| Electromagnetic Field |
Article Index for Electromagnetic |
Website Links For Electromagnetic Field |
Information About ™Electromagnetic Field |
| CATEGORIES ABOUT ELECTROMAGNETIC FIELD | |
| fundamental physics concepts | |
| electromagnetism | |
| equations | |
|
The electromagnetic field is a physical influence (a Field ) that permeates through all of Space and which arises from Charge d objects and describes one of the four Fundamental Force s of nature - Electromagnetism . It can be viewed as the combination of an Electric Field and a Magnetic Field . The electric field is produced by non-moving charges, the magnetic field by moving charges (currents), these two often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is dictated by Maxwell's Equations and the Lorentz Force Law . NATURE OF THE ELECTROMAGNETIC FIELD As with many physical concepts, there are various ways of thinking about the electromagnetic field. The field may be viewed in two distinct ways. Continuous structure Oscillating electric and magnetic fields may be viewed in a 'smooth', continuous, wavelike manner. These fields are sometimes assumed to vary sinusoidally with a single Frequency . In this case, energy is viewed as being transferred continuously through the electromagnetic field between any two locations. For example, 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 Photon s with a fixed frequency. Planck's relation links the energy of a photon to its frequency through the equation: : where is Planck's Constant , named in honour of Max Planck . For example, in the Photoelectric Effect - the emission of electrons from metallic surfaces by electromagnetic radiation - it is found that increasing the intensity of the incident radiation has no effect and 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 which describes the interaction of electromagnetic radiation with charged matter. Dynamics 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 realised 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. Maxwells Equations and the Lorentz Force Law describe how the electromagnetic field interacts with charged objects. MATHEMATICAL DESCRIPTION There are different mathematical ways of representing the electromagnetic field. Vector field approach The electric and magnetic fields are usually described by the use of three-dimensional Vector Field s. 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 (electric field) and (magnetic field). If only the Electric Field () is non-zero, and is constant in time, the field is said to be an Electrostatic Field . Similarly, if only the Magnetic Field () is non-zero and is constant in time, the feild 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 . The behaviour of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or Electrodynamics (electromagnetic fields), is governed by Maxwell's Equations : : (Gauss' Law - electrostatics) : (Gauss' Law - magnetostatics) : (Faraday's Law) : (Ampère-Maxwell Law) where is the charge density, which can and often is a function of time and position, is the Permittivity of free space, is the Permiability of free space, and is the current density vector, also a function of time and position. The units used above are the standard SI units. The electric and magnetic fields transform under a Lorentz Boost , a relativistic transformation of coordinates, in the direction as: : : Tensor field approach The electric and magnetic fields can be combined together mathematically to form an antisymmetric, second-rank Tensor , or a Bivector , usually written as . This is called the Electromagnetic Field Tensor , and it puts the electric and magnetic forces on the same footing. In matrix form, the tensor is as below. : There is actually another way of merging the electric and magnetic fields into an antisymmetric tensor, by replacing and , to get the dual tensor . : In the context of Special Relativity , both of these transform according to the Lorentz Transformation like . Using this tensor notation, Maxwell's Equations have the following form. : : In the above, the tensor notation is used to denote partial derivatives, . The four-vector is called the Current Density Four-vector , which is the relativistic analogue to the charge density and current density. This four-vector is as follows. : This short form of writing Maxwell's equations illustrates an idea shared amongst some physicists, namely that the laws of physics take on a simpler form when written using Tensors . PROPERTIES OF THE FIELD Reciprocal behaviour 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 motor. 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. Light as an electromagnetic disturbance Maxwell's Equations take the following, free space, form in an area that is very far away from any charges or currents - that is where and are zero. : : : : In the above, the substitution has been made, where is the speed of light. Taking the curl of the last two equations, the result is as follows. : : However, the first two equations mean . So plugging this in, and moving the curls within the time derivates and then plugging in for the resultant curls, the result is as follows. : : Or: : : Or even: : : In this last form, the is the D'Alembertian , which is , so the last two forms are the same thing written in two different ways. However, these equations are wave equations, that is valid 's and 's have an oscillatory form, such as a sinusoid. Moreover, the first two of the free space Maxwell's equations imply that the waves are Transverse Wave s. The last two of the free space Maxwell's equations imply that the wave of the electric field is in phase with and perpindicular to the magnetic field wave. Moreover, the term represents the speed of the wave. So these Electromagnetic Wave s travel at the speed of light. James Clerk Maxwell , afterwhom Maxwell's equations are named, suggested when he made these calculations that as these waves travel at the same speed as light, that light would actually be such a wave. His suggestion proved correct, and light is indeed an electromagnetic wave. RELATION TO AND COMPARISON WITH OTHER PHYSICAL FIELDS Being one of the four Fundamental Force s of nature, it is useful to compare the electromagnetic field with the Gravitational , Strong and Weak nuclear forces. The word 'force' is sometimes replaced by 'interaction'. 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'. OTHER DESCRIPTIONS OF THE ELECTROMAGNETIC FIELD Classical fluid interpretation See Also: Hydrodynamic interpretation of the electromagnetic field The electromagnetic field may be visualised in analogy to a fluid. In particular, the electric and magnetic vector fields can be thought of as being the velocities of a pair of Incompressible Fluids which permeate space. In the absence of charges, these fluids would be at rest, so that their velocity fields would be zero. Since both fluids are incompressible, their densities do not change: it is not possible to compress magnetic or electric fluid into a smaller space. Photonic fluid interpretation An alternative interpretation would be that the field is not actually a velocity field, but a , independent of the speed of the observer (the charged object). Photonic fluid never changes speed but can change net direction and the intensity of its net movement in that direction. The velocity field interpretation is related to the hypothesis of a Luminiferous Aether through which electromagnetic waves would propagate. The proposition that the motion of the earth relative to the aether might be detectable (i.e. through an "aether wind") was disproven by the Michelson-Morley Experiment , whereupon it was argued that the experiment had disproved the very existence of the aether. This opinion prevailed, but remains disputed by some who equate the classical concept of the aether with the modern notion of a Quantum Electrodynamic fluid. (The disputants argue that proving that the earth does not travel through an "aether wind" is no more nor less significant than proving that the earth does not travel through its own gravitational or magnetic fields.) The necessity of an aether was seen to have vanished when it was replaced by Einstein 's Theory Of Relativity . According to Special Relativity , the Lorentz Force equation reduces to the equation : The magnetic field becomes a relativistic by-product of the electric field, i.e. Lorentz Transformations cause magnetic fields to be induced from electric fields, and vice versa. So the photonic fluid describes the electric field, and relativistic effects account for the derivative magnetic field. (This can be derived by applying a Lorentz transformation to a simplified version of Maxwell's Equations , and it is mentioned by Einstein in his paper ''On The Electrodynamics Of Moving Bodies'' {Link without Title} .) The varies with the velocity of the charged particle. 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 Bomb s, as well as more down to earth devices such as Barcode Reader s and CD Players . 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:
Phenomena in the list are marked with a star () if they consist of magnetic fields and moving charges which can be reduced by suitable Lorentz Transformation s 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. SEE ALSO
EXTERNAL LINKS
|
|
|