Tag Archives: EMR

Could Wireless Antennas Be the Next Asbestos?

September 14, 2010

Read the entire article by Gloria Vogel in the September 13, 2010 issue of Business Insurance.


Ms. Vogel is the managing director of New York-based Vogel Capital Management.  She begins her analysis stating:

. . . an issue that mimics asbestos and is being ignored by insurers could soon hit their pocketbooks. Simply stated, everyone’s favorite form of wireless communication and commerce depends on radio frequency-producing base station antennas, which emit radio waves and microwaves that can harm humans.

Few insurance claims have been filed to date; but in all respects, RF radiation closely tracks with the early development of asbestos claims.

She continues:

Based upon data from the Bureau of Labor Statistics and U.S. Census Bureau, it is estimated that as many as 250,000 workers a year are compelled to work in close proximity and in front of RF transmitting antennas. When combined with the 15 years this issue has been in existence, the pool of potential claimants could be staggering.

Ms. Vogel clearly delineates the breadth of the issue in her definition of “the wireless ecosystem:”

The wireless ecosystem should not be confused with the much smaller commercial telecom industry. The wireless ecosystem encompasses all FCC licensees (federal, state, local and commercial), site owners, property managers, contractors, third-party workers, the utility industry, hospitals, schools and universities, church organizations, banks/financial institutions, and the insurance industry. It involves every person or entity that may be physically or financially harmed by RF radiation.

Ms. Vogel explains how workers’ antenna exposure differs from cellphone exposure and references the legal precedent from Alaska  that awarded total disability to a worker whose antenna exposure only slightly exceeded the FCC RF radiation safety limit:

The significance of this topic is overlooked by insurers because of confusion between the harmful effects of cell phones and the damage caused by wireless antennas. Because there is no proven link yet established between cell phones and cancer, insurers see little exposure from this risk.

However, there is a marked difference between radiation exposure from cell phones and exposure from wireless antenna systems: The antennas are hundreds of times more powerful. More importantly, there already is peer-reviewed science from the Institute of Electrical and Electronics Engineers linking RF radiation exposure to cognitive injuries.

In addition, legal precedent has been established for such claims in AT&T Alascom and Ward North America Inc. vs. John Orchitt; State of Alaska, Department of Labor and Workforce Development, Division of Workers’ Compensation. The July 2007 ruling affirmed a 100% disability award to a worker exposed to RF radiation that only slightly exceeded the FCC human exposure limits.

By doing so, the Alaska Supreme Court established a legal precedent that recognizes the causal link between an RF radiation exposure and cognitive or psychological injuries including reduced brain function, memory loss, sleep disorders, mood disorders and depression.

Ms. Vogel concludes by encouraging the insurance industry to be proactive about worker RF radiation safety and push for a solution from the private sector rather than to wait for government to act:

The insurance industry tends to look backwards at historical claims to project future losses. In cases of emerging risk such as the issue of third-party worker overexposure to RF radiation, it would be far better for the industry to be anticipatory rather than reactive, as claims could develop quickly. It would be in the industry’s best interests to pre-empt the plaintiffs’ bar on this issue and secure a safe workplace for those third-party workers.

P.O. Box 117 | Marshfield, VT 05658 US

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Are Your Mattress And Bedframe Killing You With EMF?

by Lloyd Alter, Toronto on 08. 2.10

The Robinsons model the latest in tinfoil pyjamas

Forget the tinfoil hat, it is time for tinfoil pyjamas. Scientific American tells us that the bed frames and box springs in most American beds are half the wavelength of TV and FM signals and are acting as antennae, causing skin and breast cancers on victims’ left sides, which are usually right were the maximum strength of the EMF would be.

How to make a tinfoil hat: instructions here

R. Douglas Fields, Ph. D, writes in Scientific American about the Swedish study by Örjan Hallberg of Hallberg Independent Research in Sweden and Olle Johansson of The Karolinska Institute in Sweden, that describes the effect:

As we sleep on our coil-spring mattresses, we are in effect sleeping on an antenna that amplifies the intensity of the broadcast FM/TV radiation. Asleep on these antennas, our bodies are exposed to the amplified electromagnetic radiation for a third of our life spans. As we slumber on a metal coil-spring mattress, a wave of electromagnetic radiation envelops our bodies so that the maximum strength of the field develops 75 centimeters above the mattress in the middle of our bodies. When sleeping on the right side, the body’s left side will thereby be exposed to field strength about twice as strong as what the right side absorbs.

The author notes that the rate of breast cancer in Japan is a lot lower than in the west, and attributes this to the fact that they do not sleep on mattresses, and their TVs operate on a different frequency.

A commenter at Apartment Therapy noted that study co-author Ollie Johansson was awarded the Misleader of the Year Award in 2004 for his work in EMF. The citation includes:

Olle Johansson receives the award as one of the most prominent representatives of the far too many scientists who, to draw attention to themselves and funding for their own activities, disseminate worry among the public in mass media by presenting unsubstantiated hypotheses as established facts…..Olle Johansson insinuates that a large number of diseases such as cancer, blood pressure problems, asthma, allergies and sleep disorders, may be caused by electromagnetic fields. He has also come to the conclusion that malignant melanomas may be caused by TV- and FM-transmissions. A few years ago Johansson received particular attention after he claimed that brain damage, and specifically mad cow disease could be caused by the use of mobile phones.

But then again, everyone is just so certain whenever we write about the possible dangers of EMF, that all those cellphone towers and cellphones, microwave ovens and electric blankets, not to mention routers and wifi are perfectly harmless. How can they be so sure?

More in TreeHugger on EMF

Should Cell Phone Towers Be Put on Residential Buildings?
Are Hybrids an EMF Health Risk?
EMF: Richard Box’s Graphic Demonstrations
A Univerisity without WifI
Spray-on Defense from WiFi and Cellphones
New Study Proves EMF Affects Living Things, Discovers Electro-bonsai Effect

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Filed under awareness, cancer, cell phone, cell tower, children, electromagnetic radiation, EMR, radiation interference, WiFi


July 23, 2010 by Paul Doyon

International Coalition for an Electromagnetic-Safe Planet (IC-ESP)

Education! Awareness! Support! Action!

(From denial to acceptance, from ignorance to awareness, from apathy to action, from selfishness to compassion.)

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International Coalition for an Electromagnetic-Safe Planet (IC-ES

received eMail 12 jul 10 by Paul Doyon.  Thank you Paul.

EMR-Updates: July 4th, 2010

International Coalition for an Electromagnetic-Safe Planet (IC-ESP)

Education! Awareness! Support! Action!

(From denial to acceptance, from ignorance to awareness, from apathy to action, from selfishness to compassion.)

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Mobile Phone Electromagnetic Radiation and Sleep

Special thank you to Angela Flynn for posting


Research from other laboratories has shown that the radio waves from a mobile phone affect the electrical activity of the sleeping brain (the ‘EEG’)’. However, these studies have mostly used one standard radio frequency, whereas the phone signal differs depending on whether we are talking, listening or leave the phone in ‘stand-by’ mode. We have separated out these three signals and find different effects on the EEG. This research program, in conjunction with the Centre for Mobile Communications Research, here at Loughborough, has shown that 30 minutes exposure to the ‘talk’ mode signal delays sleep onset.

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Lab rats with cellphones?

Our wireless lifestyle is making us all unwitting test subjects.

By Christopher Ketcham

February 23, 2010

We love our digital gadgets — “magic” devices that define cool and promise to remake our lives for the better. But there is growing evidence of a dark side to the techno-magic. Your cellphone, and any other wireless device that depends on electromagnetic (EM) microwave radiation to function, may be hazardous to your health.

Most of the bad news comes from major labs and research institutions in Europe. What they’re reporting is that using cellphones and Wi-Fi transmitters — which operate using similar frequencies — can have biological effects on the brain and body.

The scientific debate remains heated and far from resolved, as the Health section in The Times reported last week. But the research to date suggests a number of chilling possibilities as to what EM radiation may be doing to us.

For example, in 2008, neuroscientists at Swinburne University of Technology in Australia strapped Nokia phones to subjects’ heads, then turned the phones on and off. On — the brain’s alpha waves spiked. Off — the brain settled. The researchers speculated that the effect was the result of the brain “concentrating to overcome the electrical interference in brain circuits caused by the pulsed microwave radiation.”

Swedish neuro-oncologist Leif Salford, chairman of the department of neurosurgery at Lund University, has found that cellphone radiation kills brain cells in rats, especially those cells associated with memory and learning. The damage occurred after an exposure of just two hours. In duplicating earlier research, Salford also found that cellphone microwaves produce holes in the barrier between the circulatory system and the brain in rats. One potential outcome, according to Salford, is dementia.

Meanwhile, Austrian researchers reported in 2004 that cellphone radiation can induce double-strand breaks in DNA, one of the undisputed causes of cancer.

So why isn’t this a bigger issue in the U.S.? Partly because there are countervailing studies and other scientists telling us not to be worried, that the risks are low or that we just don’t know enough to say that the risks are real.

Consider the biggest study being done on the question of whether cellphones cause cancers of the brain, mouth and ear — the 13-country Interphone study conducted under the auspices of the International Agency for Research on Cancer in France. The study’s epidemiologists have looked at cancer patients and worked backward to establish cellphone habits.

The study, alas, has been fraught with controversy. The multinational researchers — U.S. scientists conspicuously not among them — have fallen into warring camps, and the full study has not been released.

However, pieces of the study have been made public. One Interphone study, for example, found that after a decade of cellphone use, the chance of getting a brain tumor goes up as much as 40% for adults. Another Interphone study reported a nearly 300% increased risk of acoustic neuroma, a tumor of the acoustic nerve. But still other Interphone researchers say their data show no increase in brain tumors — or any tumor — caused by cellphone use.

The cellphone industry lobby, CTIA — the Wireless Assn., recently said in a statement that “peer-reviewed scientific evidence has overwhelmingly indicated that wireless devices do not pose a public health risk.” Meanwhile, watchdog groups keep it vague. “The available science,” says the Food and Drug Administration, “does not allow us to conclude that mobile phones are absolutely safe, or that they are unsafe.”

So whom to believe, and what to do?

First, consider research done by Henry Lai, a biologist at the University of Washington: Only 25% of studies funded by the wireless industry show some type of biological effect from microwave radiation. Independently funded studies, however, are far more damning: 75% of those studies — free of industry influence — show a bioeffect. Some 30% of funding for the Interphone research was provided by industry, which critics say has resulted in a favorable skewing of some Interphone data.

Obviously, we need to demand more independent research into microwave radiation. In the meantime, we should also treat cellphones and other wireless gadgets with less adoration and more suspicion, and as individuals we may want to follow the lead of many nations and regulate the way we use them for ourselves.

For example, Belgium, France, Finland, Germany, Russia and Israel have publicly discouraged use of cellphones by children. (Independent research in Sweden last year concluded there was an astonishing 420% increased chance of getting brain cancer for cellphone users who were teenagers or younger when they first started using their phones.) France has gone so far as to issue a generalized national cellphone health warning, banned cellphones in elementary schools and considered outlawing marketing the phones to children.

The personal equivalent? For starters, don’t get rid of your land line. Buy a hands-free device; keep your cellphone away from your head, face and neck. Don’t carry it in your pocket for hours on end(there’s some evidence cellphones aren’t good for your sperm count).

Salford, the neuro-oncologist, has called the unregulated use of cellphones by 4.5 billion people worldwide “the largest human biological experiment ever.” It’s only common sense to do what you can to take yourself out of the guinea pig pool.

Christopher Ketcham is the author of “Warning: Your Cell Phone May Be Hazardous to Your Health” in February’s GQ.

Copyright © 2010, The Los Angeles Times

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The Basics on eSmog, electromagnetic radiation

There are so many sources, controversy, documented health hazards, testing, proof, Congressional activities, but how many know the basics, allowing them to relate it, then, to their life.

Ignorance is NOT bliss on this topic


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Electromagnetic radiation (sometimes abbreviated EMR) is a ubiquitous phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It consists of electric and magnetic field components which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. Electromagnetic radiation is classified into several types according to the frequency of its wave; these types include (in order of increasing frequency and decreasing wavelength): radio waves, microwaves, terahertz radiation, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. A small and somewhat variable window of frequencies is sensed by the eyes of various organisms; this is what we call the visible spectrum, or light.

EM radiation carries energy and momentum that may be imparted to matter with which it interacts.




[edit] Physics

[edit] Theory

Shows three electromagnetic modes (blue, green and red) with a distance scale in micrometres along the x-axis.

Main article: Maxwell’s equations

Electromagnetic waves were first postulated by James Clerk Maxwell and subsequently confirmed by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, revealing the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.

According to Maxwell’s equations, a time-varying electric field generates a magnetic field and vice versa. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on. These oscillating fields together form an electromagnetic wave.

A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of quantum electrodynamics.

[edit] Properties

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized wave propagating from right to left. The electric field is in a vertical plane, the magnetic field in a horizontal plane.

Onde electromagnetique.svg

The physics of electromagnetic radiation is electrodynamics, a subfield of electromagnetism. Electric and magnetic fields obey the properties of superposition so that a field due to any particular particle or time-varying electric or magnetic field will contribute to the fields present in the same space due to other causes: as they are vector fields, all magnetic and electric field vectors add together according to vector addition. For instance, a travelling EM wave incident on an atomic structure induces oscillation in the atoms of that structure, thereby causing them to emit their own EM waves, emissions which alter the impinging wave through interference. These properties cause various phenomena including refraction and diffraction.

Since light is an oscillation it is not affected by travelling through static electric or magnetic fields in a linear medium such as a vacuum. However in nonlinear media, such as some crystals, interactions can occur between light and static electric and magnetic fields — these interactions include the Faraday effect and the Kerr effect.

In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by Snell’s law. Light disperses into a visible spectrum as light is shone through a prism because of the wavelength dependent refractive index of the prism material (Dispersion).

EM radiation exhibits both wave properties and particle properties at the same time (see wave-particle duality). Both wave and particle characteristics have been confirmed in a large number of experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when the average number of photons in the cube of the relevant wavelength is much smaller than 1. Upon absorption the quantum nature of the light leads to clearly non-uniform deposition of energy.

There are experiments in which the wave and particle natures of electromagnetic waves appear in the same experiment, such as the diffraction of a single photon. When a single photon is sent through two slits, it passes through both of them interfering with itself, as waves do, yet is detected by a photomultiplier or other sensitive detector only once. Similar self-interference is observed when a single photon is sent into a Michelson interferometer or other interferometers.

[edit] Wave model

White light being separated into its components.

An important aspect of the nature of light is frequency. The frequency of a wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, where one hertz is equal to one oscillation per second. Light usually has a spectrum of frequencies which sum together to form the resultant wave. Different frequencies undergo different angles of refraction.

A wave consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the wavelength. Waves of the electromagnetic spectrum vary in size, from very long radio waves the size of buildings to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation:

\displaystyle v=f\lambda

where v is the speed of the wave (c in a vacuum, or less in other media), f is the frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant.

Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference.

The energy in electromagnetic waves is sometimes called radiant energy.

[edit] Particle model

Electromagnetic radiation has particle-like properties as discrete packets of energy, or quanta, called photons.[1] The frequency of the wave is proportional to the particle’s energy. Because photons are emitted and absorbed by charged particles, they act as transporters of energy. The energy per photon can be calculated from the Planck–Einstein equation:[2]

\displaystyle E=hf

where E is the energy, h is Planck’s constant, and f is frequency. This photon-energy expression is a particular case of the energy levels of the more general electromagnetic oscillator whose average energy, which is used to obtain Planck’s radiation law, can be shown to differ sharply from that predicted by the equipartition principle at low temperature, thereby establishes a failure of equipartition due to quantum effects at low temperature.[3]

As a photon is absorbed by an atom, it excites an electron, elevating it to a higher energy level. If the energy is great enough, so that the electron jumps to a high enough energy level, it may escape the positive pull of the nucleus and be liberated from the atom in a process called photoionisation. Conversely, an electron that descends to a lower energy level in an atom emits a photon of light equal to the energy difference. Since the energy levels of electrons in atoms are discrete, each element emits and absorbs its own characteristic frequencies.

Together, these effects explain the emission and absorption spectra of light. The dark bands in the absoption spectrum are due to the atoms in the intervening medium absorbing different frequencies of the light. The composition of the medium through which the light travels determines the nature of the absorption spectrum. For instance, dark bands in the light emitted by a distant star are due to the atoms in the star’s atmosphere. These bands correspond to the allowed energy levels in the atoms. A similar phenomenon occurs for emission. As the electrons descend to lower energy levels, a spectrum is emitted that represents the jumps between the energy levels of the electrons. This is manifested in the emission spectrum of nebulae. Today, scientists use this phenomenon to observe what elements a certain star is composed of. It is also used in the determination of the distance of a star, using the red shift.

[edit] Speed of propagation

Main article: Speed of light

Any electric charge which accelerates, or any changing magnetic field, produces electromagnetic radiation. Electromagnetic information about the charge travels at the speed of light. Accurate treatment thus incorporates a concept known as retarded time (as opposed to advanced time, which is unphysical in light of causality), which adds to the expressions for the electrodynamic electric field and magnetic field. These extra terms are responsible for electromagnetic radiation. When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the electric current. At the quantum level, electromagnetic radiation is produced when the wavepacket of a charged particle oscillates or otherwise accelerates. Charged particles in a stationary state do not move, but a superposition of such states may result in oscillation, which is responsible for the phenomenon of radiative transition between quantum states of a charged particle.

Depending on the circumstances, electromagnetic radiation may behave as a wave or as particles. As a wave, it is characterized by a velocity (the speed of light), wavelength, and frequency. When considered as particles, they are known as photons, and each has an energy related to the frequency of the wave given by Planck’s relation E = hν, where E is the energy of the photon, h = 6.626 × 10-34 J·s is Planck’s constant, and ν is the frequency of the wave.

One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the speed of light, relative to the observer, regardless of the observer’s velocity. (This observation led to Albert Einstein‘s development of the theory of special relativity.)

In a medium (other than vacuum), velocity factor or refractive index are considered, depending on frequency and application. Both of these are ratios of the speed in a medium to speed in a vacuum.

[edit] Thermal radiation and electromagnetic radiation as a form of heat

Main article: Thermal radiation

The basic structure of matter involves charged particles bound together in many different ways. When electromagnetic radiation is incident on matter, it causes the charged particles to oscillate and gain energy. The ultimate fate of this energy depends on the situation. It could be immediately re-radiated and appear as scattered, reflected, or transmitted radiation. It may also get dissipated into other microscopic motions within the matter, coming to thermal equilibrium and manifesting itself as thermal energy in the material. With a few exceptions such as fluorescence, harmonic generation, photochemical reactions and the photovoltaic effect, absorbed electromagnetic radiation simply deposits its energy by heating the material. This happens both for infrared and non-infrared radiation. Intense radio waves can thermally burn living tissue and can cook food. In addition to infrared lasers, sufficiently intense visible and ultraviolet lasers can also easily set paper afire. Ionizing electromagnetic radiation can create high-speed electrons in a material and break chemical bonds, but after these electrons collide many times with other atoms in the material eventually most of the energy gets downgraded to thermal energy, this whole process happening in a tiny fraction of a second. That infrared radiation is a form of heat and other electromagnetic radiation is not, is a widespread misconception in physics. Any electromagnetic radiation can heat a material when it is absorbed.

The inverse or time-reversed process of absorption is responsible for thermal radiation. Much of the thermal energy in matter consists of random motion of charged particles, and this energy can be radiated away from the matter. The resulting radiation may subsequently be absorbed by another piece of matter, with the deposited energy heating the material. Radiation is an important mechanism of heat transfer.

The electromagnetic radiation in an opaque cavity at thermal equilibrium is effectively a form of thermal energy, having maximum radiation entropy. The thermodynamic potentials of electromagnetic radiation can be well-defined as for matter. Thermal radiation in a cavity has energy density (see Planck’s Law) of

{U\over V} = \frac{8\pi^5(kT)^4}{15 (hc)^3},

Differentiating the above with respect to temperature, we may say that the electromagnetic radiation field has an effective volumetric heat capacity given by

 \frac{32\pi^5 k^4 T^3}{15 (hc)^3},

[edit] Electromagnetic spectrum

Electromagnetic spectrum with light highlighted

γ = Gamma rays
HX = Hard X-rays
SX = Soft X-Rays
EUV = Extreme ultraviolet
NUV = Near ultraviolet
Visible light
NIR = Near infrared
MIR = Moderate infrared
FIR = Far infrared

Radio waves:
EHF = Extremely high frequency (Microwaves)
SHF = Super high frequency (Microwaves)
UHF = Ultrahigh frequency
VHF = Very high frequency
HF = High frequency
MF = Medium frequency
LF = Low frequency
VLF = Very low frequency
VF = Voice frequency
ELF = Extremely low frequency

Generally, EM radiation (the designation ‘radiation’ excludes static electric and magnetic and near fields) is classified by wavelength into radio, microwave, infrared, the visible region we perceive as light, ultraviolet, X-rays and gamma rays. Arbitrary electromagnetic waves can always be expressed by Fourier analysis in terms of sinusoidal monochromatic waves which can be classified into these regions of the spectrum.

The behavior of EM radiation depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. When EM radiation interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries. Spectroscopy can detect a much wider region of the EM spectrum than the visible range of 400 nm to 700 nm. A common laboratory spectroscope can detect wavelengths from 2 nm to 2500 nm. Detailed information about the physical properties of objects, gases, or even stars can be obtained from this type of device. It is widely used in astrophysics. For example, hydrogen atoms emit radio waves of wavelength 21.12 cm.

[edit] Light

Main article: Light

EM radiation with a wavelength between approximately 400 nm and 700 nm is detected by the human eye and perceived as visible light. Other wavelengths, especially nearby infrared (longer than 700 nm) and ultraviolet (shorter than 400 nm) are also sometimes referred to as light, especially when visibility to humans is not relevant.

If radiation having a frequency in the visible region of the EM spectrum reflects off of an object, say, a bowl of fruit, and then strikes our eyes, this results in our visual perception of the scene. Our brain’s visual system processes the multitude of reflected frequencies into different shades and hues, and through this not-entirely-understood psychophysical phenomenon, most people perceive a bowl of fruit.

At most wavelengths, however, the information carried by electromagnetic radiation is not directly detected by human senses. Natural sources produce EM radiation across the spectrum, and our technology can also manipulate a broad range of wavelengths. Optical fiber transmits light which, although not suitable for direct viewing, can carry data that can be translated into sound or an image. The coding used in such data is similar to that used with radio waves.

[edit] Radio waves

Main article: Radio waves

Radio waves can be made to carry information by varying a combination of the amplitude, frequency and phase of the wave within a frequency band.

When EM radiation impinges upon a conductor, it couples to the conductor, travels along it, and induces an electric current on the surface of that conductor by exciting the electrons of the conducting material. This effect (the skin effect) is used in antennas. EM radiation may also cause certain molecules to absorb energy and thus to heat up; this is exploited in microwave ovens.

[edit] Derivation

Electromagnetic waves as a general phenomenon were predicted by the classical laws of electricity and magnetism, known as Maxwell’s equations. If you inspect Maxwell’s equations without sources (charges or currents) then you will find that, along with the possibility of nothing happening, the theory will also admit nontrivial solutions of changing electric and magnetic fields. Beginning with Maxwell’s equations for free space:

\nabla \cdot \mathbf{E} = 0  \qquad \qquad \qquad \ \ (1)
\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}  \qquad \qquad \ (2)
\nabla \cdot \mathbf{B} = 0 \qquad \qquad \qquad \ \ (3)
\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}  \qquad \quad \ (4)

\nabla is a vector differential operator (see Del).

One solution,


is trivial.

To see the more interesting one, we utilize vector identities, which work for any vector, as follows:

\nabla \times \left( \nabla \times \mathbf{A} \right) = \nabla \left( \nabla \cdot \mathbf{A} \right) - \nabla^2 \mathbf{A}

To see how we can use this take the curl of equation (2):

\nabla \times \left(\nabla \times \mathbf{E} \right) = \nabla \times \left(-\frac{\partial \mathbf{B}}{\partial t} \right) \qquad \qquad \qquad \quad \ \ \ (5) \,

Evaluating the left hand side:

 \nabla \times \left(\nabla \times \mathbf{E} \right) = \nabla\left(\nabla \cdot \mathbf{E} \right) - \nabla^2 \mathbf{E} =  - \nabla^2 \mathbf{E} \qquad \ \ (6) \,
where we simplified the above by using equation (1).

Evaluate the right hand side:

\nabla \times \left(-\frac{\partial \mathbf{B}}{\partial t} \right) = -\frac{\partial}{\partial t} \left( \nabla \times \mathbf{B} \right) = -\mu_0 \epsilon_0 \frac{\partial^2 \mathbf{E}}{\partial t^2} \quad \ \ \ \ (7)

Equations (6) and (7) are equal, so this results in a vector-valued differential equation for the electric field, namely

\nabla^2 \mathbf{E} = \mu_0 \epsilon_0 \frac{\partial^2 \mathbf{E}}{\partial t^2}

Applying a similar pattern results in similar differential equation for the magnetic field:

\nabla^2 \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial^2 \mathbf{B}}{\partial t^2}.

These differential equations are equivalent to the wave equation:

\nabla^2 f = \frac{1}{{c_0}^2} \frac{\partial^2 f}{\partial t^2} \,

c0 is the speed of the wave in free space and
f describes a displacement

Or more simply:

\Box f = 0
where \Box is d’Alembertian:

\Box = \nabla^2 - \frac{1}{{c_0}^2} \frac{\partial^2}{\partial t^2} = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} - \frac{1}{{c_0}^2} \frac{\partial^2}{\partial t^2} \

Notice that in the case of the electric and magnetic fields, the speed is:

c_0 = \frac{1}{\sqrt{\mu_0 \epsilon_0}}

Which, as it turns out, is the speed of light in free space. Maxwell’s equations have unified the permittivity of free space ε0, the permeability of free space μ0, and the speed of light itself, c0. Before this derivation it was not known that there was such a strong relationship between light and electricity and magnetism.

But these are only two equations and we started with four, so there is still more information pertaining to these waves hidden within Maxwell’s equations. Let’s consider a generic vector wave for the electric field.

\mathbf{E} = \mathbf{E}_0 f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)

Here \mathbf{E}_0 is the constant amplitude, f is any second differentiable function,  \hat{\mathbf{k}} is a unit vector in the direction of propagation, and  {\mathbf{x}} is a position vector. We observe that f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) is a generic solution to the wave equation. In other words

\nabla^2 f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) = \frac{1}{{c_0}^2} \frac{\partial^2}{\partial t^2} f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right),

for a generic wave traveling in the \hat{\mathbf{k}} direction.

This form will satisfy the wave equation, but will it satisfy all of Maxwell’s equations, and with what corresponding magnetic field?

\nabla \cdot \mathbf{E} = \hat{\mathbf{k}} \cdot \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) = 0
\mathbf{E} \cdot \hat{\mathbf{k}} = 0

The first of Maxwell’s equations implies that electric field is orthogonal to the direction the wave propagates.

\nabla \times \mathbf{E} = \hat{\mathbf{k}} \times \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) = -\frac{\partial \mathbf{B}}{\partial t}
\mathbf{B} = \frac{1}{c_0} \hat{\mathbf{k}} \times \mathbf{E}

The second of Maxwell’s equations yields the magnetic field. The remaining equations will be satisfied by this choice of \mathbf{E},\mathbf{B}.

Not only are the electric and magnetic field waves traveling at the speed of light, but they have a special restricted orientation and proportional magnitudes, E0 = c0B0, which can be seen immediately from the Poynting vector. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as \mathbf{E} \times \mathbf{B}.

From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left; but this picture can be rotated with the electric field oscillating right and left and the magnetic field oscillating down and up. This is a different solution that is traveling in the same direction. This arbitrariness in the orientation with respect to propagation direction is known as polarization.

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