Definitions

# electromagnetic field

Property of space caused by the motion of an electric charge. A stationary charge produces an electric field in the surrounding space. If the charge is moving, a magnetic field is also produced. A changing magnetic field also produces an electric field. The interaction of electric and magnetic fields produces an electromagnetic field, which has its own existence in space apart from the charges involved. An electromagnetic field can sometimes be described as a wave that transports electromagnetic radiation.

The electromagnetic field is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity 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, the weak interaction, and the strong interaction). The field propagates by electromagnetic radiation; in order of increasing energy (decreasing wavelength) electromagnetic radiation comprises: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

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.

From a classical perspective, the electromagnetic field can be regarded as a smooth, continuous field, propagated in a wavelike manner; whereas, from a quantum mechanical perspective, the field is seen as quantised, being composed of individual photons.

## Structure of the electromagnetic field

The electromagnetic field may be viewed in two distinct ways.

### Continuous structure

Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects. For example, oscillating charges produce electric and magnetic fields that may be viewed in a 'smooth', continuous, wavelike manner. 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). This problem leads to another view.

### Discrete structure

The electromagnetic field may be thought of in a more 'coarse' way. Experiments reveal that electromagnetic energy transfer is better described as being carried away in 'packets' or 'chunks' called photons with a fixed frequency. Planck's relation links the energy $E$ of a photon to its frequency $nu$ through the equation:

$E= , h , nu$

where $h$ is Planck's constant, named in honor of Max Planck, and $nu$ is the frequency of the photon . For example, in the photoelectric effect —the emission of electrons from metallic surfaces subjected to electromagnetic radiation— it is found that increasing the intensity of the incident radiation has no effect, and that only the frequency of the radiation is relevant in ejecting electrons.

This quantum picture of the electromagnetic field has proved very successful, giving rise to quantum electrodynamics, a quantum field theory describing the interaction of electromagnetic radiation with charged matter.

## Dynamics of the electromagnetic field

In the past, electrically charged objects were thought to produce two 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.

Once this electromagnetic field has been produced from a given charge distribution, other charged objects in this field will experience a force (in a similar way that planets experience a force in the gravitational field of the Sun). 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 electromagnetic field as a feedback loop

The behavior of the electromagnetic field can be resolved into four different parts of a loop: (1) the electric and magnetic fields are generated by electric charges, (2) the electric and magnetic fields interact only with each other, (3) the electric and magnetic fields produce forces on electric charges, (4) the electric charges move in space.

The feedback loop can be summarized in a list, including phenomena belonging to each part of the loop:

• charges generate fields
• the fields interact with each other
• fields act upon charges
• 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 ($star$)
• charges move

Phenomena in the list are marked with a star ($star$) if they consist of magnetic fields and moving charges which can be reduced by suitable Lorentz transformations to electric fields and static charges. This means that the magnetic field ends up being (conceptually) reduced to an appendage of the electric field, i.e. something which interacts with reality only indirectly through the electric field.

## 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 $mathbf\left\{E\right\}\left(x, y, z, t\right)$ (electric field) and $mathbf\left\{B\right\}\left(x, y, z, t\right)$ (magnetic field).

If only the electric field ($mathbf\left\{E\right\}$) is non-zero, and is constant in time, the field is said to be an electrostatic field. Similarly, if only the magnetic field ($mathbf B$) 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.

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 in a vacuum by Maxwell's equations. In the vector field formalism, these are:

$nabla cdot mathbf\left\{E\right\} = frac\left\{rho\right\}\left\{varepsilon_0\right\}$ (Gauss' law)

$nabla cdot mathbf\left\{B\right\} = 0$ (Gauss' law for magnetism)

$nabla times mathbf\left\{E\right\} = -frac \left\{partial mathbf\left\{B\right\}\right\}\left\{partial t\right\}$ (Faraday's law)

$nabla times mathbf\left\{B\right\} = mu_0 mathbf\left\{J\right\} + mu_0varepsilon_0 frac\left\{partial mathbf\left\{E\right\}\right\}\left\{partial t\right\}$ (Ampère-Maxwell 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 $mathbf J$ 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.

## Properties of the field

### Reciprocal behavior of electric and magnetic fields

The two Maxwell equations, Faraday's Law and the Ampère-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.

The Ampère-Maxwell 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.

### Light as an electromagnetic disturbance

Maxwell's equations take the form of an electromagnetic wave in an area that is very far away from any charges or currents (free space) - that is, where $rho$ and $mathbf J$ are zero. It can be shown, that, under these conditions, the electric and magnetic fields satisfy the electromagnetic wave equation:

$left\left(nabla^2 - \left\{ 1 over \left\{c\right\}^2 \right\} \left\{partial^2 over partial t^2\right\} right\right) mathbf\left\{E\right\} = 0$

$left\left(nabla^2 - \left\{ 1 over \left\{c\right\}^2 \right\} \left\{partial^2 over partial t^2\right\} right\right) mathbf\left\{B\right\} = 0$

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 Ampère's circuital law.

## Relation to and comparison with other physical fields

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'.

### Electromagnetic and gravitational fields

Sources of electromagnetic fields consist of two types of charge - 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 is only one type (no negative masses), or, in more colloquial terms, 'gravity is always attractive'.

The relative strengths and ranges of the four interactions and other information are tabulated below:

Theory Interaction mediator Relative Magnitude Behavior Range
Chromodynamics Strong interaction gluon 1038 1 10-15 m
Electrodynamics Electromagnetic interaction photon 1036 1/r2 infinite
Flavordynamics Weak interaction W and Z bosons 1025 1/r5 to 1/r7 10-16 m
Geometrodynamics Gravitation graviton 100 1/r2 infinite

## Applications

Properties of the electromagnetic field are exploited in many areas of industry. The use of electromagnetic radiation is seen in various disciplines. For example, X-rays are high frequency electromagnetic radiation and are used in radio astronomy, radiography in medicine and radiometry in telecommunications. Other medical applications include laser therapy, which is an example of photomedicine. Applications of lasers are found in military devices such as laser-guided bombs, as well as more down to earth devices such as barcode readers and CD players. Something as simple as a relay in any electrical device uses an electromagnetic field to engage or to disengage the two different states of output (ie, when electricity is not applied, the metal strip will connect output A and B, but if electricity is applied, an electromagnetic field will be created and the metal strip will connect output A and C).

## Health and safety

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. In workplace environments, where EMF exposures can be up to 10,000 times greater than the average, the US National Institute for Occupational Safety and Health (NIOSH) has issued some cautionary advisories but stresses that the data is currently too limited to draw good conclusions.

The potential effects of electromagnetic fields on human health vary widely depending on the frequency and intensity of the fields. For more information on the health effects due to specific parts of the electromagnetic spectrum, see the following articles with details of possible dangers (MRI) and some currently unfounded fears (mobile phones):