Electromagnetic field

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

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 with a fixed frequency. Planck's relation links the photon energy E of a photon to its frequency f through the equation:[4]

$${\displaystyle E=\,hf}$$

where h is the Planck 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 effect—the emission of electrons from metallic surfaces subjected to electromagnetic radiation—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 modeled using quantum mechanics rather than quantum field theory.

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—the electromagnetic field. Until 1820, when the Danish physicist H. C. Ørsted showed the effect of electric current on a compass needle, electricity and magnetism had been viewed as unrelated phenomena.[5] 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".[6]

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.

The behavior of the electromagnetic field can be divided into four different parts of a loop:[7]

• 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 per second and through a vacuum tube at speeds of around 1000 km/s,[8] but fields propagate at the speed of light, approximately 300 000 kilometers (or 186 000 miles) per 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 Albert Einstein showed,[9] 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:[10]

• 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
• charged particles move
  • current is movement of particles
• charged particles generate more electric and magnetic fields; cycle repeats

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.[11]

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 behavior 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:

Gauss's law

${\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}}$

Gauss's law for magnetism

${\displaystyle \nabla \cdot \mathbf {B} =0}$

Faraday's law

${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}$

Maxwell–Ampère law

${\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}}$

where ${\displaystyle \rho }$ is the charge density, which can (and often does) depend on time and position, ${\displaystyle \varepsilon _{0}}$ is the permittivity of free space, ${\displaystyle \mu _{0}}$ 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:[12]

$${\displaystyle \mathbf {E} _{1}=\mathbf {E} _{2}}$$

$${\displaystyle \mathbf {H} _{1}=\mathbf {H} _{2}}$$

(current-free)

$${\displaystyle \mathbf {D} _{1}=\mathbf {D} _{2}}$$

(charge-free)

$${\displaystyle \mathbf {B} _{1}=\mathbf {B} _{2}}$$

The angle of refraction of an electric field between media is related to the permittivity ${\displaystyle (\varepsilon )}$ of each medium:

$${\displaystyle {\frac {\tan \theta _{1}}{\tan \theta _{2}}}={\frac {\varepsilon _{r2}}{\varepsilon _{r1}}}}$$

The angle of refraction of a magnetic field between media is related to the permeability ${\displaystyle (\mu )}$ of each medium:

$${\displaystyle {\frac {\tan \theta _{1}}{\tan \theta _{2}}}={\frac {\mu _{r2}}{\mu _{r1}}}}$$

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.

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.[14] In 2011, The International Agency for Research on Cancer (IARC) classified radiofrequency electromagnetic fields as possibly carcinogenic to humans (Group 2B), based on an increased risk for glioma, a malignant type of brain cancer, associated with wireless phone use.[15]

Employees working at electrical equipment and installations can always be assumed to be exposed to electromagnetic fields. The exposure of office workers to fields generated by computers, monitors, etc. is negligible owing to the low field strengths.[16] However, industrial installations for induction hardening and melting or on welding equipment may produce considerably higher field strengths and require further examination. If the exposure cannot be determined upon manufacturers' information, comparisons with similar systems or analytical calculations, measurements have to be accomplished. The results of the evaluation help to assess possible hazards to the safety and health of workers and to define protective measures. Since electromagnetic fields may influence passive or active implants of workers, it is essential to consider the exposure at their workplaces separately in the risk assessment.[17]

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.[18]

• Media related to Electromagnetic field at Wikimedia Commons
• On the Electrodynamics of Moving Bodies by Albert Einstein, June 30, 1905.
  • On the Electrodynamics of Moving Bodies (PDF)
• Non-Ionizing Radiation, Part 1: Static and Extremely Low-Frequency (ELF) Electric and Magnetic Fields (2002) by the IARC.
• Zhang J, Clement D, Taunton J (January 2000). "The efficacy of Farabloc, an electromagnetic shield, in attenuating delayed-onset muscle soreness". Clin J Sport Med. 10 (1): 15–21. doi:10.1097/00042752-200001000-00004. PMID 10695845. S2CID 36115711.
• National Institute for Occupational Safety and Health – EMF Topic Page
• Biological Effects of Power Frequency Electric and Magnetic Fields (May 1989) (110 pages) prepared for US Congress Office of Technology Assessment by Indira Nair, M.Granger Morgan, Keith Florig, Department of Engineering and Public Policy Carnegie Mellon University
• EMF Assessment (in German) based on EU guidelines 2013/35/EU

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