharge from the Tesla coil or the sparks from the Van de Graaff generator strike the cage but do not hurt the person inside. The person inside can hold a fluorescent tube which will not light and can even touch the inside of the cage without harm. The electric currents flow on the outside of the cage, and the interior of the cage is all at the same electric potential. The person should not stick a finger or other object through a hole in the cage, however. If someone in the front row is given a fluorescent tube, it can be made to light while the one in the cage does not. After the demonstration, one can point out that the person in the cage was in fact safer than those in the front row.

With a sufficiently well-constructed Faraday cage, it should be possible to put a portable transistor radio inside and not be able to receive any radio stations on either the am or fm bands. To do this requires all the seams to be tightly sealed electrically and the holes in the conductor not to be too large. This provides a sensitive way to test the quality of the Faraday cage.

With a sufficiently large Van de Graaff generator or Tesla coil and an insulated platform for the cage to rest on, it is possible to raise the voltage of an ungrounded cage to a high level with a person inside. Metallic tinsel such as used to decorate Christmas trees when attached to the outside of the cage will stick out like the hair of a person on a Van de Graaff generator, but similar tinsel inside the cage will show no response.

#### DISCUSSION

The Faraday cage illustrates a number of important safety considerations for someone caught in a lightning storm or required to work with high voltage electricity. The safest place to be in a lightning storm is inside a closed metal container such as a building with a steel frame or an automobile (but not because of the rubber tires, which are far too small to prevent a lightning strike and contain carbon black, making them relatively poor insulators). A chicken coop or a garbage can with a lid would also do! One of the functions of a lightning rod is to shield the interior of a building by carrying the corona currents from the air around the outside of the building through a grounded conductor thereby making the building all at the same electrical potential. High voltage electrical circuits are normally constructed inside grounded metal enclosures to protect someone outside the enclosure. The metal enclosure forms an equipotential surface at the same voltage as the earth and prevents any of the voltages inside the cage from reaching the outside.

The Faraday cage is named after Michael Faraday (1791-1867), a self-educated, English physicist and chemist whose lectures for the public in the 1840's became so popular that they helped save the Royal Institution of Great Britain from near bankruptcy[1]. His lectures were attended by Charles Dickens and by Prince Albert, the husband of Queen Victoria, and Prince Edward, her son (later Edward VII). In 1826 Faraday also began a series of immensely popular, special Christmas lectures for children which have continued up to the present. Since 1966, these lectures have been televised and broadcast throughout Britain.

#### HAZARDS

There are no safety hazards to the person inside the cage so long as the cage is tightly shut and no part of the body protrudes through holes in the cage. For the safety of those outside the cage, the cage should be thoroughly grounded, but this is not required to protect the person inside. With a large Tesla coil, the experience can be frightening, and so it should only be done with a brave and willing volunteer.

#### REFERENCE

1. G. Caroe, The Royal Institution: An Informal History, John Murray: London (1985).

## Gas Discharge Tube

A partially evacuated tube filled with various gases at low pressure and connected to a high voltage electrical source illustrates properties of electrical discharges.

#### MATERIALS

• gas discharge tube
• vacuum pump
• high voltage power supply, current-limited
• various nonflammable gases
• pressure, voltage and current meters (optional)

#### PROCEDURE

Electrical discharges in low pressure gases make colorful and educational demonstrations[1-4]. The apparatus required consists of a glass tube a meter or two long and at least several centimeters in diameter. The tube can be sealed off at the ends with rubber stoppers. One of the stoppers contains a hole through which a glass tube can be inserted to allow the tube to be filled with various gases and partially evacuated. An electrode of some type such as a nail can be passed through each stopper and connected to a high-voltage, low-current source of electricity. Direct current is preferred, but 60 Hz from the power lines or even higher frequency from a small Tesla coil can also be used. A voltage of 1000 volts or more is required, but the current can as small as a few milliamperes. Higher currents produce a brighter discharge but increase the danger of electrocution. The discharge is most stable if the power supply has a relatively high output impedance, since the current drawn by the discharge is a sensitive function of the applied voltage. The tube can be evacuated by means of a water aspirator, but a mechanical vacuum pump capable of a producing a vacuum of a few millitorr is preferred. Pressure, voltage and current meters visible to the audience are useful additions. If a vacuum pump is not available, some effects can be seen using a pre-sealed discharge tube such as a fluorescent lamp or other special gaseous discharge lamp such as a geissler tube*.

*Available from Carolina Biological Supply Company, Central Scientific Company, Frey Scientific Company and Sargent-Welch Scientific Company

The tube is initially filled with air at atmospheric pressure, and the voltage is applied. Normally, there will be no glow from the tube and no current drawn. As the tube is slowly evacuated, a pressure is reached at which current abruptly begins to flow, and sparks are seen emanating from the electrodes. As the pressure is further reduced, a steady violet glow will appear throughout the tube. At even lower pressure, alternating light and dark bands (Crookes and Faraday dark spaces) can be seen along the length of the tube, until eventually the glow is completely extinguished. Note that the striations are always convex toward the cathode. The pump can then be turned off, and the progression repeated in reverse as air is bled back into the tube. The demonstration can then be repeated with other nonflammable gases such as neon, carbon dioxide and argon. Each will produce a glow with a distinctive color characteristic of the gas. A magnet placed near the discharge can be used to effect its shape. It can be pointed out that a glow discharge tube does not obey Ohm's law.

#### DISCUSSION

This demonstration illustrates how the electrical conductivity of a gas varies with pressure. Normally, gases are electrical insulators because the molecules of the gas are electrically neutral, consisting of negative electrons bound to equally positive nuclei. The few free charges that do exist, perhaps as a result of cosmic rays, are accelerated by the electric field along the length of the tube but collide with neutral gas molecules and lose their energy before they are able to ionize them. As the pressure is reduced, the mean free path for slowing down of the free charges is lengthened, and the charges acquire enough energy to ionize other gas molecules, producing additional free electrons, which in turn ionize others, resulting in electrical breakdown. The alternating light and dark bands result from electrons emitted from the cathode that are alternately accelerated and then stopped as they acquire sufficient energy to be absorbed by the gas. At even lower pressure, the mean free path will exceed the length of the tube, and the free charges will rarely collide with the gas molecules, and a discharge will not occur. The light emitted is a result of excitation of the gas atoms from their ground state to excited states and the subsequent emission of photons of light as they decay back to their ground state. Since atoms of different chemical elements have different energy levels, the color of the discharge depends upon the gas used.

This demonstration can serve as an introduction to the subject of plasma physics[5]. Plasmas represent the fourth state of matter, along with solids, liquids and gases. Plasmas represent the end result of raising the temperature of any substance, most of which transform successively through each of the four states. Plasmas differ from ordinary gases in that they are electrical conductors, a difference that is as remarkable as the differences among the other three states. Plasmas are relatively rare on the earth but constitute upwards of 99% of the matter in the universe. Examples of plasmas in nature include the Aurora Borealis, the ionosphere of the earth, the solar wind and the material of the sun and stars. Laboratory plasmas are of great current interest because certain atoms such as isotopes of hydrogen at temperatures in excess of 100 million degrees will release energy by the process of nuclear fusion, a potentially clean and abundant source of energy[6,7].

#### HAZARDS

The main hazard is electrical shock from the voltage connected to the tube. There is also a possibility of implosion of the glass tube when it is evacuated and explosion if it is pressurized above atmospheric pressure (not recommended).

#### REFERENCES

1. F. A. Maxfield and R. R. Benedict, Theory of Gaseous Conduction and Electronics, McGraw-Hill: New York (1941).

2. C. L. Strong, Scientific American 198, 112 (Feb 1958).

3. B. Z. Shakhashiri, Chemical Demonstrations, The University of Wisconsin Press: Madison, Wisconsin, Vol 2 (1985).

4. H. F. Meiners, W. Eppenstein, R. A. Oliva and Thomas Shannon, Laboratory Physics, John Wiley & Sons: New York (1987).

5. F. F. Chen, Introduction to Plasma Physics, Plenum Press: New York (1984).

6. A. S. Bishop, Project Sherwood, Addison-Wesley Publishing Company: Reading, Massachusetts (1958).

7. T. K. Fowler and R. F. Post, Scientific American 215, 21 (Dec 1966).

## 4.6

A Wimshurst electrostatic generator is used to produce high voltages at moderate currents to illustrate many principles of electrostatics.

#### MATERIALS

• Wimshurst electrostatic generator with accessories*
*Available from Carolina Biological Supply Company, Central Scientific Company, Edmund Scientific, Fisher Scientific, Frey Scientific Company and Sargent-Welch Scientific Company

#### PROCEDURE

A simple triboelectric device capable of producing moderately high voltages for electrostatic demonstrations is the Wimshurst generator, invented in 1878 by James Wimshurst. Other similar devices were invented by the German physicists, Toepler, Holtz and Musaeus and more recently by the American, A. D. Moore who performed interesting lecture demonstrations with his Dirod generator[1]. In addition to making sparks jump through the air, these devices are capable of operating X-ray tubes, cathode ray tubes, and most types of vacuum and gaseous discharge tubes. They can be used to deflect the flame of a candle burning near a pointed electrode at high voltage or between the plates of a charged capacitor[2]. A dust or ethanol vapor explosion can be ignited with the spark from these machines. They can be used to drive an electrostatic motor or a pinwheel with corona or to ring a set of chimes consisting of a metal ball suspended with an insulated thread between two bells at opposite electric potential or to separate a mixture of salt and pepper or to precipitate smoke from the air[3-8]. Accessories for such demonstrations are available from the same vendors who supply the Wimshurst generators, although many can be constructed from inexpensive, readily available components[9].

#### DISCUSSION

These devices work by means of rotating plastic or glass plates that become electrically charged and transfer their charge to a set of external combs which are typically connected to a pair of Leyden jar capacitors. The disks can be rotated by means of a hand crank connected to the disks with an insulated belt. A useful improvement is to add a motor drive with variable speed control. The capacitors can be discharged through a pair of metal balls whose proximity to one another can be adjusted. The distance over which a spark will jump between two spherical balls can be used as a reasonably accurate measure of the voltage (see Table 4.2). Although these devices produce lower voltage than Van de Graaff generators, they can produce moderately large currents. In most cases the Leyden jars can be removed from the circuit to illustrate the difference between a high-current and a low-current discharge of similar voltage.

#### HAZARDS

Most commercially available Wimshurst generators are designed so that a non-lethal amount of electrical energy is stored in the Leyden jars. However, a discharge to the body is surely painful, and might startle one into an accident. If significant additional capacitance is connected to the output of the Wimshurst generator, the hazard can increase substantially. The spark can also cause burns and ignite flammable or volatile materials nearby.

#### REFERENCES

1. A. D. Moore, Electrostatics: Exploring, Controlling, and Using Static Electricity, Doubleday-Anchor: Garden City, New York (1968).

2. M. Robinson, Am. Journ. Phys. 30, 366 (1962).

3. M. Robinson, Bibliography of Electrostatic Precipitator Literature, Southern Research Institute: Birmingham, Alabama (1969).

4. F. T. Cameron, Cottrell, Samaritan of Science, Doubleday: Garden City, New York (1952).

6. A. D. Moore, ed., Electrostatics and its Applications, John Wiley & Sons: New York (1973).

7. J. Bohm, Electrostatic Precipitators, Elsevier Scientific Publishing Company: New York (1982).

8. J. S. Miller, Physics Fun and Demonstrations, Central Scientific Company: Chicago (1974).

9. W. R. Mellen, Phys. Teach. 27, 86 (1989).

## Approximate Gap Spacing (in cm) For Electrical Breakdown Between two Identical Spheres of Varying Diameters[1]

```                          Sphere Diameter (cm)
kV        2.5       3.0       4.0       5.0       10.0

10        0.30      0.30      0.30      0.30      0.30
20        0.61      0.61      0.61      0.61      0.61
30        0.95      0.95      0.95      0.95      0.95
40        1.40      1.32      1.30      1.30      1.30
50        2.00      1.82      1.73      1.71      1.65
60        2.81      2.40      2.21      2.16      2.02
70        4.05      3.16      2.80      2.68      2.41
80                  4.40      3.50      3.26      2.82
90                            4.40      3.93      3.28
100                                      4.76      3.75```

## Exploding Wire

A thin wire or strip of aluminum foil is vaporized by discharging a large capacitor into it.

#### MATERIALS

• 60-µF, 10-kV capacitor with charging circuit*
• class A ignitron or spark gap switch
• large voltmeter, 10-kV full scale (optional)
• Thin copper wire (#22 gauge) or strip of aluminum foil
*The same apparatus can be used in a can crusher demonstration (see Chapter 5)

#### PROCEDURE

The operation of a capacitor is explained to the audience. It is likened to a car battery, but with much higher voltage. The capacitor is charged to a good fraction of its rated voltage and then discharged with an ignitron or spark gap switch into a thin wire or strip of aluminum foil, about 20 cm long which is instantly vaporized. The audience should be warned to cover their ears, since the resulting noise can be quite loud. A protective piece of plexiglas is placed between the wire and the audience, and the demonstrator wears protective eyewear and stands at least six feet away.

#### DISCUSSION

This demonstration exhibits in a dramatic way the fact that electricity is just another form of energy. In the process, the electric energy is converted into five other forms--motion, heat, sound magnetism and light. The wire or foil usually completely disappears, although it is doubtful that it all vaporizes. More likely, a portion vaporizes and the remainder is flung into some distant corner of the room by the magnetic forces.

The stored electrical energy is CV2/2 or about 1920 joules when the 60-µF capacitor is charged to 8 kV. This can be likened to a 50-kg person raised 3.9 meters into the air, or the energy in about 8 food calories.

#### HAZARDS

The amount of energy contained in a capacitor of this size is deadly. Electrocution can result instantly if one comes into contact with the terminals of the capacitor while it is charged. The wire explodes with considerable force and noise. Some voltage is generally left on the capacitor after the wire explodes. One should practice at reduced voltages, and take the necessary precautions to prevent the hot wire from being thrown out into the audience. The audience should be warned of the impending noise. Capacitors have been known to short internally and explode. The capacitor should not be in direct line-of-sight of the audience. The charging supply should be interlocked so that a curious spectator can't initiate a charge after the lecture.

J. C. Sprott