Kinetic art - art that depends on movement for its effects - has its origins in the Dadaist andConstructivist movements that emerged in the 1910s. It flourished into a lively avant-garde trend following the landmark exhibition Le Mouvement at Galerie Denise Rene in Paris in 1955, after which it attracted a wide international following. At its heart were artists who were fascinated by the possibilities of movement in art - its potential to create new and more interactive relationships with the viewer and new visual experiences. It inspired new kinds of art that went beyond the boundaries of the traditional, handcrafted, static object, encouraging the idea that the beauty of an object could be the product of optical illusions or mechanical movement. But the group was split between those such as Jean Tinguely, who were interested in employing actual movement, and those such as Victor Vasarely, who were interested in optical effects and the illusion of movement and went on to be more closely associated with the Op art movement. Kinetic art thrived for a decade and achieved considerable prominence. But Op art proved almost too successful in capturing the public's imagination, while Kinetic art eventually began to be seen as a stale and accepted genre. By the mid-1960s, these developments led to a decline in artists' interest in movement.

Bicycle Wheel is famous above all as the first example of a "readymade" sculpture, an art object comprised of commonplace parts not manufactured by the artist. However, it has also been seen as the first work of Kinetic art, by virtue of the fact that the wheel affixed to the stool can be spun. For Duchamp, this movement was essential to the object's effect; "I enjoyed looking at it," he said, "just as I enjoyed looking at the flames dancing in a fireplace. It was like having a fireplace in my studio, the movement of the wheel reminded me of the movement of flames." Even though the piece was made outside of the context of the Kinetic art movement of the 1950s, artists of that time looked upon it as an important precursor, one that justified their claim that there had been a tradition of Kinetic art throughout the early 20th century. The importance of Duchamp's piece to the later Kinetic artists also reflected the influence of Dada on the later movement. For while some Kinetic artists were optimistic about technology, others were skeptical, and they drew inspiration from works such as this, in which the wheel turns almost senselessly, secured in one spot and going nowhere.

http://io9.gizmodo.com/5843116/use-that-built-up-static-electricity-to-create-a-shocking-work-of-art

Lichtenberg figures are branching patterns, like frozen lightning, that appear when electric discharge runs up against an insulator.

In the late 1700s, Georg Christoph Lichtenberg was doing some eighteenth century science; zapping various things with electricity to see if he could create gold or a Frankenstein monster or possibly discover a new law of physics. He was not having a lot of luck zapping plates covered with resin, and so he moved on. The work room he was in was dusty. When he wandered back to his plates, they had acquired a layer of grit. In that layer was the frozen impression of lightning bolts. He experimented further. It seemed the electric current, while not moving through the insulator, left regions of positive and negative charge on the surface. When he sprinkled positively or negatively charged powders onto the plates, they clung to differently charged pieces of the plates, making intricate figures.

The main aim of Electroconvulsive Therapy is to cause a massive convulsion in the brain (a massive epileptic fit).  This is achieved by giving the brain an electric shock using an ECT Machine.  ECT machines are, basically, transformers which modify Mains Current so that it is transmitted to the patient's skull in timed pulses.  

Two of the most common fallacies regarding Electroconvulsive Therapy (and ECT machines) are that:

Nothing could be further from the truth.  As can be seen from the table below, the smallest current is 0.75 amps. more than enough to kill if applied across the chest.  A voltage as high as 450 volts speaks for itself. 

The main parameters associated with Electroconvulsive Therapy and ECT Machines are Voltage, Current,Charge, Time, and Threshold Value. 

Voltage, Current and Resistance are connected by the formula:

It can be seen from the formula that if the current is kept fixed, then increasing the resistance will cause the voltage to increase; decreasing the resistance will cause the voltage to decrease. 

Electrical Quantity (Charge), Current and Time are connected by the formula:

Time is the time in seconds during which the current is flowing.  It can be seen from this formula that if the current is kept fixed, then the quantity of electricity is completely dependent on the time.  The longer the Shock, the more electricity flows through the brain. 

The Thymatron, manufactured by Somatics Inc, is an extremely popular machine (with psychiatrists) and is one of the machines recommended by the Royal College of Psychiatrists in their 1995 ECT Handbook. 

The UK version of the Thymatron has the following specifications: 

Like most modern ECT machines, the Thymatron is a fixed-current machine which means that it will try and maintain the current (0.9 amps) going through the patient's brain no matter the resistance.  If the patient's head has a high resistance, the machine will increase the voltage in order to overcome the resistance and keep the current at 0.9 amps.  If the patient's head has a low resistance the voltage will drop.  Remember that voltage, current and resistance are connected by a formula (see above). 

The Thymatron is also a brief-pulse machine which means that it sends the electricity through the patient's brain in a series of short pulses.  Each of these pulses lasts 1.5 milliseconds (thousandths of a second).
It can be seen from the table that the Thymatron has a frequency of 70 hertz which means that it goes through 70 cycles per second.  It is also a bi-phasic machine which means that it sends two pulses on every cycle, thus it sends 140 pulses of electricity through the patient's brain every second.  Since the shock can last up to 5.3 seconds, the machine will send 742 pulses of electricity through the patient's brain in this time.  This means that – at maximum shock length – a current of 0.9 amps would actually be flowing in the patient's brain for 1113 milliseconds (i.e. 742 pulses x 1.5 milliseconds).   Current would be flowing for more than a second. 

The unit of energy in the SI system of units is the "Joule".   In an electrical system, the Energy(E) in Joules is the product of the voltage(V), the current(I) and the time(t) for which the current flows. 

Assuming maximum voltage (450 volts), the energy delivered to the patient's head by each pulse would be: 

Since the machine delivers 140 pulses per second then the energy delivered to the patient's head every second is: 

Since Power (watts) is the rate of transfer of energy (joules per second), 85.05 joules per second represents a power output of 85.05 watts.  This machine can deliver enough power to keep a large lightbulb glowing brightly for more than 5 seconds. 

(Source - http://www.ect.org/resources/machines.html)

Overview

Introduction

Electroconvulsive therapy (ECT) has been demonstrated to be an effective and safe treatment for many psychiatric disorders.^[1] The use of ECT still generates significant controversy, however. One review concluded that ECT is only marginally more effective than placebo (ie, sham ECT).^[2] ECT has been viewed as harmful by the general public,^[3] psychiatric patients,^[4] and mental health professionals.^[5]

ECT has also been perceived as a form of violence against women.^[6] It has been negatively portrayed in movies such as One Flew Over the Cuckoo's Nest, House on Haunted Hill, and Requiem for a Dream.^[7]

Despite such debate, ECT is used in the United States and endorsed by the American Psychiatric Association.^[8] Approximately 100,000 patients annually receive ECT in the United States.^[9] Professional associations in Austria, Canada, Australia, Denmark, Netherlands, Germany, and India have offered professional guidelines for its use.^[10]

The image below depicts electroconvulsive therapy.

Electroconvulsive therapy (ECT) can help some people with bipolar disorder. ECT uses an electric current to cause a seizure in the brain and is one of the fastest ways to ease severe symptoms. It is usually a last resort when a patient does not improve with medication or psychotherapy.

History

In the 1500s, the Swiss physician Paracelsus (Auroleus Phillipus Theostratus Bombastus von Hohenheim) induced seizures by administering camphor by mouth to treat psychiatric illness.^[9] The first published report of the use of seizure induction to treat mania using camphor was in 1785.^[9]

In 1934, the Hungarian neuropathologist Ladislas Joseph von Meduna began the modern era of convulsive therapy by using intramuscular injection of camphor (soon replaced with pentylenetetrazol) to treat catatonic schizophrenia.^[9] In 1938, Italian psychiatrist Lucio Bini and neurologist Ugo Cerletti performed the first electrical induction of a series of seizures in a catatonic patient and produced a successful treatment response.^[9] One year later, ECT was introduced to the United States.^[11]

Lack of adequate anesthesia or muscle relaxation during ECT led to fractures and dislocations, and insufficient knowledge about the dose parameters of electrical stimulation led to more severe cognitive adverse effects.^[11] In 1940, curare was developed for use as a muscle relaxant during ECT.^[9] Until effective antipsychotic drugs were developed in the 1950s, the only effective alternatives to ECT were insulin shock therapy and lobotomy.^[11]

In the 1950s, Max Fink was the first to apply rigorous scientific research methods to ECT.^[12] Succinylcholine, a depolarizing muscle relaxant, was introduced in 1951, and the first controlled study of unilateral ECT was conducted in 1958.^[9] In the 1960s, randomized clinical trials of the efficacy of ECT versus medications in the treatment of depression showed response rates that were significantly higher with ECT.^[9]

 

In 1978, the American Psychiatric Association published the first Task Force Report on ECT, with the goal of establishing standards for consent and the technical and clinical aspects of the conduct of ECT.^[9] In 1985, the National Institutes of Health and National Institute of Mental Health Consensus Conference on ECT endorsed a role for the use of ECT and advocated research and national standards of practice.^[9]

In 1988, randomized controlled clinical trials of ECT versus lithium showed that they were equally effective in treating mania.^[9] In 2000, Sarah Lisanby and colleagues from Columbia University induced convulsive treatment with magnetic stimulation.^[9]

Mechanism of action

The mechanism of action of ECT is not fully known. ECT affects multiple central nervous system components, including hormones, neuropeptides, neurotrophic factors, and neurotransmitters.^[13]

 

The induction of a bilateral generalized seizure is required for both the beneficial and adverse effects of ECT.^[9] An increase in gamma-aminobutyric acid (GABA) transmission and receptor antagonism has been observed, which raises the seizure threshold during ECT.^[14] ECT may also lead to an increase of endogenous opioids, which may also have anticonvulsant properties.^[12]

Positron emission tomography (PET) has been used to study the neurophysiological effects of ECT.^[9] In a literature review of studies assessing possible changes in cerebral glucose metabolism by PET before and after ECT, reduction in glucose metabolism after ECT in bilateral anterior and posterior frontal areas represented the most consistent findings.^[15]

Nearly every neurotransmitter system is affected by ECT, including beta-adrenergic, serotonin, muscarinic, cholinergic, and dopaminergic systems.^[9] Brain-derived neurotrophic factor (BDNF),^{[16, 17]} second-messenger systems,^[9] and catechol-O-methyltransferase (COMT) polymorphisms^[18] may play a role in ECT.

 

Although many biomarkers have been studied, no ECT biomarker is routinely used in clinical practice.^[17]

Relevant Anatomy

In the central nervo/us system, the brain and spinal cord are the main centers where correlation and integration of nervous information occur. Both the brain and spinal cord are covered with a system of membranes, called meninges, and are suspended in the cerebrospinal fluid; they are further protected by the bones of the skull and the vertebral column.

 

The central nervous system is composed of large numbers of excitable nerve cells and their processes, called neurons, which are supported by specialized tissue called neuroglia. The long processes of a nerve cell are called axons or nerve fibers. The interior of the central nervous system is organized into gray and white matter. Gray matter consists of nerve cells embedded in neuroglia; it has a gray color. White matter consists of nerve fibers embedded in neuroglia; it has a white color due to the presence of lipid material in the myelin sheaths of many of the nerve fibers. The billions of neurons in the brain are connected to neurons throughout the body by trillions of synapses.

For more information about the relevant anatomy, see Central Nervous System Anatomy and Brain Anatomy.

Indications

ECT is indicated for selected patients with major depressive disorder, bipolar disorder, schizophrenia, and other disorders.

Major depressive disorder

ECT should be considered for patients in the acute phase of major depressive disorder who have a high degree of symptom severity and functional impairment or who have psychotic symptoms or catatonia.^{[19, 20]} ECT may also be the treatment of choice for patients in whom treatment response is urgently needed, such as patients who are suicidal^{[19, 21]} or those who are refusing food and are nutritionally compromised.^[19]

Bipolar disorder

ECT may be considered for patients with severe or treatment-resistant manic or mixed episodes of bipolar disorder,^{[22, 23]} or (in consultation with the psychiatrist) for patients who prefer this treatment modality.^[24] ECT also is a potential treatment for those experiencing severe mania or depression during pregnancy.^[24]ECT may be efficacious in patients with rapid cycling bipolar disorder.^[25] Mania resulting from ECT is rare.^[1]

 

In patients with life-threatening inanition (the exhausted condition that results from lack of food and water), suicidality,^[21] or psychosis, ECT is a reasonable alternative treatment.^[24] For patients who have depression with psychotic or catatonic features, ECT should be considered.^[24] Maintenance ECT may be considered for patients whose acute episode of depression responded to ECT.^[24]

Schizophrenia

ECT is effective for symptoms of acute schizophrenia but is not effective for chronic schizophrenia.^[9] In combination with antipsychotics, ECT may be considered for patients with severe psychosis that has not responded to treatment with antipsychotic medications.^[26]

 

The greatest therapeutic benefit appears to occur when ECT is administered concurrently with antipsychotic medications.^{[26, 27, 28]} ECT also should be considered for patients with prominent catatonic features that have not responded to lorazepam.^[26]

For patients with comorbid depression, ECT may be beneficial if depressive symptoms are treatment-resistant or if features such as suicidal ideation and behaviors or inanition are present.^[26]

In the stable phase of schizophrenia, ECT may benefit some patients whose condition has responded to ECT in the acute phase but for whom pharmacological prophylaxis alone has been ineffective or cannot be tolerated.^[26] ECT may be especially effective when marked positive and affective symptoms are present.^[29]

Other psychotic disorders

ECT is effective for psychotic disorders related to schizophrenia, such asschizophreniform disorder and schizoaffective disorder.^[1] In combination with antipsychotics, ECT may be considered for patients with schizoaffective disorder with severe psychosis that has not responded to treatment with antipsychotic medications.^[26]

Comorbid disorders

ECT is not recommended for the treatment of obsessive-compulsive disorder(OCD) but may be considered for treating comorbid disorders such as major depressive disorder, mania, and schizophrenia in patients with OCD.^[30]

Other disorders and indications

ECT has been effective in the treatment of catatonia,^[31] neuroleptic malignant syndrome,^[32] depression associated with Parkinson disease,^{[33, 34]} pain,^[35]particular cases of delirium,^[36] and acute confusion psychosis.^[37] It has also been effective in treating patients with intellectual disabilities who have treatment-resistant mood or psychotic disorders.^[38]

 

ECT may be useful in patients with major depressive disorder for whom medication or psychotherapy has not been effective in maintaining stability during the continuation phase.^[19] ECT should be considered in patients whose condition has failed to respond to medication trials, individuals who have not tolerated indicated medications, or those who have previously shown a response to ECT.^{[9, 19]} ECT also should be considered in patients with melancholic^[39] and atypical^[40]depression.

Contraindications

ECT has no absolute contraindications. Many medical conditions place patients at an increased risk for complications and warrant closer monitoring, however.^[9]

 

In a study of patients with major depressive disorder and comorbid borderline personality disorder (BPD), patients with BPD did not experience the same degree of improvement when treated with ECT as did patients with other personality disorders or with no personality disorder.^[41]

 

(Source - http://emedicine.medscape.com/article/1525957-overview)

- The screaming woman

- irish legend

- believed to be able to predict death

- also called the wailing woman

- is a spirit much like and sometimes people see her just before they die

- usually found around water bodies - lakes

A banshee, or Bean Sidhe, is a fairy from Irish folklore whose scream was an omen of death. Her thin scream is referred to as ?caoine,? which translates to ?keening.? It is said that a banshee?s cry predicts the death of a member of one of Ireland?s five major families: the O?Grady?s, the O?Neills, the O?Briens, the O?Connors or the Kavanaghs. Over time as families blended, it was said that most Irish families had their own banshee. It is also said that the banshees followed their families as they emigrated from Ireland to other places across the globe, though some stayed behind to grieve at the original family estate. Various versions of the banshee have been described, from a woman with long, red hair and very pale skin to an older woman with stringy, gray hair, rotten teeth and fiery red eyes. She is often depicted with a comb in her hair and this has led to an Irish superstition that finding a comb on the ground is considered bad luck. It is believed that a single banshee can take on any of these forms and shift between them, much like the goddesses of Celtic folklore. Other forms of the banshee include the Bean Nighe and the washer woman, both more attributed to Scotland than Ireland. The Bean Nighe is said to be the ghost of a woman who died during childbirth and would be seen wearing the clothes of the person about to die while the washer woman is dressed like a countrywoman and is cleaning bloody rags on a river shore.

websites -

http://www.ancient-origins.net/myths-legends-europe/songs-and-shrouds-mythical-banshee-and-bean-nighe-harbingers-002876

http://www.messagetoeagle.com/mystery-of-the-banshee-is-the-celtic-death-messenger-linked-to-the-tuatha-dedannan-race/

https://en.wikipedia.org/wiki/Banshee

Alexa Meade is a Los Angeles-based artist who is known for her portraits painted on the human body, making people into seemingly 2-D works of art. Her work has been exhibited worldwide and received critical acclaim from CNN, Wired, NPR, the Wall Street Journal, and more. She has lectured at the California Institute of the Arts, UC-Berkeley, Apple, Adobe, and National Geographic London. Her TED Global talk “Your Body is my Canvas,” has been viewed over 2 million times.

Growing up in Washington D.C., Alexa originally carved out a neat path in the life of politics. She interned on Capitol Hill and worked for the 2008 Obama campaign in Colorado as a press staffer. After graduating from Vassar College with Honors in Political Science, Alexa decided that what she really wanted to be was an artist. She had a simple idea to put black paint over natural shadows, which evolved into something much larger. By painting the mapping of light directly on top of a 3D space, Alexa was able to create the illusion that the world was a 2D painting. Alexa travels the world creating art installations and commissioned portraits. 

Alexa plays with a lot of projects on the side. She is collaborating with scientists researching spacetime at the Perimeter Institute For Theoretical Physics. Alexa is making a series of magical paintings with David Blaine. She is transforming her home into a "Fun House" with Chris Hughes, developing a line of toys, and volunteering in the art program at the Braille Institute.

The Earth has a substantial magnetic field, a fact of some historical importance because of the role of the magnetic compass in exploration of the planet.

Structure of the Field

The field lines defining the structure of the magnetic field are similar to those of a simple bar magnet, as illustrated in the following figure.

The Earth's magnetic field and Van Allen radiation belts

It is well known that the axis of the magnetic field is tipped with respect to the rotation axis of the Earth. Thus, true north (defined by the direction to the north rotational pole) does not coincide with magnetic north (defined by the direction to the north magnetic pole) and compass directions must be corrected by fixed amounts at given points on the surface of the Earth to yield true directions.

Van Allen Radiation Belts

A fundamental property of magnetic fields is that they exert forces on moving electrical charges. Thus, a magnetic field can trap charged particles such as electrons and protons as they are forced to execute a spiraling motion back and forth along the field lines.

As illustrated in the adjacent figure, the charged particles are reflected at "mirror points" where the field lines come close together and the spirals tighten. One of the first fruits of early space exploration was the discovery in the late 1950s that the Earth is surrounded by two regions of particularly high concentration of charged particles called the Van Allen radiation belts.

The inner and outer Van Allen belts are illustrated in the top figure. The primary source of these charged particles is the stream of particlesemanating from the Sun that we call the solar wind. As we shall see in a subsequent section, the charged particles trapped in the Earth's magnetic field are responsible for the aurora (Northern and Southern Lights).

Origin of the Magnetic Field

Magnetic fields are produced by the motion of electrical charges. For example, the magnetic field of a bar magnet results from the motion of negatively charged electrons in the magnet. The origin of the Earth's magnetic field is not completely understood, but is thought to be associated with electrical currents produced by the coupling of convective effects and rotation in the spinning liquid metallic outer core of iron and nickel. This mechanism is termed the dynamo effect.

Rocks that are formed from the molten state contain indicators of the magnetic field at the time of their solidification. The study of such "magnetic fossils" indicates that the Earth's magnetic field reverses itself every million years or so (the north and south magnetic poles switch). This is but one detail of the magnetic field that is not well understood.

The Earth's Magnetosphere

The solar wind mentioned above is a stream of ionized gases that blows outward from the Sun at about 400 km/second and that varies in intensity with the amount of surface activity on the Sun. The Earth's magnetic field shields it from much of the solar wind. When the solar wind encounters Earth's magnetic field it is deflected like water around the bow of a ship, as illustrated in the adjacent image (Source).

The imaginary surface at which the solar wind is first deflected is called the bow shock. The corresponding region of space sitting behind the bow shock and surrounding the Earth is termed the magnetosphere; it represents a region of space dominated by the Earth's magnetic field in the sense that it largely prevents the solar wind from entering. However, some high energy charged particles from the solar wind leak into the magnetosphere and are the source of the charged particles trapped in the Van Allen belts.

(http://csep10.phys.utk.edu/astr161/lect/earth/magnetic.html)

In 1905, a team of construction workers in the small village of Shoreham, New York labored to erect a truly extraordinary structure. Over a period of several years the men had managed to assemble the framework and wiring for the 187-foot-tall Wardenclyffe Tower, in spite of severe budget shortfalls and a few engineering snags. The project was overseen by its designer, the eccentric-yet-ingenious inventor Nikola Tesla (10 July 1856 – 7 January 1943). Atop his tower was perched a fifty-five ton dome of conductive metals, and beneath it stretched an iron root system that penetrated more than 300 feet into the Earth’s crust. “In this system that I have invented, it is necessary for the machine to get a grip of the earth,” he explained, “otherwise it cannot shake the earth. It has to have a grip… so that the whole of this globe can quiver.”

Though it was far from completion, it was rumored to have been tested on several occasions, with spectacular, crowd-pleasing results. The ultimate purpose of this unique structure was to change the world forever.

Tesla’s inventions had already changed the world on several occasions, most notably when he developed modern alternating current technology. He had also won fame for his victory over Thomas Edison in the well-publicized “battle of currents,” where he proved that his alternating current was far more practical and safe than Edison-brand direct current. Soon his technology dominated the world’s developing electrical infrastructure, and by 1900 he was widely regarded as America’s greatest electrical engineer. This reputation was reinforced by his other major innovations, including the Tesla coil, the radio transmitter, and fluorescent lamps.

In 1891, Nikola Tesla gave a lecture for the members of the American Institute of Electrical Engineers in New York City, where he made a striking demonstration. In each hand he held a gas discharge tube, an early version of the modern fluorescent bulb. The tubes were not connected to any wires, but nonetheless they glowed brightly during his demonstration. Tesla explained to the awestruck attendees that the electricity was being transmitted through the air by the pair of metal sheets which sandwiched the stage. He went on to speculate how one might increase the scale of this effect to transmit wireless power and information over a broad area, perhaps even the entire Earth. As was often the case, Tesla’s audience was engrossed but bewildered.

Illustration showing Tesla's demonstration of wireless electricity.

Back at his makeshift laboratory at Pike’s Peak in Colorado Springs, the eccentric scientist continued to wring the secrets out of electromagnetism to further explore this possibility. He rigged his equipment with the intent to produce the first lightning-scale electrical discharges ever accomplished by mankind, a feat which would allow him to test many of his theories about the conductivity of the Earth and the sky. For this purpose he erected a 142-foot mast on his laboratory roof, with a copper sphere on the tip. The tower’s substantial wiring was then routed through an exceptionally large high-voltage Tesla coil in the laboratory below. On the night of his experiment, following a one-second test charge which momentarily set the night alight with an eerie blue hum, Tesla ordered his assistant to fully electrify the tower.

Though his notes do not specifically say so, one can only surmise that Tesla stood at Pike’s Peak and cackled diabolically as the night sky over Colorado was cracked by the man-made lightning machine. Colossal bolts of electricity arced hundreds of feet from the tower’s top to lick the landscape. A curious blue corona soon enveloped the crackling equipment. Millions of volts charged the atmosphere for several moments, but the awesome display ended abruptly when the power suddenly failed. All of the windows throughout Colorado Springs went dark as the local power station’s industrial-sized generator collapsed under the strain. But amidst such dramatic discharges, Tesla confirmed that the Earth itself could be used as an electrical conductor, and verified some of his suspicions regarding the conductivity of the ionosphere. In later tests, he recorded success in an attempt to illuminate light bulbs from afar, though the exact conditions of these experiments have been lost to obscurity. In any case, Tesla became convinced that his dream of world-wide wireless electricity was feasible.

In 1900, famed financier J.P. Morgan learned of Tesla’s convictions after reading an article in Century Magazine, wherein the scientist described a global network of high-voltage towers which could one day control the weather, relay text and images wirelessly, and provide ubiquitous electricity via the atmosphere. Morgan, hoping to capitalize on the future of wireless telegraphy, immediately invested $150,000 to relocate Tesla’s lab to Long Island to construct a pilot plant for this “World Wireless System.” Construction of Wardenclyffe Tower and its dedicated power generating facility began the following year.

Tesla's lab at pike's peak

In December 1901, a scant few months after construction began, a competing scientist named Guglielmo Marconi executed the world’s first trans-Atlantic wireless telegraph signal. Tesla’s investors were deeply troubled by the development despite the fact that Marconi borrowed from seventeen Tesla patents to accomplish his feat. Though Marconi’s plans were considerably less ambitious in scale, his apparatus was also considerably less expensive. Work at Wardenclyffe continued, but Tesla realized that this his competitor’s success with simple wireless telegraphy had greatly diminished the likelihood of further investments in his own, much grander project.

In 1908, Tesla described his sensational aspirations in an article for Wireless Telegraphy and Telephony magazine:

“As soon as completed, it will be possible for a business man in New York to dictate instructions, and have them instantly appear in type at his office in London or elsewhere. He will be able to call up, from his desk, and talk to any telephone subscriber on the globe, without any change whatever in the existing equipment. An inexpensive instrument, not bigger than a watch, will enable its bearer to hear anywhere, on sea or land, music or song, the speech of a political leader, the address of an eminent man of science, or the sermon of an eloquent clergyman, delivered in some other place, however distant. In the same manner any picture, character, drawing, or print can be transferred from one to another place. Millions of such instruments can be operated from but one plant of this kind. More important than all of this, however, will be the transmission of power, without wires, which will be shown on a scale large enough to carry conviction.”

In essence, Tesla’s global power grid was designed to “pump” the planet with electricity which would intermingle with the natural telluric currents that move throughout the Earth’s crust and oceans. At the same time, towers like the one at Wardenclyffe would fling columns of raw energy skyward into the electricity-friendly ionosphere fifty miles up. To tap into this energy conduit, customers’ homes would be equipped with a buried ground connection and a relatively small spherical antenna on the roof, thereby creating a low-resistance path to close the giant Earth-ionosphere circuit. Oceangoing ships could use a similar antenna to draw power from the network while at sea. In addition to electricity, these currents could carry information over great distances by bundling radio-frequency energy along with the power, much like the modern technology to send high-speed Internet data over power lines.

(http://www.damninteresting.com/teslas-tower-of-power/)

Electromagnetism, science of charge and of the forces and fields associated with charge. Electricity and magnetism are two aspects of electromagnetism.

Electricity and magnetism were long thought to be separate forces. It was not until the 19th century that they were finally treated as interrelated phenomena. In 1905Albert Einstein’s special theory of relativity established beyond a doubt that both are aspects of one common phenomenon. At a practical level, however, electric and magnetic forces behave quite differently and are described by different equations.Electric forces are produced by electric charges either at rest or in motion. Magnetic forces, on the other hand, are produced only by moving charges and act solely on charges in motion.

Electric phenomena occur even in neutral matterbecause the forces act on the individual charged constituents. The electric force, in particular, is responsible for most of the physical and chemical properties of atoms and molecules. It is enormously strong compared with gravity. For example, the absence of only one electron out of every billion molecules in two 70-kilogram (154-pound) persons standing two metres (two yards) apart would repel them with a 30,000-ton force. On a more familiar scale, electric phenomena are responsible for the lightning and thunder accompanying certain storms.

Electric and magnetic forces can be detected in regions called electric and magnetic fields. These fields are fundamental in nature and can exist in space far from the charge or current that generated them. Remarkably, electric fields can produce magnetic fields and vice versa, independent of any external charge. A changingmagnetic field produces an electric field, as the English physicist Michael Faradaydiscovered in work that forms the basis of electric power generation. Conversely, a changing electric field produces a magnetic field, as the Scottish physicist James Clerk Maxwell deduced. The mathematical equations formulated by Maxwell incorporated light and wave phenomena into electromagnetism. He showed that electric and magnetic fields travel together through space as waves ofelectromagnetic radiation, with the changing fields mutually sustaining each other. Examples of electromagnetic waves traveling through space independent of matter are radio and television waves, microwaves, infrared rays, visible light, ultraviolet light, X-rays, and gamma rays. All of these waves travel at the same speed—namely, the velocity of light (roughly 300,000 kilometres, or 186,000 miles, per second). They differ from each other only in the frequency at which their electric and magnetic fields oscillate.

Maxwell’s equations still provide a complete and elegant description of electromagnetism down to, but not including, the subatomic scale. The interpretation of his work, however, was broadened in the 20th century. Einstein’sspecial relativity theory merged electric and magnetic fields into one common fieldand limited the velocity of all matter to the velocity of electromagnetic radiation. During the late 1960s, physicists discovered that other forces in nature have fields with a mathematical structure similar to that of the electromagnetic field. These other forces are the nuclear force, responsible for the energy released in nuclear fusion, and the weak force, observed in the radioactive decay of unstable atomic nuclei. In particular, the weak and electromagnetic forces have been combined into a common force called the electroweak force. The goal of many physicists to unite all of the fundamental forces, including gravity, into one grand unified theory has not been attained to date.

An important aspect of electromagnetism is the science of electricity, which is concerned with the behaviour of aggregates of charge, including the distribution of charge within matter and the motion of charge from place to place. Different types of materials are classified as either conductors or insulators on the basis of whether charges can move freely through their constituent matter. Electric current is the measure of the flow of charges; the laws governing currents in matter are important in technology, particularly in the production, distribution, and control of energy.

The concept of voltage, like those of charge and current, is fundamental to the science of electricity. Voltage is a measure of the propensity of charge to flow from one place to another; positive charges generally tend to move from a region of high voltage to a region of lower voltage. A common problem in electricity is determining the relationship between voltage and current or charge in a given physical situation.

This article seeks to provide a qualitative understanding of electromagnetism as well as a quantitative appreciation for the magnitudes associated with electromagnetic phenomena.

Fundamentals

Everyday modern life is pervaded by electromagnetic phenomena. When a light bulbis switched on, a current flows through a thin filament in the bulb; the current heats the filament to such a high temperature that it glows, illuminating its surroundings. Electric clocks and connections link simple devices of this kind into complex systems such as traffic lights that are timed and synchronized with the speed of vehicular flow. Radio and television sets receive information carried by electromagnetic waves traveling through space at the speed of light. To start an automobile, currents in anelectric starter motor generate magnetic fields that rotate the motor shaft and drive engine pistons to compress an explosive mixture of gasoline and air; the spark initiating the combustion is an electric discharge, which makes up a momentary current flow.

Coulomb’s law

Many of these devices and phenomena are complex, but they derive from the same fundamental laws of electromagnetism. One of the most important of these is Coulomb’s law, which describes the electric force between charged objects. Formulated by the 18th-century French physicist Charles-Augustin de Coulomb, it is analogous to Newton’s law for the gravitational force. Both gravitational and electric forces decrease with the square of the distance between the objects, and both forces act along a line between them. In Coulomb’s law, however, the magnitude and sign of the electric force are determined by the charge, rather than the mass, of an object. Thus, charge determines how electromagnetism influences the motion of charged objects. (Charge is a basic property of matter. Every constituent of matter has anelectric charge with a value that can be positive, negative, or zero. For example, electrons are negatively charged, and atomic nuclei are positively charged. Mostbulk matter has an equal amount of positive and negative charge and thus has zero net charge.)

According to Coulomb, the electric force for charges at rest has the following properties:

(1) Like charges repel each other; unlike charges attract. Thus, two negative charges repel one another, while a positive charge attracts a negative charge.

(2) The attraction or repulsion acts along the line between the two charges.

(3) The size of the force varies inversely as the square of the distance between the two charges. Therefore, if the distance between the two charges is doubled, the attraction or repulsion becomes weaker, decreasing to one-fourth of the original value. If the charges come 10 times closer, the size of the force increases by a factor of 100.

(4) The size of the force is proportional to the value of each charge. The unit used to measure charge is the coulomb (C). If there were two positive charges, one of 0.1 coulomb and the second of 0.2 coulomb, they would repel each other with a force that depends on the product 0.2 × 0.1. If each of the charges were reduced by one-half, the repulsion would be reduced to one-quarter of its former value.

Static cling is a practical example of the Coulomb force. In static cling, garments made of synthetic material collect a charge, especially in dry winter air. A plastic or rubber comb passed quickly through hair also becomes charged and will pick up bits of paper. The synthetic fabric and the comb are insulators; charge on these objects cannot move easily from one part of the object to another. Similarly, an office copy machine uses electric force to attract particles of ink to paper.

Principle of charge conservation

Like Coulomb’s law, the principle of charge conservation is a fundamental law of nature. According to this principle, the charge of an isolated system cannot change. If an additional positively charged particle appears within a system, a particle with a negative charge of the same magnitude will be created at the same time; thus, the principle of conservation of charge is maintained. In nature, a pair of oppositely charged particles is created when high-energy radiation interacts with matter; an electron and a positron are created in a process known as pair production.

The smallest subdivision of the amount of charge that a particle can have is the charge of one proton, +1.602 × 10^?19 coulomb. The electron has a charge of the same magnitude but opposite sign—i.e., ?1.602 × 10^?19 coulomb. An ordinary flashlight battery delivers a current that provides a total charge flow of approximately 5,000 coulomb, which corresponds to more than 10²² electrons, before it is exhausted.

Electric current is a measure of the flow of charge, as, for example, charge flowing through a wire. The size of the current is measured in amperes and symbolized by i. An ampere of current represents the passage of one coulomb of charge per second, or 6.2 billion billion electrons (6.2 × 10¹⁸ electrons) per second. A current is positive when it is in the direction of the flow of positive charges; its direction is opposite to the flow of negative charges.

Electric fields and forces

The force and conservation laws are only two aspects of electromagnetism, however. Electric and magnetic forces are caused by electromagnetic fields. The term field denotes a property of space, so that the field quantity has a numerical value at each point of space. These values may also vary with time. The value of the electric or magnetic field is a vector—i.e., a quantity having both magnitude and direction. The value of the electric field at a point in space, for example, equals the force that would be exerted on a unit charge at that position in space.

Every charged object sets up an electric field in the surrounding space. A second charge “feels” the presence of this field. The second charge is either attracted toward the initial charge or repelled from it, depending on the signs of the charges. Of course, since the second charge also has an electric field, the first charge feels its presence and is either attracted or repelled by the second charge, too.

The electric field from a charge is directed away from the charge when the charge is positive and toward the charge when it is negative. The electric field from a charge at rest is shown in Figure 1 for various locations in space. The arrows point in the direction of the electric field, and the length of the arrows indicates the strength of the field at the midpoint of the arrows.

If a positive charge were placed in the electric field, it would feel a force in the direction of the field. A negative charge would feel a force in the direction opposite the direction of the field.

In calculations, it is often more convenient to deal directly with the electric field than with the charges; frequently, more is known about the field than about the distribution of charges in space. For example, the distribution of charges in conductors is generally unknown because the charges move freely within the conductor. In static situations, however, the electric field in a conductor inequilibrium has a definite value, zero, because any force on the charges inside the conductor redistributes them until the field vanishes. The unit of electric field is newtons per coulomb, or volts per metre.

The electric potential is another useful field. It provides an alternative to the electric field in electrostatics problems. The potential is easier to use, however, because it is a single number, a scalar, instead of a vector. The difference in potential between two places measures the degree to which charges are influenced to move from one place to another. If the potential is the same at two places (i.e., if the places have the same voltage), charges will not be influenced to move from one place to the other. The potential on an object or at some point in space is measured in volts; it equals the electrostatic energy that a unit charge would have at that position. In a typical 12-volt car battery, the battery terminal that is marked with a + sign is at a potential 12 volts greater than the potential of the terminal marked with the ? sign. When a wire, such as the filament of a car headlight, is connected between the + and the ? terminals of the battery, charges move through the filament as an electric currentand heat the filament; the hot filament radiates light.

Magnetic fields and forces

The magnetic force influences only those charges that are already in motion. It is transmitted by the magnetic field. Both magnetic fields and magnetic forces are more complicated than electric fields and electric forces. The magnetic field does not point along the direction of the source of the field; instead, it points in a perpendicular direction. In addition, the magnetic force acts in a direction that is perpendicular to the direction of the field. In comparison, both the electric force and the electric field point directly toward or away from the charge.

The present discussion will deal with simple situations in which the magnetic field is produced by a current of charge in a wire. Certain materials, such as copper, silver, and aluminum, are conductors that allow charge to flow freely from place to place. If an external influence establishes a current in a conductor, the current generates a magnetic field. For a long straight wire, the magnetic field has a direction that encircles the wire on a plane perpendicular to the wire. The strength of the magnetic field decreases with distance from the wire. The arrows in Figure 2 represent the size and direction of the magnetic field for a current moving in the direction indicated.Figure 2A shows an end view with the current coming toward the reader, whileFigure 2B provides a three-dimensional view of the magnetic field at one position along the wire.

In subsequent figures, continuous lines will be used to represent the direction of electric and magnetic fields. These lines emphasize the important fact that electric fields begin on positive charges and end on negative charges, while magnetic fields do not have beginnings or ends and close on themselves. The magnetic field shown in Figure 2 is unusually simple. Highly complex and useful magnetic fields can be generated by the proper choice of conductors to carry electric currents. Under development are thermonuclear fusion reactors for obtaining energy from the fusion of light nuclei in the form of very hot plasmas of hydrogen isotopes. The plasmas have to be confined by magnetic fields (dubbed “magnetic bottles”) as no material container can withstand such high temperatures. Charged particles are also confined by magnetic fields in nature. Large numbers of charged particles, mostly protons and electrons, are trapped in huge bands around the Earth by its magnetic field. These bands are known as the Van Allen radiation belts. Disturbance of the Earth’s confining magnetic field produces spectacular displays, the so-called northern lights, in which trapped charged particles are freed and crash through the atmosphere to Earth.

Interaction of a magnetic field with a charge

How does the magnetic field interact with a charged object? If the charge is at rest, there is no interaction. If the charge moves, however, it is subjected to a force, the size of which increases in direct proportion with the velocity of the charge. The force has a direction that is perpendicular both to the direction of motion of the charge and to the direction of the magnetic field. There are two possible precisely opposite directions for such a force for a given direction of motion. This apparent ambiguity is resolved by the fact that one of the two directions applies to the force on a moving positive charge while the other direction applies to the force on a moving negative charge. Figure 3 illustrates the directions of the magnetic force on positive charges and on negative charges as they move in a magnetic field that is perpendicular to the motion.

Depending on the initial orientation of the particle velocity to the magnetic field, charges having a constant speed in a uniform magnetic field will follow a circular or helical path.

Electric currents in wires are not the only source of magnetic fields. Naturally occurring minerals exhibit magnetic properties and have magnetic fields. These magnetic fields result from the motion of electrons in the atoms of the material. They also result from a property of electrons called the magnetic dipole moment, which is related to the intrinsic spin of individual electrons. In most materials, little or no field is observed outside the matter because of the random orientation of the various constituent atoms. In some materials such as iron, however, atoms within certain distances tend to become aligned in one particular direction.

Magnets have numerous applications, ranging from use as toys and paper holders on home refrigerators to essential components in electric generators and machines that can accelerate particles to speeds approaching that of light. The practical application of magnetism in technology is greatly enhanced by using iron and other ferromagnetic materials with electric currents in devices like motors. These materials amplify the magnetic field produced by the currents and thereby create more powerful fields.

While electric and magnetic effects are well separated in many phenomena and applications, they are coupled closely together when there are rapid time fluctuations. Faraday’s law of induction describes how a time-varying magnetic field produces an electric field (see below Faraday’s law of induction). Important practical applications include the electric generator and transformer. In a generator, the physical motion of a magnetic field produces electricity for power. In a transformer, electric power is converted from one voltage level to another by the magnetic field of one circuit inducing an electric current in another circuit.

The existence of electromagnetic waves depends on the interaction between electric and magnetic fields. Maxwell postulated that a time-varying electric field produces a magnetic field. His theory predicted the existence of electromagnetic waves in which each time-varying field produces the other field. For example, radio waves are generated by electronic circuits known as oscillators that cause rapidly oscillating currents to flow in antennas; the rapidly varying magnetic field has an associated varying electric field. The result is the emission of radio waves into space (seeelectromagnetic radiation: Generation of electromagnetic radiation).

Many electromagnetic devices can be described by circuits consisting of conductors and other elements. These circuits may operate with a steady flow of current, as in a flashlight, or with time-varying currents. Important elements in circuits include sources of power called electromotive forces; resistors, which control the flow of current for a given voltage; capacitors, which store charge and energy temporarily; and inductors, which also store electrical energy for a limited time. Circuits with these elements can be described entirely with algebra. (For more complicated circuit elements such as transistors, see semiconductor device and integrated circuit).

Two mathematical quantities associated with vector fields, like the electric field Eand the magnetic field B, are useful for describing electromagnetic phenomena. They are the flux of such a field through a surface and the line integral of the field along a path. The flux of a field through a surface measures how much of the field penetrates through the surface; for every small section of the surface, the flux is proportional to the area of that section and depends also on the relative orientation of the section and the field. The line integral of a field along a path measures the degree to which the field is aligned with the path; for every small section of path, it is proportional to the length of that section and is also dependent on the alignment of the field with that section of path. When the field is perpendicular to the path, there is no contribution to the line integral. The fluxes of E and B through a surface and the line integrals of these fields along a path play an important role in electromagnetic theory. As examples, the flux of the electric field E through a closed surface measures the amount of charge contained within the surface; the flux of the magnetic field B through a closed surface is always zero because there are no magnetic monopoles (magnetic charges consisting of a single pole) to act as sources of the magnetic field in the way that charge is a source of the electric field.

Effects of varying magnetic fields

The merger of electricity and magnetism from distinct phenomena into electromagnetism is tied to three closely related events. The first was Hans Christian Ørsted’s accidental discovery of the influence of an electric current on a magnetic needle—namely, that magnetic fields are produced by electric currents. Ørsted’s 1820 report of his observation spurred an intense effort by scientists to prove that magnetic fields can induce currents. The second event was Faraday’s experimental proof that a changing magnetic field can induce a current in a circuit. The third was Maxwell’s prediction that a changing electric field has an associated magnetic field. The technological revolution attributed to the development of electric power and radio communications can be traced to these three landmarks (see below).

Faraday’s law of induction

Faraday’s discovery in 1831 of the phenomenon of magnetic induction is one of the great milestones in the quest toward understanding and exploiting nature. Stated simply, Faraday found that (1) a changing magnetic field in a circuit induces anelectromotive force in the circuit; and (2) the magnitude of the electromotive forceequals the rate at which the flux of the magnetic field through the circuit changes. The flux is a measure of how much field penetrates through the circuit. The electromotive force is measured in volts and is represented by the equation

Here, ?, the flux of the vector field B through the circuit, measures how much of the field passes through the circuit. To illustrate the meaning of flux, imagine how much water from a steady rain will pass through a circular ring of area A. When the ring is placed parallel to the path of the water drops, no water passes through the ring. The maximum rate at which drops of rain pass through the ring occurs when the surface is perpendicular to the motion of the drops. The rate of water drops crossing the surface is the flux of the vector field ?v through that surface, where ? is the density of water drops and v represents the velocity of the water. Clearly, the angle betweenv and the surface is essential in determining the flux. To specify the orientation of the surface, a vector A is defined so that its magnitude is the surface area A in units of square metres and its direction is perpendicular to the surface. The rate at which raindrops pass through the surface is ?v cos ?A, where ? is the angle between v andA. Using vector notation, the flux is ?v · A. For the magnetic field, the amount of flux through a small area represented by the vector dA is given by B · dA. For a circuit consisting of a single turn of wire, adding the contributions from the entire surface that is surrounded by the wire gives the magnetic flux ? of equation (43). The rate of change of this flux is the induced electromotive force. The units of magnetic flux arewebers, with one weber equaling one tesla per square metre. Finally, the minus sign in equation (43) indicates the direction of the induced electromotive force and hence of any induced current. The magnetic flux through the circuit generated by the induced current is in whatever direction will keep the total flux in the circuit from changing. The minus sign in equation (43) is an example of Lenz’s law for magnetic systems. This law, deduced by the Russian-born physicist Heinrich Friedrich Emil Lenz, states that “what happens is that which opposes any change in the system.”

Faraday’s law is valid regardless of the process that causes the magnetic flux to change. It may be that a magnet is moved closer to a circuit or that a circuit is moved closer to a magnet. Figure 4 shows a magnet brought near a conducting ring and gives the direction of the induced current and field, thus illustrating both Faraday’s and Lenz’s laws. Another alternative is that the circuit may change in size in a fixed external magnetic field or, as in the case of alternating-current generation, that the circuit may be a coil of conducting wire rotating in a magnetic field so that the flux ? varies sinusoidally in time.

The magnetic flux ? through a circuit has to be considered carefully in the application of Faraday’s law given in equation (43). For example, if a circuit consists of a coil with five closely spaced turns and if ? is the magnetic flux through a single turn, then the value of ? for the five-turn circuit that must be used in Faraday’s law is ? = 5?. If the five turns are not the same size and closely spaced, the problem of determining ? can be quite complex.

Self-inductance and mutual inductance

The self-inductance of a circuit is used to describe the reaction of the circuit to a changing current in the circuit, while the mutual inductance with respect to a second circuit describes the reaction to a changing current in the second circuit. When a current i₁ flows in circuit 1, i₁ produces a magnetic field B₁; the magnetic flux through circuit 1 due to current i₁ is ?₁₁. Since B₁ is proportional to i₁, ?₁₁ is as well. The constant of proportionality is the self-inductance L₁ of the circuit. It is defined by the equation

As indicated earlier, the units of inductance are henrys. If a second circuit is present, some of the field B₁ will pass through circuit 2 and there will be a magnetic flux ?₂₁in circuit 2 due to the current i₁. The mutual inductance M₂₁ is given by

The magnetic flux in circuit 1 due to a current in circuit 2 is given by ?₁₂ = M₁₂i₂. An important property of the mutual inductance is that M₂₁ = M₁₂. It is therefore sufficient to use the label M without subscripts for the mutual inductance of two circuits.

The value of the mutual inductance of two circuits can range from +?L₁L₂ to ??L₁L₂, depending on the flux linkage between the circuits. If the two circuits are very far apart or if the field of one circuit provides no magnetic flux through the other circuit, the mutual inductance is zero. The maximum possible value of the mutual inductance of two circuits is approached as the two circuits produce B fields with increasingly similar spatial configurations.

If the rate of change with respect to time is taken for the terms on both sides of equation (44), the result is d?₁₁/dt = L₁di₁/dt. According to Faraday’s law, d?₁₁/dt is the negative of the induced electromotive force. The result is the equation frequently used for a single inductor in an AC circuit—i.e.,

The phenomenon of self-induction was first recognized by the American scientistJoseph Henry. He was able to generate large and spectacular electric arcs by interrupting the current in a large copper coil with many turns. While a steady current is flowing in a coil, the energy in the magnetic field is given by ¹/₂Li². If both the inductance L and the current i are large, the amount of energy is also large. If the current is interrupted, as, for example, by opening a knife-blade switch, the current and therefore the magnetic flux through the coil drop quickly. Equation (46) describes the resulting electromotive force induced in the coil, and a large potential difference is developed between the two poles of the switch. The energy stored in the magnetic field of the coil is dissipated as heat and radiation in an electric arc across the space between the terminals of the switch. Due to advances in superconducting wires for electromagnets, it is possible to use large magnets with magnetic fields of several teslas for temporarily storing electric energy as energy in the magnetic field. This is done to accommodate short-term fluctuations in the consumption of electric power.

A transformer is an example of a device that uses circuits with maximum mutual induction. Figure 5 illustrates the configuration of a typical transformer. Here, coils of insulated conducting wire are wound around a ring of iron constructed of thin isolated laminations or sheets. The laminations minimize eddy currents in the iron. Eddy currents are circulatory currents induced in the metal by the changing magnetic field. These currents produce an undesirable by-product—heat in the iron. Energy loss in a transformer can be reduced by using thinner laminations, very “soft” (low-carbon) iron and wire with a larger cross section, or by winding the primary and secondary circuits with conductors that have very low resistance. Unfortunately, reducing the heat loss increases the cost of transformers. Transformers used to transmit and distribute power are commonly 98 to 99 percent efficient. While eddy currents are a problem in transformers, they are useful for heating objects in a vacuum. Eddy currents are induced in the object to be heated by surrounding a relatively nonconducting vacuum enclosure with a coil carrying a high-frequency alternating current.

In a transformer, the iron ensures that nearly all the lines of B passing through one circuit also pass through the second circuit and that, in fact, essentially all the magnetic flux is confined to the iron. Each turn of the conducting coils has the same magnetic flux; thus, the total flux for each coil is proportional to the number of turns in the coil. As a result, if a source of sinusoidally varying electromotive force is connected to one coil, the electromotive force in the second coil is given by

Thus, depending on the ratio of N₂ to N₁, the transformer can be either a step-up or a step-down device for alternating voltages. For many reasons, including safety, generation and consumption of electric power occur at relatively low voltages. Step-up transformers are used to obtain high voltages before electric power is transmitted, since for a given amount of power, the current in the transmission lines is much smaller. This minimizes energy lost by resistive heating of the conductors.

Faraday’s law constitutes the basis for the power industry and for the transformation of mechanical energy into electric energy. In 1821, a decade before his discovery of magnetic induction, Faraday conducted experiments with electric wires rotating around compass needles. This earlier work, in which a wire carrying a current rotated around a magnetized needle and a magnetic needle was made to rotate around a wire carrying an electric current, provided the groundwork for the development of the electric motor.

Effects of varying electric fields

Maxwell’s prediction that a changing electric field generates a magnetic field was a masterstroke of pure theory. The Maxwell equations for the electromagnetic field unified all that was hitherto known about electricity and magnetism and predicted the existence of an electromagnetic phenomenon that can travel as waves with the velocity of 1/??₀?₀ in a vacuum. That velocity, which is based on constants obtained from purely electric measurements, corresponds to the speed of light. Consequently, Maxwell concluded that light itself was an electromagnetic phenomenon. Later, Einstein’s special relativity theory postulated that the value of the speed of light is independent of the motion of the source of the light. Since then, the speed of light has been measured with increasing accuracy. In 1983 it was defined to be exactly 299,792,458 metres per second. Together with the cesium clock, which has been used to define the second, the speed of light serves as the new standard for length.

The circuit in Figure 6 is an example of a magnetic field generated by a changing electric field. A capacitor with parallel plates is charged at a constant rate by a steady current flowing through the long, straight leads in Figure 6A.

The objective is to apply Ampère’s circuital law for magnetic fields to the path P, which goes around the wire in Figure 6A. This law (named in honour of the French physicist André-Marie Ampère) can be derived from the Biot and Savart equation for the magnetic field produced by a current (equation [34]). Using vector calculus notation, Ampère’s law states that the integral ?B · dl along a closed path surrounding the current i is equal to ?₀i. (An integral is essentially a sum, and, in this case, ?B · dl is the sum of B cos ?dl taken for a small length of the path until the complete loop is included. At each segment of the path dl, ? is the angle between the field B and dl. ) The current i in Ampère’s law is the total flux of the current density Jthrough any surface surrounded by the closed path. In Figure 6A, the closed path is labeled P, and a surface S₁ is surrounded by path P. All the current density through S₁ lies within the conducting wire. The total flux of the current density is the current iflowing through the wire. The result for surface S₁ reflects the value of the magnetic field around the wire in the region of the path P. In Figure 6B, path P is the same but the surface S₂ passes between the two plates of the capacitor. The value of the total flux of the current density through the surface should also be i. There is, however, clearly no motion of charge at all through the surface S₂. The dilemma is that the value of the integral ?B · dl for the path P cannot be both ?₀i and zero.

Maxwell’s resolution of this dilemma was his conclusion that there must be some other kind of current density, called the displacement current J_d, for which the total flux through the surface S₂ would be the same as the current i through the surface S₁. J_d would take, for the surface S₂, the place of the current density J associated with the movement of charge, since J is clearly zero due to the lack of charges between the plates of the capacitor. What happens between the plates while the current i is flowing? Because the amount of charge on the capacitor increases with time, the electric field between the plates increases with time too. If the current stops, there is an electric field between the plates as long as the plates are charged, but there is no magnetic field around the wire. Maxwell decided that the new type of current density was associated with the changing of the electric field. He found that

where D = ?₀E and E is the electric field between the plates. In situations where matter is present, the field D in equation (48) is modified to include polarizationeffects; the result is D = ?₀E + P. The field D is measured in coulombs per square metre. Adding the displacement current to Ampère’s law represented Maxwell’s prediction that a changing electric field also could be a source of the magnetic fieldB. Following Maxwell’s predictions of electromagnetic waves, the German physicistHeinrich Hertz initiated the era of radio communications in 1887 by generating and detecting electromagnetic waves.

Using vector calculus notation, the four equations of Maxwell’s theory of electromagnetism are

where D = ?₀E + P, and H = B/?₀ ? M. The first equation is based on Coulomb’sinverse square law for the force between two charges; it is a form of Gauss’s law, which relates the flux of the electric field through a closed surface to the total charge enclosed by the surface. The second equation is based on the fact that apparently no magnetic monopoles exist in nature; if they did, they would be point sources of magnetic field. The third is a statement of Faraday’s law of magnetic induction, which reveals that a changing magnetic field generates an electric field. The fourth is Ampère’s law as extended by Maxwell to include the displacement current discussed above; it associates a magnetic field to a changing electric field as well as to an electric current.

Maxwell’s four equations represent a complete description of the classical theory of electromagnetism. His discovery that light is an electromagnetic wave meant thatoptics could be understood as part of electromagnetism. Only in microscopic situations is it necessary to modify Maxwell’s equations to include quantum effects. That modification, known as quantum electrodynamics (QED), accounts for certain atomic properties to a degree of precision exceeding one part in 100 million.

Sometimes it is necessary to shield apparatus from external electromagnetic fields. For a static electric field, this is a simple matter; the apparatus is surrounded by a shield made of a good conductor (e.g., copper). Shielding apparatus from a steady magnetic field is more difficult because materials with infinite magnetic permeability ? do not exist; for example, a hollow shield made of soft iron will reduce the magnetic field inside to a considerable extent but not completely. As discussed earlier, it is sometimes possible to superpose a field in the opposite direction to produce a very low field region and then to use additional material with a high ? for shielding. In the case of electromagnetic waves, the penetration of the waves in matter varies, depending on the frequency of the radiation and the electricconductivity of the medium. The skin depth ? (which is the distance in the conducting medium traversed for an amplitude decrease of 1/e, about 1/3) is given by

At high frequency, the skin depth is small. Therefore, to transmit electronic messages through seawater, for example, a very low frequency must be used to get a reasonable fraction of the signal far below the surface.

A metal shield can have some holes in it and still be effective. For instance, a typicalmicrowave oven has a frequency of 2.5 gigahertz, which corresponds to a wavelength of about 12 centimetres for the electromagnetic wave inside the oven. The metal shield on the door has small holes about two millimetres in diameter; the shield works because the wavelength of the microwave radiation is much greater than the size of the holes. On the other hand, the same shield is not effective with radiation of a much shorter wavelength. Visible light passes through the holes in the shield, as evidenced by the fact that it is possible to see inside a microwave oven when the door is closed.