Editing Electromagnetic field (section)

== Properties of the field ==
=== Electrostatics and magnetostatics ===
{{main|Electrostatics|Magnetostatics}}
[[File:VFPt image charge plane horizontal.svg|thumb|250px|Electric field of a positive point [[electric charge]] suspended over an infinite sheet of conducting material. The field is depicted by [[field line|electric field lines]], lines which follow the direction of the electric field in space.]]
The Maxwell equations simplify when the charge density at each point in space does not change over time and all electric currents likewise remain constant. All of the time derivatives vanish from the equations, leaving two expressions that involve the electric field,
<math display=block>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}</math>
and
<math display=block>\nabla\times\mathbf{E} = 0,</math>
along with two formulae that involve the magnetic field:
<math display=block>\nabla \cdot \mathbf{B} = 0</math>
and
<math display=block>\nabla \times \mathbf{B} = \mu_0 \mathbf{J}.</math>
These expressions are the basic equations of [[electrostatics]], which focuses on situations where electrical charges do not move, and [[magnetostatics]], the corresponding area of magnetic phenomena.{{sfnp|ps=|Feynman|Leighton|Sands|1970|loc=[https://www.feynmanlectures.caltech.edu/II_04.html §4.1]}}

=== Transformations of electromagnetic fields ===
{{further|Classical electromagnetism and special relativity|Electromagnetic four-potential|Electromagnetic tensor}}

Whether a physical effect is attributable to an electric field or to a magnetic field is dependent upon the observer, in a way that [[special relativity]] makes mathematically precise. For example, suppose that a laboratory contains a long straight wire that carries an electrical current. In the frame of reference where the laboratory is at rest, the wire is motionless and electrically neutral: the current, composed of negatively charged electrons, moves against a background of positively charged ions, and the densities of positive and negative charges cancel each other out. A test charge near the wire would feel no electrical force from the wire. However, if the test charge is in motion parallel to the current, the situation changes. In the rest frame of the test charge, the positive and negative charges in the wire are moving at different speeds, and so the positive and negative charge distributions are [[Lorentz contraction|Lorentz-contracted]] by different amounts. Consequently, the wire has a nonzero net charge density, and the test charge must experience a nonzero electric field and thus a nonzero force. In the rest frame of the laboratory, there is no electric field to explain the test charge being pulled towards or pushed away from the wire. So, an observer in the laboratory rest frame concludes that a {{em|magnetic}} field must be present.{{sfnp|ps=|Purcell|Morin|2012|pp=259–263}}{{sfnp|ps=|Feynman|Leighton|Sands|1970|loc=[https://www.feynmanlectures.caltech.edu/II_13.html §13.6]}}

In general, a situation that one observer describes using only an electric field will be described by an observer in a different inertial frame using a combination of electric and magnetic fields. Analogously, a phenomenon that one observer describes using only a magnetic field will be, in a relatively moving reference frame, described by a combination of fields. The rules for relating the fields required in different reference frames are the [[Classical electromagnetism and special relativity|Lorentz transformations of the fields]].{{sfnp|ps=|Purcell|Morin|2012|p=309}}

Thus, electrostatics 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 a consequence of different frames of measurement. The fact that the two field variations can be reproduced just by changing the motion of the observer is further evidence that there is only a single actual field involved which is simply being observed differently.

=== Reciprocal behavior of electric and magnetic fields ===
{{Main | Faraday's law of induction | Ampère's circuital law }}
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 inside a loop creates an electric voltage around the loop". This is the principle behind the [[electric generator]].

Ampere's Law roughly states that "an electrical current around a loop creates a magnetic field through the loop". 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 ===
[[File:Onde electromagnetique.svg|thumb|upright=1.8|A [[linear polarization|linearly polarized]] electromagnetic [[plane wave]] propagating parallel to the z-axis is a possible solution for the [[electromagnetic wave equation]]s in [[free space]]. The [[electric field]], {{math|'''E'''}}, and the [[magnetic field]], {{math|'''B'''}}, are perpendicular to each other and the direction of propagation.|400x200px]]
[[Maxwell's equations]] can be combined to derive [[wave equation]]s.  The solutions of these equations take the form of an [[electromagnetic wave]].  In a volume of space not containing charges or currents ([[free space]]) – that is, where <math>\rho</math> and {{math|'''J'''}} are zero, the electric and magnetic fields satisfy these [[electromagnetic wave equation]]s:{{sfnp|ps=|Feynman|Leighton|Sands|1970|loc=[https://www.feynmanlectures.caltech.edu/II_20.html §20.1]}}{{sfnp|ps=|Cheng|1989|loc=Intermediate-level textbook}}
: <math> \left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{E} \ \ = \ \ 0</math>
: <math> \left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{B} \ \ = \ \ 0</math>

[[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]]. This unified the physical understanding of electricity, magnetism, and light: visible light is but one portion of the full range of electromagnetic waves, the [[electromagnetic spectrum]].

=== Time-varying EM fields in Maxwell's equations ===
{{main|near and far field|near field optics|virtual particle|dielectric heating|Electromagnetic induction}}
An electromagnetic field very far from currents and charges (sources) is called [[electromagnetic radiation]] (EMR) since it radiates from the charges and currents in the source. Such radiation can occur across a wide range of frequencies called the [[electromagnetic spectrum]], including [[radio wave]]s, [[microwave]], [[infrared]], [[visible light]], [[ultraviolet light]], [[X-rays]], and [[gamma ray]]s. The many commercial applications of these radiations are discussed in the named and linked articles.

A notable application of visible light is that this type of energy from the Sun powers all life on Earth that either makes or uses oxygen.

A changing electromagnetic field which is physically close to currents and charges (see [[near and far field]] for a definition of "close") will have a [[dipole]] characteristic that is dominated by either a changing [[electric dipole]], or a changing [[magnetic dipole]]. This type of dipole field near sources is called an electromagnetic ''near-field''.

Changing {{em|electric}} dipole fields, as such, are used commercially as near-fields mainly as a source of [[dielectric heating]]. Otherwise, they appear parasitically around conductors which absorb EMR, and around antennas which have the purpose of generating EMR at greater distances.

Changing {{em|magnetic}} dipole fields (i.e., magnetic near-fields) are used commercially for many types of [[Electromagnetic induction|magnetic induction]] devices. These include motors and electrical transformers at low frequencies, and devices such as [[RFID]] tags, [[metal detector]]s, and [[MRI]] scanner coils at higher frequencies.