Here is yet another essay about electromagnetic field (EMF) cancer scares. But hear me out—this essay is different from all of the previous demands for an epidemiological recount. We have been, and will continue to be, in a never-ending war involving epidemiology—population studies that point to an increased risk of cancer, especially childhood leukemia, for those living under the influence of electromagnetic fields. But if EMFs cause cancer, the effect is so slight that every epidemiological result is open to statistical question.

As an example of “statistical variation”: Honestly toss an honest coin into the air 10 times, and keep track of the number of heads and tails. Repeat over-and-over again. The results are plotted in Fig. 1. The probability of getting 5 heads and 5 tails is not at all 100%; it is only 25%. The probability of getting 6 heads and 4 tails is 21%; and so forth. The point is that statistical variation is a fact of life (and cancer) that lends itself to endless dispute.

Fig. 1- Illustration of what is meant by “statistical variation.” The diagram depicts the probability of getting various combinations if a coin is honestly tossed into the air 10 times. The probability of getting 0 heads and 10 tails, or 10 heads and 0 tails, is 1/1024 ≈ 0.001; the probability of getting 1 head and 9 tails, or 9 heads and 1 tail, is 10/1024 ≈ 0.010; and so forth. The probability of getting 5 heads and 5 tails is only 252/1024 ≈ 0.246. The summation of all the probabilities is, of course, one.

Consider this story associated with cellular telephones: In one of the well-publicized claims that was initiated in 1993, a man blamed his wife’s use of a handheld cell phone for her death due to brain cancer. The media, ever eager to report information on any situation that might be construed as being harmful to citizens, whether fully substantiated by scientific evidence or not, “exposed” this incident as a hitherto unknown cause of cancer. In a few days, cell phone stock prices dropped by 17%. (The court eventually dismissed the case.) The Cellular Telephone Industry Association (CTIA), despite its own studies that concluded there was very low or negligible probability for producing any adverse health effects due to using cell phones, decided to allot additional funds to further study the issue. Now, after spending $25 million, the results are as confusing as ever, for the reason given above (statistical variation).

But I propose to completely bypass and ignore the epidemiological monster by only considering the actual effects that EMFs have on the body. The following is offered by way of background information:

(Much of this essay is lifted from [1].)

With the full knowledge of the uncertainties inherent in many of the studies of EMFs, and that scientific data must always be accompanied by qualifying statements about probability, accuracy, and precision, experts long ago decided that the best course of action was to examine and select the best available scientific studies and to construct guidance and reasonable exposure limits in the overall interest of protecting public health. The designers of electrical equipment and power stations, as well as architects, could then adhere to valid safety standards that would, it was hoped, reassure the general public. This the American National Standards Institute (ANSI), the Institute of Electrical and Electronics Engineers (IEEE), and other relevant organizations set out to do many decades ago.

One of the main activities of ANSI, IEEE, and similar organizations is to generate consensus exposure standards before people go off in many different directions. With regard to non-ionizing radiation, the IEEE set up an interdisciplinary group of approximately 125 people, including biomedical engineers, biophysicists, and cancer researchers. The committee revised a previous publication, issued by the American National Standards Institute as ANSI C95.1-1982. The group started out by compiling a data base consisting of 321 papers, all peer reviewed before publication, all representative of the current state of knowledge on radio-frequency bioeffects. Eventually, the committee produced a 76-page document, IEEE C95.1-1991 [2]. The lengthy title tells it all: *IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300 GHz*. Notice that the document does not consider EMFs below 3 kHz. (A new document, C95.6, covers the 0 to 3 kHz range.)

This ANSI/IEEE standard is supposed to be subjected to review at least every five years for revision or reaffirmation, depending on the significance and validity of new information.

Strong EMFs can produce harm via shock, burns, or internal heating. Professionals who employ electromagnetic energy in their work are usually well trained on how to avoid injury when employed in a high-field environment that may exceed the ANSI/IEEE safety levels. For the general public, however, the ANSI/IEEE standard sets limits at which there is scientific consensus that the general public can safely experience continuous whole-body exposure. The standard for safety levels is summarized in the curves of Fig. 2. The curves depict electric and magnetic field strengths and power density versus frequency. (Minor changes have been made to simplify the presentation for the present essay.)

Fig. 2- Maximum permissible exposure (MPE) limits of ANSI/IEEE C95.1-1991 (with minor changes made to simplify the presentation). The valley at a frequency of 100 MHz approximately corresponds to resonance of the human body. The three MPE curves meet at 100 MHz because the power density of 2 W/m^{2} is the same as that of the 27 V/m electric field or the 0.1 µT magnetic field. Some important applications are not shown, for the sake of clarity: Cordless phones at 900 and 2400 MHz (33.3 and 12.5 cm); cellular phones from 800 to 2000 MHz (37.5 to 15 cm).

For the electric field, below f = 1.34 MHz, the standard specifies a maximum permissible exposure (MPE) level of 600 volts/meter (V/m). For the magnetic field, below f = 100 kHz, it specifies an MPE level of 200 microteslas (µT). A phenomenon that was confirmed from prior studies is a valley at the center, at around 100 MHz; the reason for the dip is that the human body is resonant in this region. The wavelength at 100 MHz is 3 m; for a structure shaped like a human body, resonance occurs at around 0.4 wavelength, or a length of 1.2 m (4 ft). The MPE dip is very broad, to accommodate infants as well as tall adults. The significance of resonance is that the body more efficiently absorbs incident radiation at this frequency, so the safety levels have to be reduced.

At frequencies below resonance, where the human body is much less than 0.4 wavelength long, one must consider separately the electric and magnetic fields because their effects are different. In keeping with this, in Fig. 2 the magnetic and electric field curves are separated below 100 MHz. At 100 MHz, the MPE power density value is 2 W/m^{2}, and the three MPE curves are identical. For an electric field, the MPE is 27 V/m, as shown. For a magnetic field, the MPE is 0.1 µT.

For the electric-field curve: The induced current increases as the frequency is increased; at the same time, because of the inertia of ions, body cell membranes becomes more immune to external-field stimulation. The two effects tend to cancel each other, so the 600 V/m MPE limit is allowed to remain constant up to a frequency of 1.34 MHz. To maintain safe MPE levels above 1.34 MHz, however, the ANSI/IEEE limits are gradually lowered. At 30 MHz, the safe limit of 27 V/m is reached; this is the MPE for Citizens Band radio (30 MHz) and cordless telephones (50 MHz). Manufacturers of these devices are well aware of, and take great pains to abide by, the ANSI/IEEE limits.

For the magnetic field curve: As frequency increases, so does the induced voltage, but the current density needed to stimulate the nervous system also increases because ion movement is replaced by vibration, as implied above. Therefore, the 200 µT MPE limit is allowed to remain constant up to 100 kHz. To remain within safe limits above 100 kHz, however, the MPE magnetic field limit becomes more stringent, decreasing gradually until, at 100 MHz, it is only 0.1 µT.

We next shift our attention to the MPE power density curve: At resonance, at 100 MHz, how much of the incident power is absorbed by the body? This cannot be answered exactly because there are too many variables: weight, body shape, size, orientation with respect to the field lines, and so forth.

At resonance, as mentioned above, the ANSI/IEEE safe limit for power density is 2 W/m^{2}. In what follows, it is more “user friendly” to look at the safe level on a cm^{2} basis: 2 W/m^{2} equals 0.0002 W/cm^{2}, or 0.2 mW/cm^{2}. It then becomes obvious that 0.2 mW, spread over a square centimeter, is flea power; it is far below the level at which an appreciable temperature rise can occur.

What happens at the very high frequencies above 100 MHz? Now the length of a wave becomes relatively small compared with the length of a human body. The electric and magnetic fields become inseparable; each of them becomes equally important. In that event, it is most convenient to combine them, in effect, as is done in the single power-density curve of Fig. 2.

To a first approximation the body can be considered to be a large container of water. At and above 100 MHz, three effects are important when an EMF encounters this biological material:

1)*Current enhancement due to resonance*: As previously noted, a sharp departure from the idealized situation occurs around 100 MHz. Here there can be increased circulating currents because of resonance; the MPE valley compensates for this in the vicinity of 100 MHz.

2)*Reflection*: Because the biological media is different from air, some of the energy is reflected and the remainder is absorbed.

3)*Limited depth of penetration*: Because the body is a poor electrical conductor relative to copper, say (it is a “lossy medium”), the absorbed power is rapidly attenuated.

Nobody expects the simple air-water interface model to be accurate for a human at and above 100 MHz. It is necessary to experimentally determine the reflection coefficient and other properties. Fortunately, reliable data were published by C.C. Johnson and A.W. Guy [3]. Some of the pertinent values for an air-muscle interface and associated MPE values based on Fig. 2 are given in Table 2. (The “Incident power density” values in Table 2 are the MPE values given in Fig. 2.)

As frequency increases above 100 MHz, there is a sharp reduction in the depth of penetration. Because of the net effects, above 300 MHz the ANSI/IEEE power-density limit is accordingly allowed to increase gradually until, at 15 GHz, it is 10 mW/cm^{2}. Along the way we have cellular telephones at around 800 MHz (safe limit 0.5 mW/cm^{2}; microwave ovens at 2.4 GHz (safe limit outside the oven is 1.6 mW/cm^{2}); and police radars above 15 GHz (safe limit 10 mW/cm^{2}). In all of these applications, the energy entering the body is minuscule.

According to Table 2, the MPE absorbed power at f = 1 GHz is 0.27 mW/cm^{2} (mostly absorbed in the first 3 cm of muscle tissue); at f = 10 GHz, it is 3 mW/cm^{2} (mostly absorbed in the first 0.34 cm of muscle tissue). The latter depth of penetration is little more than skin deep, and therefore renders EMFs at 10 GHz (and higher) harmless to internal tissues.

Specifically, with regard to cell phones, at a frequency of 1 GHz (or 1 billion cycles/sec), which is approximately where they operate, the ANSI/IEEE MPE is around 0.7 mW/cm^{2}. Hold a cell phone next to your ear, and assume that it puts out 0.7 mW/cm^{2}. But your body reflects most of this, absorbing only 0.3 mW/cm^{2}.**This is the “body power.”** What can it do? What does it do?

You know that a microwave oven puts out plenty of heat; many people, surrounded by all of this electronic stuff, visualize themselves as living in a sort of microwave oven. Are they realistic? Well, with 0.3 mW spread over a square centimeter, the heating effect is completely negligible. There are more insidious effects to worry about. Besides, your head temperature normally varies; bear in mind that a 7ºF (4ºC) rise above a normal temperature of 98.6ºF (37ºC) is one of the body’s defense mechanisms during an infection. In other words, a hot-headed cell-phone conversation is a figment of the imagination.

As noted above, the cell-phone transmission has a depth of penetration, into the body, of 3 cm. That is scary; just visualize the 1 GHz signal getting into your body to a depth of 3 cm. But before you discard the cell phone (or at least remove its puny battery), reflect upon the fact that every radio station imaginable is generating a signal that deeply penetrates your body. Swallow a radio receiver, hook it up to an earphone, and listen to your favorite AM program (but remember to tune it beforehand).

So how can the feeble cell-phone signal cause cancer? Supposedly, by shaking-up the DNA molecule in a typical cell, such as the one portrayed in Fig. 3. Just inside the body, before it dies out, the signal has an electric field strength of 0.1 volt/cm. (Remember that this is the maximum permissible exposure — it is much stronger than an ordinary radio signal.) Let’s take the worst case: The field seizes the lightest ion, a hydrogen ion, and violently shakes it back and forth. Your body is full of hydrogen, of course (and it doesn’t depend on what you had for lunch). How much will it shake? At a frequency of one billion shakes per second, not much. Since we know the weight of a hydrogen ion, and how much electric charge it carries, one can calculate that it will vibrate around 0.3 angstrom. What does that mean in plain English? The diameter of a water molecule is 3 angstroms, so judge for yourself. In my opinion, this cannot cause changes in a DNA molecule. But this is only a personal opinion; it is not for me to suggest that the millions spent by the CTIA should have been spent, more wisely and morally, on the prevention of cancer by changing some other aspects of our life style.

Fig. 3- An idealized excitable cell, at rest, in the human body. Only the membrane and DNA molecule are pertinent to the “cancer scare.” The membrane is a good electrical insulator: 75 mV across a thickness of 7.5 nm corresponds to an electric field of ten million V/m. The membrane shields the DNA molecule, in the cell’s interior, from external voltages and currents.

The above calculation is not valid at lower frequencies because an ion that is surrounded by water molecules, say, cannot undergo a relatively large vibration amplitude without bumping into its neighbors (this is an example of “ion immobility”). The notion that the DNA molecule can be torn apart by vibration is difficult to sustain because *all *of the elements of the body are under constant bombardment in accordance with the kinetic theory of heat; in fact, the constant shaking is vitally important for the completion of physical and chemical processes.

What are the other EMF transmissions that we have to worry about? Manufacturers of microwave ovens guarantee that, if you close the door, the transmission that reaches the outside, and the resulting body power, are below the MPE level. (Ironically, in diathermy equipment, energy at microwave-oven frequencies is used to destroy tumors via hyperthermia, and to effect mild heating of internal tissues in physical therapy.) Cordless telephones operate on much less power than cell phones, so they are harmless. What remains to worry about is the great bugaboo of the electric power industry — the danger from 60 Hz power. Here the cancer claims come from epidemiological surveys and animal studies. As a result, many people have been led to believe that we should prudently avoid EMFs. Underground power lines are expensive to install, but perfectly safe. Above ground, however, we should abandon electric blankets and hair dryers, move beds away from walls, use manual rather than electrical appliances, reside in a house far removed from overhead transmission lines, and avoid sitting in front of a video display or television screen (although here there is also some concern for deadening program material). According to one authority [4], in 1994, it was “… estimated that the cost of prohibiting the installation of new power transmission lines could amount to 16 billion dollars each year in the United States alone.” The power companies are notoriously lax in fighting cancer scares; the costs are inevitably passed on to the consumers in this generation and the next.

For technical reasons, not surprisingly, the effects at a frequency of 60 Hz are quite different from those at 1 billion Hz. Now the electric and magnetic fields have to be considered separately:

For the electric field, a reasonable MPE level is 6 V/cm. Under a high-voltage transmission line, visualize all of that voltage between the line and your head, as illustrated in Fig. 4. Again, a scary situation. But the transmission line is high above ground for this very reason, and field cancellation configurations are used; when you figure it out, the field is certain to be 6 V/cm or less even if you are directly underneath the line. The distance is all-important.

Fig. 4- Electric fields in the presence of a human body. The intensity under the source is 600 V/m. The originally vertical electric field lines become warped because the body is an electrical conductor. (a)”Direct current” (dc) conditions result in a head-to-toe voltage that is zero; (b)”Alternating current” (ac) conditions result in an induced current (and voltage) that oscillates back and forth, through the body, in synchronism with the electric field. The dual arrows symbolize the alternating nature of the field.

What does this electric field do that is detrimental? If you are standing under a transmission line, it causes current to flow from head to toes, and back again from toes to head, 60 complete cycles per second, even though no current actually enters the body through the air insulator (your body acts as a capacitor). But the head-to-toes voltage is close to zero, and the amount of current is only 0.0002 µA/cm^{2}. This is so small that it requires a heroic degree of self-deception to imagine that it could produce any adverse biological effects. With regard to triggering any nerve cells, the peak current during a nerve cell discharge is 800 µA/cm^{2} [5], so the 60-Hz induced current is minuscule. There are thousands of 800 µA/cm^{2} discharges in your nervous system every second—that is what an EEG and ECG picks up.

With the magnetic field, however, we cannot be so complacent. Here a reasonable MPE is 200 µT (which is about four times as strong as the Earth’s magnetic field). But your body is a semiconductor—somewhere between copper and an insulator such as glass—so it acts like (you’ve been called many things but never this) a one-turn transformer secondary. Exposure in the home rarely exceeds 10 µT; with 200 µT, however, your torso picks up around 0.6 µA/cm^{2} in the loop that is indicated in Fig. 5. Is this serious? Again, with regard to a heating effect, it is completely negligible. Compared to a normal discharge, can 0.6 µA/cm^{2}damage a DNA molecule? Only untold millions devoted to further research can answer that one. But such research should be funded in proportion to the probability of adverse health effects being produced by EMFs compared with a myriad of other environmental carcinogenic influences.

Fig. 5- A human body in the presence of an alternating magnetic field. In this case, the field lines are horizontal, at right angles to the front surface of the body. Although the body is almost completely nonmagnetic, the field results in circulating induced currents (and voltages). The most important of these, the torso current, is shown.

It remains to be seen if judges and juries will respect the present weight of scientific evidence represented by the ANSI/IEEE levels, or if they will bow to emotional appeals that claim that illness is caused by some external source of energy, such as EMFs. We are exposed to natural radioactivity from radon; manmade pollutants from automobile exhaust and industrial gases; cigarette smoke; chemical residues from pesticides and herbicides; and self-inflicted abuse from excessive dietary fat, alcohol consumption, and ultraviolet rays from the sun. There are plenty of non-electromagnetic-field issues to choose from, for children as well as adults.

**Appendix**

In Table 1, frequency times wavelength equals the velocity of light, 2.998 X 10^{8} m/s in air or vacuum. This is rounded out to 3 X 10^{8}.

For the probability plot of Fig. 1: The combination of n elements taken r at a time is given by

(1) C(n,r) = n!/[r!(n – r)!].

For example, the number of different ways of getting 6 heads and 4 tails is C(10,6) = 10!/[6!(4!)] = 210 out of a total of 2^{10} = 1024 combinations; then the probability is 2^{10}/1024 = 0.2051.

For a plane EMF in a vacuum, one can calculate the magnetic flux density (B) from field strength (H) via

(2) B = 4 π X 10^{-7}H.

Below f = 100 kHz, the standard specifies an MPE level of 163 A/m. Substituting into Eq. (2), we get B = 204.8 µT; this is rounded out to 200 µT in Fig. 2.

For a plane electric field in a vacuum, the strength E is given by

(3) E = (377P)^{1/2},

where P is the power density. Substituting P = 2 W/m^{2}, we get E = 27.5 V/m (rounded to 27 V/m, as shown). For the magnetic field,

(4) H = (P/377)^{1/2}.

For P = 2 W/m^{2}, we get H = 0.0728 A/m, and Eq. (2) translates this into B = 0.0915 µT. This is rounded to 0.1 µT in Fig. 2.

In Table 2: Characteristic impedance is given by

(5) Z_{0} = (µ/ε)^{1/2},where µ is magnetic permeability (4 X 10^{-7} for vacuum), ε is dielectric permittivity (8.854 X 10^{-12} for vacuum). Substituting these values, we get Z_{vacuum} = 377 ohms. For water, which has a dielectric constant of 81, we get Z_{water} = 41.9 ohms. The reflection coefficient is given by

(6) Γ = (Z_{2}-Z_{1})/(Z_{2} + Z_{1}).

For an EMF propagating from air to water, then, the reflection coefficient has a magnitude of 0.8; in other words, if the incident field has a magnitude V_{i}, the reflected field magnitude is 0.8V_{i} while the absorbed field entering the body of water has a magnitude of 0.2V_{i}. Power is given by V^{2}/R; therefore, if the incident field power is V_{i}^{2}/377, the reflected power is 0.64V_{i}^{2}/377, while the power entering the body of water is 0.04Vi^{2}/41.9, or 0.36V_{i}^{2}/377. Energy is thus conserved, of course. In general,

(7) P_{absorbed }= (1- Γ^{2})P_{incident}.

It is a simple matter to calculate the amount of shaking involved if an ion is completely mobile. Here are the figures for a representative frequency, f = 1000 MHz:

The ANSI/IEEE standard allows an incident power density of 6.67 W/m^{2}. The Johnson – Guy [3] data give a tissue reflection coefficient of 0.770, so the power absorbed is 6.67(1-0.770^{2}), or 2.71 W/m^{2}. With a characteristic impedance of 41.9 ohms, the electric field in the tissue immediately under the antenna is the square root of 41.9 X 2.71, or 10.66 V/m. A hydrogen ion has a charge of 1.602 X 10^{-19} C, so the force on an ion is this multiplied by 10.66, or F = 1.708 X 10^{-18} newton. The ion has a mass of m = 1.673 X 10^{-27} kg. The rms shaking is therefore given by F/[m(2 π f)^{2}] = 2.6 X 10^{-11 } m. This should be compared with the diameter of a water molecule, 30 X 10^{-11 }m.

In Fig. 4(b), suppose that the field originates from an infinite flat plate located 1 m above the head. Consider a 1 cm^{2} area of the head of the person depicted in the figure (the results are independent of the size of the head). Capacitance in general is given by

(8) C = 8.854 X 10^{-12}KA/L,

where K is the dielectric constaant, A is the area, and L is the distance. Substituting, the capacitance between 1 cm^{2} on the flat plate and 1 cm^{2} on the head is C = 8.854 X 10^{-16} F/cm^{2} (approximately, because curvature of field lines is ignored). The impedance is given by

(9) X_{C} = 1/(2 πfC).

At 60 Hz, we get X_{C }= 3 X 10^{12} ohm/cm^{2}. The resulting induced current in the head, in response to the 600 V/m field, is 0.0002 µA/cm^{2}.

In Fig. 5, the torso can be regarded as a one-turn transformer secondary. The induced voltage per turn depends on the magnetic flux lines within the turn:

(10) V = 2πfBA,

where A is the cross-sectional area within the one-turn torso, and B is the flux density. As an example, suppose the human torso is approximated by a rectangle that has a height of 60 cm and width of 30 cm, so that the area is 1800 cm^{2}. For a 200-µT flux density, at f = 60 Hz, the total induced voltage around the torso is 13.6 mV. The resulting current depends upon the path – less current in high-resistivity bone and fat, more in low-resistance blood. The resistivity of the most vulnerable component, axoplasm of the nervous system, is around 125 ohm-cm. One can therefore picture a loop around the torso, of cross-sectional area 1 cm^{2}, whose resistance is given by

(11) R = pL/A,

where p is resistivity, L is the length of the path, and A is the cross section. Since the length of the path is 180 cm, Eq. (11) results in R = 22,500 ohms for an “axoplasm loop,” and Ohm’s law then indicates a current density of 0.6 µA/cm^{2} at 60 Hz.

**References**

[1] Sid Deutsch & George M. Wilkening, “Electromagnetic Field Cancer Scares,” *Health Physics*, Aug 1997.

[2] IEEE C95.1-1991, “Safety levels with respect to human exposure to radio frequency electromagnetic fields, 3 kHz to 300 GHz,” IEEE, 1991.

[3] C.C. Johnson & A.W. Guy, “Nonionizing electromagnetic wave effects in biological materials and systems,” Proc. IEEE, 1972.

[4] George M. Wilkening, “Report on 30th annual meeting of the National Council on Radiation Protection and Measurement,” American Industrial Hygiene Assoc., 1994.

[5] Sid Deutsch & Alice Deutsch, *Understanding the Nervous System: An Engineering Perspective*, IEEE Press, 1993.

(Published in a shorter version in IEEE Engineering in Medicine and Biology Magazine, Jan/Feb 2002.)