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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.|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|date=21 January 2013
<math>F=k_e{q_1q_2\over r^2}</math>
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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
* 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.|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|date=21 January 2013
: <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
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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.|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|date=21 January 2013
<math>\mathbf F=q(\mathbf E + \mathbf v \times \mathbf B)</math>
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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
=== Electric potential and potential energy ===
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=== 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.|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|date=21 January 2013
<math>\Phi_B = 0</math>
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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.)|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|isbn=0-471-92711-2|edition=2nd|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.)|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|isbn=0-471-92711-2|edition=2nd|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-|url=https://www.worldcat.org/oclc/1021068059|title=Introduction to electrodynamics|date=29 June 2017
<math>B(r) = {\mu_0 \over 4\pi} {q |\mathbf v \times \mathbf \hat{r}| \over r^2} =
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=== Maxwell's equations and electromagnetic radiation ===
[[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.)|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|isbn=0-471-92711-2|edition=2nd|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|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|
=== 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 reference]]. 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
== Conductors, insulators and circuits ==
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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.|url=https://www.worldcat.org/oclc/868939953|title=Solid State Physics|date=2010|publisher=John Wiley & Sons|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 properties of conductors are:<ref>{{Cite book|last=Purcell|first=Edward M.|title=Electricity and magnetism|date=2013
# ''The electric field is zero inside a perfect conductor.'' Because charges are free to move in a conductor, when they are disturbed by an external electric field they rearrange themselves such that the field that their configuration produces exactly cancels the external electric field inside the conductor.
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=== Inductors ===
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.|url=https://www.worldcat.org/oclc/805015622|title=Electricity and magnetism|date=21 January 2013
=== Other circuit components ===
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