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{{short description|Electric and magnetic fields produced by moving charged objects}}{{for|the British hacker convention|Electromagnetic Field (festival)}}{{Electromagnetism|cTopic=Electrodynamics}}An electromagnetic field (also EMF or EM field) is a physical field produced by moving electrically charged objects.BOOK, Richard Feynman, The Feynman Lectures on Physics Vol II, Addison Wesley Longman, 1970, 978-0-201-02115-8,weblink "A â€œfieldâ€ is any physical quantity which takes on different values at different points in space.", It affects the behavior of non-comoving charged objects at any distance of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature (the others are gravitation, weak interaction and strong interaction).The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law.Purcell. p5-11;p61;p277-296 The force created by the electric field is much stronger than the force created by the magnetic field.Purcell, p235: We then calculate the electric field due to a charge moving with constant velocity; it does not equal the spherically symmetric Coulomb field.From a classical perspective in the history of electromagnetism, the electromagnetic field can be regarded as a smooth, continuous field, propagated in a wavelike manner; whereas from the perspective of quantum field theory, the field is seen as quantized, being composed of individual particles.

## Structure

The electromagnetic field may be viewed in two distinct ways: a continuous structure or a discrete structure.

### Continuous structure

Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects. For example, oscillating charges produce variations in electric and magnetic fields that may be viewed in a 'smooth', continuous, wavelike fashion. In this case, energy is viewed as being transferred continuously through the electromagnetic field between any two locations. For instance, the metal atoms in a radio transmitter appear to transfer energy continuously. This view is useful to a certain extent (radiation of low frequency), but problems are found at high frequencies (see ultraviolet catastrophe).BOOK, Introduction to Electrodynamics, Griffiths, David J., Prentice Hall, 1999, 0-13-805326-X, Upper Saddle River, New Jersey 07458, 364,weblink

### Discrete structure

The electromagnetic field may be thought of in a more 'coarse' way. Experiments reveal that in some circumstances electromagnetic energy transfer is better described as being carried in the form of packets called quanta (in this case, photons) with a fixed frequency. Planck's relation links the photon energy E of a photon to its frequency f through the equation:BOOK, Spencer, James N., etal, Chemistry: Structure and Dynamics, John Wiley & Sons, 2010, 9780470587119, 78,weblink
E= , h f
where h is Planck's constant, and f is the frequency of the photon . Although modern quantum optics tells us that there also is a semi-classical explanation of the photoelectric effectâ€”the emission of electrons from metallic surfaces subjected to electromagnetic radiationâ€”the photon was historically (although not strictly necessarily) used to explain certain observations. It is found that increasing the intensity of the incident radiation (so long as one remains in the linear regime) increases only the number of electrons ejected, and has almost no effect on the energy distribution of their ejection. Only the frequency of the radiation is relevant to the energy of the ejected electrons.This quantum picture of the electromagnetic field (which treats it as analogous to harmonic oscillators) has proven very successful, giving rise to quantum electrodynamics, a quantum field theory describing the interaction of electromagnetic radiation with charged matter. It also gives rise to quantum optics, which is different from quantum electrodynamics in that the matter itself is modelled using quantum mechanics rather than quantum field theory.

## Dynamics

In the past, electrically charged objects were thought to produce two different, unrelated types of field associated with their charge property. An electric field is produced when the charge is stationary with respect to an observer measuring the properties of the charge, and a magnetic field as well as an electric field is produced when the charge moves, creating an electric current with respect to this observer. Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole â€” the electromagnetic field. Until 1820, when the Danish physicist H. C. Ã˜rsted showed the effect of electric current on a compass needle, electricity and magnetism had been viewed as unrelated phenomenaJOURNAL, Stauffer, Robert C., Speculation and experiment in the background of Oersted's discovery of electromagnetism, Isis, 1957, 48, 33-50, 226900, . In 1831, Michael Faraday made the seminal observation that time-varying magnetic fields could induce electric currents and then, in 1864, James Clerk Maxwell published his famous paper A Dynamical Theory of the Electromagnetic Field.Maxwell 1864 5, page 499; also David J. Griffiths (1999), Introduction to electrodynamics, third Edition, ed. Prentice Hall, pp. 559-562"(as quoted in Gabriela, 2009)Once this electromagnetic field has been produced from a given charge distribution, other charged or magnetised objects in this field may experience a force. If these other charges and currents are comparable in size to the sources producing the above electromagnetic field, then a new net electromagnetic field will be produced. Thus, the electromagnetic field may be viewed as a dynamic entity that causes other charges and currents to move, and which is also affected by them. These interactions are described by Maxwell's equations and the Lorentz force law. This discussion ignores the radiation reaction force.

## Feedback loop

The behavior of the electromagnetic field can be divided into four different parts of a loop:BOOK, Introduction to Electrodynamics, Griffith, David J., Prentice, 1999, 0-13-805326-X, Upper Saddle River, New Jersey, 07458, 321, Chapter 7.3, Maxwell's Equations,weblink
• the electric and magnetic fields are generated by moving electric charges,
• the electric and magnetic fields interact with each other,
• the electric and magnetic fields produce forces on electric charges,
• the electric charges move in space.
A common misunderstanding is that (a) the quanta of the fields act in the same manner as (b) the charged particles, such as electrons, that generate the fields. In our everyday world, electrons travel slowly through conductors with a drift velocity of a fraction of a centimeter (or inch) per second and through a vacuum tube at speeds of around 1 thousand km/s,WEB, Hoag, JB, Velocity of Electrons in a Vacuum Tube,weblink Basic Radio, 22 June 2019, 2009, but fields propagate at the speed of light, approximately 300 thousand kilometers (or 186 thousand miles) a second. The speed ratio between charged particles in a conductor and field quanta is on the order of one to a million. Maxwell's equations relate (a) the presence and movement of charged particles with (b) the generation of fields. Those fields can then affect the force on, and can then move other slowly moving charged particles. Charged particles can move at relativistic speeds nearing field propagation speeds, but, as Einstein showed{{Citation needed|date=May 2011}}, this requires enormous field energies, which are not present in our everyday experiences with electricity, magnetism, matter, and time and space.The feedback loop can be summarized in a list, including phenomena belonging to each part of the loop:{{citation needed|date=August 2015}}
• charged particles generate electric and magnetic fields
• the fields interact with each other
• changing electric field acts like a current, generating 'vortex' of magnetic field
• Faraday induction: changing magnetic field induces (negative) vortex of electric field
• Lenz's law: negative feedback loop between electric and magnetic fields
• fields act upon particles
• Lorentz force: force due to electromagnetic field
• electric force: same direction as electric field
• magnetic force: perpendicular both to magnetic field and to velocity of charge
• particles move
• current is movement of particles
• particles generate more electric and magnetic fields; cycle repeats

## Mathematical description

There are different mathematical ways of representing the electromagnetic field. The first one views the electric and magnetic fields as three-dimensional vector fields. These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates. As such, they are often written as E(x, y, z, t) (electric field) and B(x, y, z, t) (magnetic field).If only the electric field (E) is non-zero, and is constant in time, the field is said to be an electrostatic field. Similarly, if only the magnetic field (B) is non-zero and is constant in time, the field is said to be a magnetostatic field. However, if either the electric or magnetic field has a time-dependence, then both fields must be considered together as a coupled electromagnetic field using Maxwell's equations.Electromagnetic Fields (2nd Edition), Roald K. Wangsness, Wiley, 1986. {{ISBN|0-471-81186-6}} (intermediate level textbook)With the advent of special relativity, physical laws became susceptible to the formalism of tensors. Maxwell's equations can be written in tensor form, generally viewed by physicists as a more elegant means of expressing physical laws.The behaviour of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics (electromagnetic fields), is governed by Maxwell's equations. In the vector field formalism, these are:
nabla cdot mathbf{E} = frac{rho}{varepsilon_0} (Gauss's law)
nabla cdot mathbf{B} = 0 (Gauss's law for magnetism)
nabla times mathbf{E} = -frac {partial mathbf{B}}{partial t} (Faraday's law)
nabla times mathbf{B} = mu_0 mathbf{J} + mu_0varepsilon_0 frac{partial mathbf{E}}{partial t} ((AmpÃ¨re's circuital law#Extending the original law: the Maxwellâ€“AmpÃ¨re equation|Maxwellâ€“AmpÃ¨re law))
where rho is the charge density, which can (and often does) depend on time and position, epsilon_0 is the permittivity of free space, mu_0 is the permeability of free space, and J is the current density vector, also a function of time and position. The units used above are the standard SI units. Inside a linear material, Maxwell's equations change by switching the permeability and permittivity of free space with the permeability and permittivity of the linear material in question. Inside other materials which possess more complex responses to electromagnetic fields, these terms are often represented by complex numbers, or tensors.The Lorentz force law governs the interaction of the electromagnetic field with charged matter.When a field travels across to different media, the properties of the field change according to the various boundary conditions. These equations are derived from Maxwell's equations.The tangential components of the electric and magnetic fields as they relate on the boundary of two media are as follows:Schaum's outline of theory and problems of electromagnetics(2nd Edition), Joseph A. Edminister, McGraw-Hill, 1995. {{ISBN|0070212341}}(Examples and Problem Practice)
mathbf{E}_{1} = mathbf{E}_{2}
mathbf{H}_{1} = mathbf{H}_{2} (current-free)
mathbf{D}_{1} = mathbf{D}_{2} (charge-free)
mathbf{B}_{1} = mathbf{B}_{2}
The angle of refraction of an electric field between media is related to the permittivity (varepsilon) of each medium:
frac{{tantheta_1}}{{tantheta_2}} = frac{{varepsilon_{r2}}}{{varepsilon_{r1}}}
The angle of refraction of a magnetic field between media is related to the permeability (mu) of each medium:
frac{{tantheta_1}}{{tantheta_2}} = frac{{mu_{r2}}}{{mu_{r1}}}

## Properties of the field

### Reciprocal behavior of electric and magnetic fields

The two Maxwell equations, Faraday's Law and the AmpÃ¨re-Maxwell Law, illustrate a very practical feature of the electromagnetic field. Faraday's Law may be stated roughly as 'a changing magnetic field creates an electric field'. This is the principle behind the electric generator.Ampere's Law roughly states that 'a changing electric field creates a magnetic field'. Thus, this law can be applied to generate a magnetic field and run an electric motor.

### Behavior of the fields in the absence of charges or currents

Maxwell's equations take the form of an electromagnetic wave in a volume of space not containing charges or currents (free space) â€“ that is, where rho and J are zero. Under these conditions, the electric and magnetic fields satisfy the electromagnetic wave equation:Field and Wave Electromagnetics (2nd Edition), David K. Cheng, Prentice Hall, 1989. {{ISBN|978-0-201-12819-2}} (Intermediate level textbook)
left( nabla^2 - { 1 over {c}^2 } {partial^2 over partial t^2} right) mathbf{E} = 0 left( nabla^2 - { 1 over {c}^2 } {partial^2 over partial t^2} right) mathbf{B} = 0
James Clerk Maxwell was the first to obtain this relationship by his completion of Maxwell's equations with the addition of a displacement current term to Ampere's circuital law.

## Relation to and comparison with other physical fields

{{Expand section|date=June 2008}}Being one of the four fundamental forces of nature, it is useful to compare the electromagnetic field with the gravitational, strong and weak fields. The word 'force' is sometimes replaced by 'interaction' because modern particle physics models electromagnetism as an exchange of particles known as gauge bosons.

### Electromagnetic and gravitational fields

Sources of electromagnetic fields consist of two types of charge â€“ positive and negative. This contrasts with the sources of the gravitational field, which are masses. Masses are sometimes described as gravitational charges, the important feature of them being that there are only positive masses and no negative masses. Further, gravity differs from electromagnetism in that positive masses attract other positive masses whereas same charges in electromagnetism repel each other.The relative strengths and ranges of the four interactions and other information are tabulated below:{| class="wikitable"! Theory !! Interaction !! mediator !! Relative Magnitude !! Behavior !! Range
Chromodynamics >Strong interaction >gluon >| 10âˆ’15 m
Electrodynamics >Electromagnetic interaction >photon >r2 >| infinite
Flavordynamics >Weak interaction >W and Z bosons >r5 to 1/r7 >| 10âˆ’16 m
Geometrodynamics >Gravitation >graviton (hypothesised) >r2 >| infinite

## Applications

### Static E and M fields and static EM fields

When an EM field (see electromagnetic tensor) is not varying in time, it may be seen as a purely electrical field or a purely magnetic field, or a mixture of both. However the general case of a static EM field with both electric and magnetic components present, is the case that appears to most observers. Observers who see only an electric or magnetic field component of a static EM field, have the other (electric or magnetic) component suppressed, due to the special case of the immobile state of the charges that produce the EM field in that case. In such cases the other component becomes manifest in other observer frames.A consequence of this, is that any case that seems to consist of a "pure" static electric or magnetic field, can be converted to an EM field, with both E and M components present, by simply moving the observer into a frame of reference which is moving with regard to the frame in which only the â€œpureâ€ electric or magnetic field appears. That is, a pure static electric field will show the familiar magnetic field associated with a current, in any frame of reference where the charge moves. Likewise, any new motion of a charge in a region that seemed previously to contain only a magnetic field, will show that the space now contains an electric field as well, which will be found to produces an additional Lorentz force upon the moving charge.Thus, electrostatics, as well as magnetism and magnetostatics, are now seen as studies of the static EM field when a particular frame has been selected to suppress the other type of field, and since an EM field with both electric and magnetic will appear in any other frame, these "simpler" effects are merely the observer's. The "applications" of all such non-time varying (static) fields are discussed in the main articles linked in this section.

### Other

• Electromagnetic field can be used to record data on static electricity.
• Old televisions can be traced with Electromagnetic fields.

## Health and safety

The potential effects of electromagnetic fields on human health vary widely depending on the frequency and intensity of the fields.The potential health effects of the very low frequency EMFs surrounding power lines and electrical devices are the subject of on-going research and a significant amount of public debate. The US National Institute for Occupational Safety and Health (NIOSH) and other US government agencies do not consider EMFs a proven health hazard. NIOSH has issued some cautionary advisories but stresses that the data are currently too limited to draw good conclusions.WEB,weblink NIOSH Fact Sheet: EMFs in the Workplace, 31 August 2015, United States National Institute for Occupational Safety and Health, 1996, On the other hand, radiation from other parts of the electromagnetic spectrum, such as ultraviolet light and gamma rays, are known to cause significant harm in some circumstances. For more information on the health effects due to specific electromagnetic phenomena and parts of the electromagnetic spectrum, see the following articles:

{{Div col|colwidth=25em}} {{Div col end}}

## References

{{reflist}}

• BOOK, Griffiths, David J., Introduction to Electrodynamics, 1999, Prentice Hall, Upper Saddle River, NJ, 978-0138053260, 3rd,weblink
• JOURNAL, Maxwell, J. C., A Dynamical Theory of the Electromagnetic Field, Philosophical Transactions of the Royal Society of London, 1 January 1865, 155, 0, 459â€“512, 10.1098/rstl.1865.0008, (This article accompanied a December 8, 1864 presentation by Maxwell to the Royal Society.)
• BOOK, Purcell, Edward M., Morin, David J., Electricity and magnetism, 2012, Cambridge Univ. Press, Cambridge, 9781-10701-4022, 3rd,

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