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Shapeyness (talk | contribs) Rewrote paragraph on B-fields being equivalent to E-fields under Lorentz transformation; it's longer but also a lot clearer and assumes less knowledge of the reader. Tags: Visual edit Mobile edit Mobile web edit Advanced mobile edit |
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== Electric charge ==
[[File:CoulombsLaw scal.svg|thumb|[[Coulomb's law|Coulomb's force]] for like (top) and opposite charges (bottom).]]
[[File:VFPt charges plus minus thumb.svg|thumb|[[Field line|Electric field lines]] point from positive charges to negative charges.]]
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| image2 = Openstax college-physics 22.17 Lorentz-force-right-hand.jpg
| caption2 = The force exerted on a positive charge by an electric field (top) and a magnetic field (bottom) combine to give the [[Lorentz force]].
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Electromagnetism is one of the [[Fundamental interaction|fundamental forces of nature]] alongside [[gravity]], the [[Strong interaction|strong force]] and the [[Weak interaction|weak force]] . Whereas gravity acts on all things that have mass, electromagnetism acts on all things that have [[electric charge]]. But unlike gravity, whilst mass can only be positive, charge can be both positive and negative. Furthermore, whilst positive masses exert an attractive [[Newton's law of universal gravitation|gravitational force]] on one another, positive charges exert an attractive [[Coulomb's law|electric force]] only on oppositely charged negative charges (and vice versa) and a repulsive electric force on other positive charges (negative charges also repel other negative charges).<ref name=":0">{{Cite book|last=Purcell, Edward M.|first=|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|publisher=|year=|isbn=978-1-107-01402-2|edition=Third|___location=Cambridge|pages=3-4|oclc=805015622}}</ref> The electric force between charged particles is called the Coulomb force and is described by [[Coulomb's law]] which states that the electric force between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them:<ref>{{Cite book|last=Walker, Jearl, 1945-|first=|url=https://www.worldcat.org/oclc/435710913|title=Fundamentals of physics|date=2011|publisher=Wiley|others=Halliday, David, 1916-2010., Resnick, Robert, 1923-2014.|year=|isbn=978-0-470-46911-8|edition=9th|___location=Hoboken, NJ|pages=578|oclc=435710913}}</ref>
<math>F=k_e{q_1q_2\over r^2}</math>
where ''F'' is the Coulomb force, ''k<sub>e</sub>'' is the [[Coulomb constant]], ''q<sub>1</sub>'' and ''q<sub>2</sub>'' are the charges of the two particles, and ''r<sup>2</sup>'' is the square of the distance between them.
Electric charge has several important properties:
* it is ''quantised'': this means that it can only take integer multiple values of the [[elementary charge]] ''e'' of an electron or proton (i.e. it can only take values of ''q'' = 0, ±''e'', ±2''e'', ±3''e'' , ...).<ref name=":1">{{Cite book|last=Serway|first=Raymond A.|title=Physics for Scientists and Engineers, Technology Update|publisher=Cengage Learning|year=2015|isbn=9781305465398|edition=9th|___location=|pages=692}}</ref> Although it is only a matter of definition, by convention the electron is said to have a negative charge −''e'' and the proton is said to have a positive charge +''e'' .<ref name=":0" /><ref name=":1" /> The first measurement of and experimental confirmation of the quantisation of charge was [[Robert Andrews Millikan|Robert Millikan's]] [[oil drop experiment]] in which the electric force on the particle is set to exactly counter the gravitational force that pulls it down, and the [[terminal velocity]] of this particle can be used to calculate its charge.<ref>{{Cite web|last=|first=|last2=|first2=|date=|title=UChicago Breakthroughs: 1910s|url=https://www.uchicago.edu/breakthroughs/1910s/|url-status=live|archive-url=|archive-date=|access-date=2020-11-26|website=The University of Chicago|language=en}}</ref><ref>{{Cite web|last=|first=|date=|title=Robert Millikan|url=http://www.aps.org/programs/outreach/history/historicsites/millikan.cfm|url-status=live|archive-url=|archive-date=|access-date=2020-11-26|website=APS physics|language=en}}</ref> This experiment is still one of the best confirmations of the quantisation of charge; one large experiment concluding in 2015 used over 100 million oil drops finding no evidence for charges that were not integer multiple values of ''e.<ref>{{cite web|last=|first=|date=January 2007|title=SLAC – Fractional Charge Search – Results|url=http://www.slac.stanford.edu/exp/mps/FCS/FCS_rslt.htm|url-status=live|archive-url=|archive-date=|accessdate=26 November 2020|website=|publisher=Stanford Linear Accelerator Center}}</ref>''
* it is ''conserved'': according to the [[Charge conservation|law of charge conservation]], the overall charge of a [[closed system]] (where no charge can leave or enter) cannot change. Quantum theory tells us that charges can be created but only in the [[pair production]] of oppositely charged [[Particle|particles]] and [[Antiparticle|antiparticles]] whose charges exactly cancel out so that charge is always conserved overall.<ref name=":0" /> Research suggests that the overall charge in the universe is neutral so we know that all the positive charges and negative charges in the universe will always cancel out in total.<ref>S. Orito; M. Yoshimura (1985). "Can the Universe be Charged?". ''Physical Review Letters''. '''54''' (22): 2457–60. {{Bibcode|1985PhRvL..54.2457O}}. {{doi|10.1103/PhysRevLett.54.2457}}. {{PMID|10031347}}.</ref><ref>E. Masso; F. Rota (2002). "Primordial helium production in a charged universe". ''Physics Letters B''. '''545''' (3–4): 221–25. {{arXiv|astro-ph/0201248}}. {{Bibcode|2002PhLB..545..221M}}. {{doi|10.1016/S0370-2693(02)02636-9}}.</ref>
* it produces [[Electric field|electric fields]]: by convention, electric [[Field line|field lines]] start at positive charges and end at negative charges, pointing in the direction of the electric force on a positive charge in the field (and in the opposite direction to the direction of the force on negative charges).<ref name=":2">{{Cite web|last=Pumplin|first=Jon|date=2000|title=Electric field lines|url=https://web.pa.msu.edu/courses/2000fall/phy232/lectures/efields/efieldlines.html|access-date=18 October 2018|website=Michigan State University Physics}}</ref><ref name=":3">{{Cite web|last=Nave|first=R|title=Electric Field|url=http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html|access-date=16 October 2018|website=Georgia State University Hyperphysics}}</ref> Electric field lines are drawn more densely the stronger the electric field to visualise the strength of the electric force on charged particles in the field.<ref name=":2" /> The electric field is defined as the force on a charge per unit charge so that Coulomb's law can be rewritten in terms of the electric field as shown:<ref name=":3" /><ref>{{Cite book|last=Purcell, Edward M.|first=|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|publisher=|year=|isbn=978-1-107-01402-2|edition=Third edition|___location=Cambridge|pages=7|oclc=805015622}}</ref>
: <math>\mathbf E_i=k_e{q_i\over r^2}\qquad \Longrightarrow \qquad \mathbf F_{12} = q_2 \mathbf E_1
\quad \And \quad \mathbf F_{21} = q_1\mathbf E_2 \qquad \Longrightarrow \qquad
\mathbf F = q\mathbf E </math>
:where <math display="inline">\mathbf E_i</math> is the electric field generated by charge <math display="inline">q_i</math> and <math display="inline">\mathbf F_{12}</math> is the force of charge ''q<sub>1</sub>'' on ''q<sub>2</sub>'' (and vice versa for <math display="inline">\mathbf F_{21}</math>). The final equation gives the general equation for the force exerted on a charged particle by an electric field.
* moving charges also produce [[Magnetic field|magnetic fields]]: moving charges (such as charged [[Free particle|free particles]] and [[Electric current|electric currents]]) and [[Magnet|permanent magnets]] produce magnetic fields that attract other moving charges and magnets.<ref>{{Cite web|title=The Feynman Lectures on Physics Vol. II Ch. 1: Electromagnetism|url=http://www.feynmanlectures.caltech.edu/II_01.html#Ch1-S2|access-date=2018-10-30|website=www.feynmanlectures.caltech.edu}}</ref> The direction of the force on a moving charge from a magnetic field is perpendicular to both the direction of motion and the direction of the magnetic field lines and can be found using the [[right-hand rule]] .<ref name=":6">{{Cite web|title=Magnetic forces|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html#c2|access-date=2020-11-26|website=hyperphysics.phy-astr.gsu.edu}}</ref> The magnitude of the force <math display="inline">|\mathbf F|</math> is given by the equation<ref name=":6" />
: <math>|\mathbf F| = q|\mathbf v \times \mathbf B| = q|\mathbf v| |\mathbf B|\sin\theta</math>
:where ''q'' is the charge of the particle and <math display="inline">|\mathbf v \times \mathbf B|</math> is the magnitude of the [[cross product]] between the velocity of the charge '''v''' and the magnetic field <math display="inline">\mathbf B</math> which is equal to the product of their magnitudes times the sine of the angle between them <math display="inline">\theta</math>.
The overall electromagnetic force on a charged particle is a combination of the electric and magnetic forces on it and is called the [[Lorentz force]]:<ref name=":6" /><ref>{{Cite book|last=Purcell, Edward M.|first=|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|publisher=|year=|isbn=978-1-107-01402-2|edition=Third edition|___location=Cambridge|pages=277|oclc=805015622}}</ref>
<math>\mathbf F=q(\mathbf E + \mathbf v \times \mathbf B)</math>
In all equations shown, symbols in bold are [[Vector (mathematics and physics)|vector quantities]] and the electric and magnetic fields are [[Vector field|vector fields]]. For more information on the mathematics used here, see [[cross product]] and [[vector calculus]].
=== Electric flux and Gauss' law ===
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| caption2 = The amount of electric flux through the closed surface (above) depends on the amount of charge enclosed by it. The flux also depends on other factors (left).
| image3 = GaussLaw2.svg
| caption3 = The amount of flux flowing into the enclosed volume is exactly cancelled by the flux flowing out of it because there are no charges enclosed.
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[[Flux]] can be thought of as the flow of the electric or magnetic field through a surface. Flux flowing through a surface is analogous to the flow of a fluid through a surface; the greater the density of flow and the greater the size of the surface, the more that can flow through it and the greater the angle between the surface and the direction of flow, the less that can flow through.<ref name=":4">{{Cite book|last=Grant, I. S. (Ian S.)|first=|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|year=|isbn=0-471-92711-2|edition=2nd ed|series=The Manchester Physics Series|___location=Chichester [England]|pages=17-22|oclc=21447877}}</ref> [[Gauss's law|Gauss' law]] is the first of [[Maxwell's equations]] and states that the [[electric flux]] <math display="inline">\Phi_E</math> through a closed surface is proportional to the amount of charge enclosed within it:<ref name=":4" /><ref>{{Cite web|title=Gauss's Law|url=http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html|access-date=2018-10-30|website=hyperphysics.phy-astr.gsu.edu}}</ref>
<math>\Phi_E = \frac{Q}{\varepsilon_0}</math>
where ''Q'' is the total charge enclosed by the surface, and <math display="inline">\varepsilon_0</math> is the [[permittivity of free space]].
This means that the more electric charge there is, the more electric flux is produced. From the equation, we can see that when there is a net positive charge inside the surface (with flux flowing out of the enclosed volume because electric field lines start at positive charges), the electric flux is defined as positive and when there is a net negative charge inside the surface (with flux flowing into the enclosed volume), the electric flux is defined as negative.
If there is no charge enclosed by the surface, then the electric flux must be zero. This means that when there is no charge enclosed by the surface either there are no field lines going through the surface at all or the flux flowing in through the surface must cancel out with the flux flowing out of the surface.<ref>{{Cite web|last=|first=|date=|title=The Feynman Lectures on Physics Vol. II Ch. 4: Electrostatics, S5: The flux of E|url=https://www.feynmanlectures.caltech.edu/II_04.html#Ch4-S5|url-status=live|archive-url=|archive-date=|access-date=2020-11-27|website=www.feynmanlectures.caltech.edu}}</ref>
=== Electric potential and potential energy ===
The [[electric potential energy]] of a system is defined as the amount of [[Work (physics)|physical work]] it would take to move all the charges in the sytem from very far away to the configuration that they are currently in and can be thought of as the energy stored in the electric field for a given configuration of charges.<ref>{{Cite book|last=Grant, I. S. (Ian S.)|first=|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|year=|isbn=0-471-92711-2|edition=2nd ed|___location=Chichester [England]|pages=33|oclc=21447877}}</ref> Another way of thinking about the electric potential energy is as analogously to [[Gravitational energy|gravitational potential energy]]; like a mass released from high up will convert its gravitational potential energy to kinetic energy as it falls to the ground, separated charges will convert their electric potential energy to kinetic energy as they are accelerated either attractively towards one another or repulsively away from one another.<ref name=":7">{{Cite book|last=Young, Hugh D., Freedman, Roger A.|first=|url=https://www.worldcat.org/oclc/897436903|title=Sears and Zemansky's University Physics with Modern Physics|publisher=[[Pearson]]|others=|year=2016|isbn=978-0-321-97361-0|edition=14th|___location=Boston|pages=776-778, 783|oclc=897436903}}</ref>
The [[electric potential]] of a system is defined as the electric potential energy per unit charge:<ref name=":7" />
<math>\phi = {U_E \over Q} </math>
where <math display="inline">\phi</math> is the electric potential, ''U<sub>E</sub>'' is the electric potential energy, and ''Q'' is the total charge of the system. The [[Voltage|potential difference]] (also known as voltage) between two points is defined as the work required to move a charge between those two points.<ref name=":7" /> Another equivalent definition of the electric potential is in terms of the electric field. For a static electric field, the electric field is defined to be minus the [[gradient]] of the electric potential and so the electric field can be thought of as a field that points away from high potentials towards low potentials.<ref>{{Cite book|last=Grant, I. S. (Ian S.)|first=|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|year=|isbn=0-471-92711-2|edition=2nd|___location=Chichester [England]|pages=65|oclc=21447877}}</ref> Electric fields point from positive charges to negative charges (and opposite charges attract) so this definition tells us that positive charges are attracted to low potentials and negative charges are attracted to high potentials.
== Magnetism ==
=== Gauss' law for magnetism ===
[[File:VFPt Earths Magnetic Field Confusion.svg|thumb|Magnets must have North and South poles so cannot be monopoles like electric charges. Therefore, the [[magnetic flux]] going out of a closed surface always cancels with the flux going in through the closed surface.]]
The second of [[Maxwell's equations|Mawell's equations]] is [[Gauss's law for magnetism|Gauss' law for magnetism]] which states that the [[magnetic flux]] <math display="inline">\Phi_B</math> through a closed surface is always equal to zero:<ref name=":5">{{Cite book|last=Purcell, Edward M.|first=|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|publisher=|year=|isbn=978-1-107-01402-2|edition=Third edition|___location=Cambridge|pages=322, 437|oclc=805015622}}</ref>
<math>\Phi_B = 0</math>
This law has colloquially been called "no magnetic monopoles" because it means that magnetic fields do not begin or end at single monopolar [[Magnetic monopole|magnetic charges]] (unlike electric fields which begin at positive charges and end at negative charges) but that magnets must always have more than one pole.<ref name=":5" /> For example, [[Magnet|permanent magnets]] have a North and a South pole and so are [[Magnetic dipole|magnetic dipoles]] and there can also be [[Quadrupole magnet|quadrupole magnets]] with four poles.<ref>{{Cite web|title=Quadrupole Magnetic Field|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magquad.html|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref>
=== Magnets ===
[[Magnet|Magnets]] are materials that produce their own magnetic fields. All magnets have North and South poles and the magnetic field produced by them points from the North to the South pole. Like electric charges, opposite magnetic poles attract one another and like magnetic poles repel one another but, unlike electric charges, magnetic poles cannot exist on their own (as shown by Gauss' law for magnetism) and so North and South poles must come together.<ref name=":8">{{Cite web|title=Magnets and Electromagnets|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c1|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref>
Materials that are attracted to magnets and which can be themselves magnetised are called [[ferromagnetic materials]]. Ferromagnetic materials can be magnetised because when their electron's [[Spin magnetic moment|spin magnetic moments]] are aligned with an external magnetic field, they sustain their own internal magnetic field even when the external magnetic field is removed. Examples of ferromagnetic materials which can be magnetised with external magnetic fields to create magnets are [[iron]], [[nickel]] and [[cobalt]].<ref name=":9">{{Cite web|title=Ferromagnetism|url=http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c4|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref>
=== The Biot–Savart law ===
{{Multiple image
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| image2 = Coil right-hand rule.svg
| caption2 = The magnetic field at a point produced by a moving charge as it travels (right). At first the point is at 90° to the charge so the sine component of the B-field equals one. When the charge moves away from the point, the angle changes and so the B-field decreases.
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[[Ampère's circuital law]] states that an electric current will induce a magnetic field.<ref>{{Cite web|title=Ampere's Law|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref>
A specific case is given by the [[Biot–Savart law]] which states that when there are no time-varying electric or magnetic fields, the strength of a magnetic field produced by a steady [[Electric current|current]] in a long, straight wire is proportional to the strength of the current and inversely proportional to the distance from the wire.<ref>{{Cite book|last=Grant, I. S. (Ian S.)|first=|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|year=|isbn=0-471-92711-2|edition=2nd ed|series=The Manchester Physics Series|___location=Chichester [England]|pages=138|oclc=21447877}}</ref> The direction of the magnetic field can be found using Ampère's [[right-hand grip rule]] which shows that the magnetic field will be curled around the current-carrying wire clockwise or anticlockwise depending on the direction of current flow.<ref>{{Cite book|last=Grant, I. S. (Ian S.)|first=|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|year=|isbn=0-471-92711-2|edition=2nd ed|series=The Manchester Physics Series|___location=Chichester [England]|pages=125|oclc=21447877}}</ref> The right-hand grip rule can also be used for current passing through a solenoidal wire producing a magnetic field inside the coil. This principle is utilised by [[Electromagnet|electromagnets]] which consist of a wire coiled around an iron core. Current is passed through the wire creating a magnetic field in the iron core. This magnetic field aligns the spins of the electrons in the iron which contribute to magnetic field making it stronger.<ref name=":8" /><ref name=":9" />
The Biot–Savart law for a charged particle states that the magnetic field ''B(r)'' produced by a moving charged particle is proportional to the charge ''q'' and velocity ''v'' of the particle and inversely proportional to the square of the distance away from it ''r<sup>2</sup>'':<ref>{{Cite book|last=Griffiths, David J. (David Jeffery), 1942-|first=|url=https://www.worldcat.org/oclc/1021068059|title=Introduction to electrodynamics|publisher=|year=|isbn=978-1-108-42041-9|edition=Fourth edition|___location=Cambridge, United Kingdom|pages=462|oclc=1021068059}}</ref>
<math>B(r) = {\mu_0 \over 4\pi} {q |\mathbf v \times \mathbf \hat{r}| \over r^2} =
{\mu_0 \over 4\pi} {qv \sin\theta \over r^2}</math>
where <math display="inline">\mu_0</math> is the [[Permeability Of Free Space|permeability of free space]] and <math display="inline">|\mathbf v \times \mathbf \hat{r}|</math> is the magnitude of the cross product between the velocity and a unit vector <math display="inline">\mathbf \hat{r}</math> pointing from the the charge to the point where the magnetic field is being calculated which is equal to the magnitude of the velocity times the sine of the angle <math display="inline">\theta</math> between the direction of motion of the charge and the direction of <math display="inline">\mathbf \hat{r}</math>.
== Electromagnetic unification ==
=== Maxwell's equations and electromagnetic radiation ===
[[File:EM_Spectrum_Properties_edit.svg|link=https://en.wikipedia.org/wiki/File:EM_Spectrum_Properties_edit.svg|thumb|473x473px|The [[electromagnetic spectrum]]]]
[[Maxwell's equations]] consist of Gauss' laws for electricity and magnetism (as described above) as well as the [[Maxwell-Faraday equation]] and the [[Ampère–Maxwell equation]].<ref name=":5" /> The Maxwell-Faraday equation states that a time-varying magnetic field produces an electric field whilst the Ampère–Maxwell equation extends Ampère's circuital law to include the statement that a time-varying electric field (as well as an electric current) will produce a magnetic field.<ref name=":5" /> Together Maxwell's equations provide a single uniform theory of electromagnetism and Maxwell's work in creating this theory has been called "the second great unification in physics" after the first great unification of [[Newton's law of universal gravitation]].<ref>{{Cite journal|last=Editors|first=AccessScience|date=2014|title=Unification theories and a theory of everything|url=https://www.accessscience.com/content/unification-theories-and-a-theory-of-everything/BR0814141|journal=Access Science|language=en|doi=10.1036/1097-8542.BR0814141}}</ref> The solution to Maxwell's equations in [[free space]] (where there are no charges or currents) produces [[Wave equation|wave equations]] corresponding to [[electromagnetic waves]] (with both electric and magnetic components) travelling at the [[speed of light]].<ref>{{Cite book|last=Grant, I. S. (Ian S.)|first=|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|year=|isbn=0-471-92711-2|edition=2nd ed|series=The Manchester Physics Series|___location=Chichester [England]|pages=365|oclc=21447877}}</ref> The observation that these wave solutions had a wave speed equal to the speed of light led Maxwell to conclude that light is a form of electromagnetic radiation and to posit that other electromagnetic radiation could exist with different wavelengths.<ref name="ADTEF">{{cite journal|last=Maxwell|first=James Clerk|date=|year=1865|title=A dynamical theory of the electromagnetic field|url=http://upload.wikimedia.org/wikipedia/commons/1/19/A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf|url-status=live|journal=Philosophical Transactions of the Royal Society of London|volume=155|pages=459–512|bibcode=1865RSPT..155..459C|doi=10.1098/rstl.1865.0008|archiveurl=https://web.archive.org/web/20110728140123/http://upload.wikimedia.org/wikipedia/commons/1/19/A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf|archivedate=28 July 2011|quote=Light and magnetism are affections of the same substance (p.499)|via=|s2cid=186207827}}</ref> The existence of electromagnetic radiation was proved by [[Heinrich Hertz]] in a series of experiments ranging from 1886 to 1889 in which he discovered the existence of [[Radio wave|radio waves]].<ref>{{Cite book|last=Huurdeman, Anton A.|first=|url=https://www.worldcat.org/oclc/50251955|title=The worldwide history of telecommunications|date=2003|publisher=J. Wiley|year=|isbn=0-471-20505-2|___location=New York|pages=202-204|oclc=50251955}}</ref> The full [[electromagnetic spectrum]] (in order of increasing frequency) consists of radio waves, [[Microwave|microwaves]], [[Infrared|infrared radiation]], [[visible light]], [[Ultraviolet|ultraviolet light]], [[X-ray|X-rays]] and [[Gamma ray|gamma rays]].<ref>{{Cite web|date=2011-08-25|title=Introduction to the Electromagnetic Spectrum and Spectroscopy {{!}} Analytical Chemistry {{!}} PharmaXChange.info|url=https://pharmaxchange.info/2011/08/introduction-to-the-electromagnetic-spectrum-and-spectroscopy/|access-date=2020-11-26|website=pharmaxchange.info|language=en-US}}</ref>
=== Special relativity ===
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}}
According to Einstein's [[Special relativity|special theory of relativity]], observers moving at different speeds relative to one another occupy different [[Frame of reference|observational frames of references]]. If one observer is in motion relative to another observer then they experience [[length contraction]] where unmoving objects appear closer together to the observer in motion than to the observer at rest. Therefore, if an electron is moving at the same speed as the current in a neutral wire, then they experience the flowing electrons in the wire as standing still relative to it and the positive charges as contracted together. In the [[lab frame]], the electron is moving and so feels a magnetic force from the current in the wire but because the wire is neutral it feels no electric force. But in the electron's [[rest frame]], the positive charges seem closer together compared to the flowing electrons and so the wire seems positively charged. Therefore, in the electron's rest frame it feels no magnetic force (because it is not moving relative to itself) but it does feel an electric force due to the positively charged wire. This result from relativity proves that magnetic fields are just electric fields in a different reference frame (and vice versa) and so the two are different manifestations of the same underlying [[electromagnetic field]].<ref>{{Cite book|last=Purcell|first=Edward M.|title=Electricity and magnetism|date=2013|publisher=|isbn=978-1107014022|edition=Third|___location=Cambridge|pages=235–68|oclc=805015622}}</ref><ref>{{Cite web|title=The Feynman Lectures on Physics Vol. II Ch. 13: Magnetostatics|url=http://www.feynmanlectures.caltech.edu/II_13.html#Ch13-S6|access-date=2018-10-30|website=www.feynmanlectures.caltech.edu}}</ref><ref>A. French (1968) ''Special Relativity'', chapter 8 – Relativity and electricity, pp. 229–65, W.W. Norton.</ref>
== Conductors, insulators and circuits ==
=== Conductors ===
[[File:Electrostatic induction.svg|thumb|301x301px|The charges in a perfect conductor rearrange so that the electric field is always zero inside.]]
A [[Electrical conductor|conductor]] is a material that allows electrons to flow easily. The most effective conductors are usually [[Metal|metals]] because they can be described fairly accurately by the [[free electron model]] in which electrons delocalize from the [[Atomic nucleus|atomic nuclei]], leaving positive [[Ion|ions]] surrounded by a cloud of free electrons.<ref>{{Cite book|last=Hook, J. R., Hall, H. E.|first=|url=https://www.worldcat.org/oclc/868939953|title=Solid State Physics|date=2010|publisher=John Wiley & Sons|others=|year=|isbn=978-1-118-72347-0|edition=2nd|___location=Chichester, West Sussex, U.K.|pages=76-77|oclc=868939953}}</ref> Examples of good conductors include [[copper]], [[Aluminium|aluminum]], and [[silver]]. Wires in electronics are often made of copper.<ref>{{Cite web|title=What Metals Make Good Conductors of Electricity?|url=https://sciencing.com/metals-make-good-conductors-electricity-8115694.html|access-date=2020-11-27|website=Sciencing|language=en}}</ref>
The main
# ''The electric field is zero inside a perfect conductor.''
# ''The electric potential is the same everywhere inside the conductor and is constant across the surface of the conductor.'' This follows from the first statement because the field is zero everywhere inside the conductor and therefore the potential is
# ''The electric field is perpendicular to the surface of a conductor.'' If this were not the case, the field would have a nonzero component on the surface of the conductor, which would cause the charges in the conductor to move around until that component of the field is zero.
# ''The net [[electric flux]] through a surface is proportional to the charge enclosed by the surface.'' This is a restatement of [[Gauss's law|Gauss' law]].
In some materials, the electrons are bound to the atomic nuclei and so are not free to move around but the energy required to set them free is low. In these materials, called [[Semiconductor|semiconductors]], the conductivity is low at low temperatures but as the temperature is increased the electrons gain more [[thermal energy]] and the conductivity increases.<ref>{{Cite web|title=The Feynman Lectures on Physics Vol. III Ch. 14: Semiconductors|url=https://www.feynmanlectures.caltech.edu/III_14.html|access-date=2020-11-26|website=www.feynmanlectures.caltech.edu}}</ref> Silicon is an example of a semiconductors that can be used to create [[Solar panel|solar panels]] which become more conductive the more energy they receive from [[Photon|photons]] from the sun.<ref>{{Cite web|title=How a Solar Cell Works|url=https://www.acs.org/content/acs/en/education/resources/highschool/chemmatters/past-issues/archive-2013-2014/how-a-solar-cell-works.html|access-date=2020-11-26|website=American Chemical Society|language=en}}</ref>
[[Superconductivity|Superconductors]] are materials that exhibit little to no [[Electrical resistance and conductance|resistance]] to the flow of electrons when cooled below a certain critical temperature. Superconductivity can only be explained by the quantum mechanical [[Pauli exclusion principle]] which states that no two [[Fermion|fermions]] (an electron is a type of fermion) can occupy exactly the same [[quantum state]]. In superconductors, below a certain temperature the electrons form [[boson]] bound pairs which do not follow this principle and this means that all the electrons can fall to the same [[energy level]] and move together uniformly in a current.<ref>{{Cite web
=== Insulators ===
[[File:Conductorenequilibrio.gif|thumb|In a dielectric material, an electric field can polarise the material.]]
[[Insulator|Insulators]] are material which are highly [[Electrical resistivity and conductivity|resistive]] to the flow of electrons and so are often used to cover conducting wires for safety. In insulators, electrons are tightly bound to atomic nuclei and the energy to free them is very high so they are not free to move and are resistive to induced movement by an external electric field.<ref>{{Cite web|title=Conductors and Insulators|url=http://hyperphysics.phy-astr.gsu.edu/hbase/electric/conins.html|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref> However, some insulators, called [[Dielectric|dielectrics]], can be [[Polarizability|polarised]] under the influence of an external electric field so that the charges are minutely displaced forming [[Dipole|dipoles]] that create a positive and negative side.<ref>{{Cite web|title=Dielectric {{!}} physics|url=https://www.britannica.com/science/dielectric|access-date=2020-11-27|website=Encyclopedia Britannica|language=en}}</ref> Dielectrics are used in [[Capacitor|capacitors]] to allow them to store more electric potential energy in the electric field between the capacitor plates.<ref name=":10">{{Cite web|title=Dielectrics|url=http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dielec.html|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref>
=== Capacitors ===
[[File:Parallel plate capacitor.svg|thumb|A parallel plate capacitor.]]
A [[capacitor]] is an [[electronic component]] that stores electrical potential energy in an electric field between two oppositely charged conducting plates. If one of the conducting plates has a [[charge density]] of +''Q/A'' and the other has a charge of -''Q/A'' where ''A'' is the area of the plates, then there will be an electric field between them. The potential difference between two parallel plates ''V'' can be derived mathematically as<ref name=":11">{{Cite book|last=Grant, I. S. (Ian S.)|first=|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|year=|isbn=0-471-92711-2|edition=2nd|series=The Manchester Physics Series|___location=Chichester [England]|pages=41-42|oclc=21447877}}</ref>
<math>V = {Qd \over \varepsilon_0 A}</math>
where ''d'' is the plate separation and <math display="inline">\varepsilon_0</math> is the [[permittivity of free space]]. The ability of the capacitor to store electrical potential energy is measured by the [[capacitance]] which is defined as <math display="inline">C=Q/V</math> and for a parallel plate capacitor this is<ref name=":11" />
<math>C = {\varepsilon_0 A \over d}</math>
If a dielectric is placed between the plates then the permittivity of free space is multiplied by the [[relative permittivity]] of the dielectric and the capacitance increases.<ref name=":10" /> The maximum energy that can be stored by a capacitor is proportional to the capacitance and the square of the potential difference between the plates<ref name=":11" />
<math>E = CV^2</math>
===
An [[inductor]] is an electronic component that stores energy in a magnetic field inside a coil of wire. A current-carrying coil of wire induces a magnetic field according to [[Ampère's circuital law]]. The greater the current ''I'', the greater the energy stored in the magnetic field and the lower the [[inductance]] which is defined <math display="inline">L= \Phi_B/I</math> where <math display="inline">\Phi_B</math> is the magnetic flux produced by the coil of wire. The inductance is a measure of the circuits resistance to a change in current and so inductors with high inductances can also be used to oppose [[alternating current]].<ref>{{Cite book|last=Purcell, Edward M.|first=|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|publisher=|year=|isbn=978-1-107-01402-2|edition=Third edition|___location=Cambridge|pages=374|oclc=805015622}}</ref>
=== Other circuit components ===
{| class="wikitable"
!Component
!Main function
!Schematic symbol
|-
|[[Resistor]]
|Impedes the flow of current
|[[File:Resistor_symbol_America.svg|link=https://en.wikipedia.org/wiki/File:Resistor_symbol_America.svg|center|120x120px]]
|-
|[[Electric battery|Battery]]
|Acts as a power source
|[[File:Battery symbol.
|-
|[[Direct current|DC voltage source]]
|Acts as a source of direct current (DC), a constant current which points in one direction
|[[File:Voltage Source.svg|center|64x64px]]
|-
|[[Alternating current|AC voltage source]]
|Acts as a source of alternating current (AC), a varying current which periodically reverses direction
|[[File:Alternative Current Symbol.png|center|64x64px]]
|-
|[[Diode]]
|Allows current to flow easily in one direction but not another
|[[File:Diode symbol.svg|center]]
|-
|[[Capacitor]]
|Stores energy in electric fields, stores charge, passes low frequency alternating current
|[[File:Capacitor symbol.
|-
|[[Inductor]]
|Stores energy in magnetic fields, resists change in current
|[[File:
|}
=== Circuit laws ===
{{Multiple image
| align =
| direction = vertical
| total_width =
| image1 = Pierwsze prawo Kirchhoffa.svg
| alt1 =
| caption1 =
| image2 = KVL.png
| caption2 = Kirchoff's junction rule (above):
I<sub>1</sub> + I<sub>2</sub> + I<sub>3</sub> = I<sub>4</sub> + I<sub>5</sub>
Kirchoff's loop rule (below):
V<sub>1</sub> + V<sub>2</sub> + V<sub>3</sub> + V<sub>4</sub> = 0
}}
[[Circuit theory]] deals with [[Electrical network|electrical networks]] where the fields are largely confined around current carrying [[Electrical conductor|conductors]]. In such circuits, simple circuit laws can be used instead of deriving all the behaviour of the circuits directly from electromagnetic laws. [[Ohm's law]] states the relationship between the current ''I'' and the voltage ''V'' of a circuit by introducing the quantity known as [[Electrical resistance and conductance|resistance]] ''R''<ref>{{Cite web|title=Ohm's Law|url=http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmlaw.html#c1|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref>
Ohm's law: <math>I = V/R</math>
[[Electric power|Power]] is defined as <math>P = IV</math> so Ohm's law can be used to tell us the power of the circuit in terms of other quantities<ref>{{Cite web|title=Electric Power|url=http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepow.html|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref>
<math>P = IV = V^2/R = I^2R</math>
[[Kirchhoff's circuit laws|Kirchhoff's junction rule]] states that the current going into a junction (or node) must equal the current that leaves the node. This comes from [[charge conservation]], as current is defined as the flow of charge over time. If a current splits as it exits a junction, the sum of the resultant split currents is equal to the incoming circuit.<ref name=":12">{{Cite book|last=Young, H. D., Freedman, R. A.|first=|url=https://www.worldcat.org/oclc/897436903|title=Sears and Zemansky's University Physics with Modern Physics|publisher=[[Pearson]]|others=|year=2016|isbn=978-0-321-97361-0|edition=14th edition|___location=Boston|pages=872-878|oclc=897436903}}</ref>
[[Kirchhoff's circuit laws|Kirchhoff's loop rule]] states that the sum of the voltage in a closed loop around a circuit equals zero. This comes from the the fact that the electric field is [[Conservative vector field|conservative]] which means that no matter the path taken, the potential at a point doesn't change when you get back there.<ref name=":12" />
Rules can also tell us how to add up quantities such as the current and voltage in [[series and parallel circuits]].<ref name=":12" />
For series circuits, the current remains the same for each component and the voltages and resistances add up:
<math>V_{tot} = V_1 + V_2 + V_3 + \ldots \qquad R_{tot} = R_1 + R_2 + R_3 + \ldots \qquad I = I_1 = I_2 = I_3 = \ldots</math>
For parallel circuits, the voltage remains the same for each component and the currents and resistances are related as shown:
<math>V_{tot} = V_1 = V_2 = V_3 = \ldots \qquad {1 \over R_{tot}} = {1 \over R_1} + {1 \over R_2} + {1 \over R_3} + \ldots \qquad I_{tot} = {1 \over I_1} + {1 \over I_2} + {1 \over I_3} + \ldots</math>
== See also ==
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