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{{short description|Non-technical introduction to topics in electromagnetism}}
{{about|a conceptual understanding of the topic|a more detailed mathematical treatment|
'''Electromagnetism''' is one of the [[Fundamental interaction|fundamental forces]] of nature. Early on, [[electricity]] and [[magnetism]] were studied separately and regarded as separate phenomena. [[Hans Christian Ørsted]] discovered that the two were related – [[electric current]]s give rise to magnetism. [[Michael Faraday]] discovered the converse, that magnetism could [[electromagnetic induction|induce]] electric currents, and [[James Clerk Maxwell]] put the whole thing together in a unified theory of [[electromagnetism]]. [[Maxwell's equations]] further indicated that [[electromagnetic wave]]s existed, and the experiments of [[Heinrich Hertz]] confirmed this, making [[radio]] possible. Maxwell also postulated, correctly, that [[light]] was a form of electromagnetic wave, thus making all of [[optics]] a branch of electromagnetism. [[Radio wave]]s differ from light only in that the [[wavelength]] of the former is much longer than the latter. [[Albert Einstein]] showed that the [[magnetic field]] arises through the [[Classical electromagnetism and special relativity|relativistic motion]] of the [[electric field]] and thus magnetism is merely a side effect of electricity. The modern theoretical treatment of electromagnetism is as a [[quantum field]] in [[quantum electrodynamics]].
In many situations of interest to [[electrical engineering]], it is not necessary to apply quantum theory to get correct results. [[Classical physics]] is still an accurate approximation in most situations involving [[macroscopic]] objects. With few exceptions, quantum theory is only necessary at the [[atomic scale]] and a simpler classical treatment can be applied. Further simplifications of treatment are possible in limited situations. [[Electrostatics]] deals only with stationary [[electric charge]]s so magnetic fields do not arise and are not considered. [[Permanent magnet]]s can be described without reference to electricity or electromagnetism. [[Circuit theory]] deals with [[electrical network]]s where the fields are largely confined around current carrying [[Electrical conductor|conductors]]. In such circuits, even Maxwell's equations can be dispensed with and simpler formulations used. On the other hand, a quantum treatment of electromagnetism is important in [[chemistry]]. [[Chemical reaction]]s and [[chemical bond]]ing are the result of [[quantum mechanical]] interactions of [[electron]]s around [[atom]]s. Quantum considerations are also necessary to explain the behaviour of many electronic devices, for instance the [[tunnel diode]].
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== Electric charge ==
[[File:CoulombsLaw-2.png|thumb|282x282px|Coulomb's law tells us that like charges repel and opposite charges attract.]]
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]]. Furthermore, as there is the [[conservation of mass]] according to which mass cannot be created or destroyed, there is also the [[conservation of charge]] which means that the charge in a closed system (where no charges are leaving or entering) must remain constant.<ref name=":0">{{Cite book|last=Purcell, Edward M.
where ''F'' is the force, ''k''<sub>e</sub>
▲<math>F=k_e{q_1q_2\over r^2}</math>
▲where ''F'' is the force, ''k<sub>e</sub>'' is the [[Coulomb constant]], ''q<sub>1</sub>'' and ''q<sub>2</sub>'' are the [[Magnitude (mathematics)|magnitudes]] of the two charges, and ''r<sup>2</sup>'' is the square of the distance between them. It describes the fact that like charges repel one another whereas opposite charges attract one another and that the stronger the charges of the particles, the stronger the force they exert on one another. The law is also an [[Inverse-square law|inverse square law]] which means that as the distance between two particles is doubled, the force on them is reduced by a factor of four.<ref>{{Cite book|last=Walker, Jearl, 1945-|url=https://www.worldcat.org/oclc/435710913|title=Fundamentals of physics|date=2011|publisher=Wiley|others=Halliday, David, 1916-2010., Resnick, Robert, 1923-2014.|isbn=978-0-470-46911-8|edition=9th|___location=Hoboken, NJ|pages=578|oclc=435710913}}</ref>
== Electric and magnetic fields ==
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In physics, [[Field (physics)|fields]] are entities that interact with matter and can be described mathematically by assigning a value to each point in space and time. [[Vector field]]s are fields which are assigned both a numerical value and a direction at each point in space and time. Electric charges produce a vector field called the [[electric field]]. The numerical value of the electric field, also called the electric field strength, determines the strength of the electric force that a charged particle will feel in the field and the direction of the field determines which direction the force will be in. By convention, the direction of the electric field is the same as the direction of the force on positive charges and opposite 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> Because positive charges are repelled by other positive charges and are attracted to negative charges, this means the electric fields point away from positive charges and towards negative charges. These properties of the electric field are encapsulated in the equation for the electric force on a charge written in terms of the electric field:
<math display="block">F = qE</math>▼
where ''F'' is the force on a charge ''q'' in an electric field ''E''.<ref name=":3" /><ref>{{Cite book|last=Purcell, Edward M. |title=Electricity and magnetism |date=21 January 2013| isbn=978-1-107-01402-2 |edition=Third |___location=Cambridge |pages=7 |oclc=805015622}}</ref>
As well as producing an electric field, charged particles will produce a [[magnetic field]] when they are in a state of motion that will be felt by other charges that are in motion (as well as [[permanent magnet]]s).<ref>{{Cite web|title=The Feynman Lectures on Physics Vol. II Ch. 1: Electromagnetism |url=https://feynmanlectures.caltech.edu/II_01.html#Ch1-S2 | access-date=2018-10-30 |website=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]]. The strength of the force is given by the equation▼
▲<math>F = qE</math>
<math display="block">F = qvB \sin\theta</math>▼
where ''F'' is the force on a charge ''q'' with speed ''v'' in
▲As well as producing an electric field, charged particles will produce a [[magnetic field]] when they are in a state of motion that will be felt by other charges that are in motion (as well as [[permanent magnet]]s).<ref>{{Cite web|title=The Feynman Lectures on Physics Vol. II Ch. 1: Electromagnetism|url=https://feynmanlectures.caltech.edu/II_01.html#Ch1-S2|access-date=2018-10-30|website=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]]. The strength of the force is given by the equation
▲<math>F = qvB\sin\theta</math>
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The combination of the electric and magnetic forces on a charged particle is called the [[Lorentz force]].<ref name=":6" /><ref>{{Cite book|last=Purcell, Edward M.
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The third of Maxwell's equations is called the [[Ampere-maxwell law|Ampère–Maxwell law]]. It states that a magnetic field can be generated by an [[electric current]].<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> The direction of the magnetic field is given by Ampère's [[right-hand grip rule]]. If the wire is straight, then the magnetic field is curled around it like the gripped fingers in the right-hand rule. If the wire is wrapped into coils, then the magnetic field inside the coils points in a straight line like the outstretched thumb in the right-hand grip rule.<ref>{{Cite book|last=Grant, I. S. (Ian S.)
[[File:
Together, Maxwell's equations provide a single uniform theory of the electric and magnetic fields 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|url-access=subscription}}</ref> The solution to Maxwell's equations in [[free space]] (where there are no charges or currents) produces [[wave equation]]s corresponding to [[electromagnetic waves]] (with both electric and magnetic components) travelling at the [[speed of light]].<ref>{{Cite book| last=Grant
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A further unification of electromagnetism came with Einstein's [[Special relativity|special theory of relativity]]. According to special 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 in its own frame) 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 | 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=https://feynmanlectures.caltech.edu/II_13.html#Ch13-S6 |access-date=2018-10-30 |website=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 ==
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=== 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.
The main properties of conductors are:<ref>{{Cite book|last=Purcell|first=Edward M.|title=Electricity and magnetism|date=2013|isbn=978-1107014022|edition=Third|___location=Cambridge|page=129|oclc=805015622}}</ref>
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# ''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://feynmanlectures.caltech.edu/III_14.html|access-date=2020-11-26|website=feynmanlectures.caltech.edu}}</ref> Silicon is an example of a semiconductors that can be used to create [[
[[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|title=The Feynman Lectures on Physics Vol. III Ch. 21: The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity|url=https://feynmanlectures.caltech.edu/III_21.html#Ch21-S5|access-date=2020-11-26|website=feynmanlectures.caltech.edu}}</ref>
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=== 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.)
<math>V = {Qd \over \varepsilon_0 A}</math>
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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 circuit's 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.
=== Other circuit components ===
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I<sub>1</sub> + I<sub>2</sub> + I<sub>3</sub> = I<sub>4</sub> + I<sub>5</sub>
V<sub>1</sub> + V<sub>2</sub> + V<sub>3</sub> + V<sub>4</sub> = 0
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<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.
[[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 fact that the electric field is [[Conservative vector field|conservative]] which means that no matter the path taken, the potential at a point does not change when you get back there.<ref name=":12" />
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