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{{short description|
{{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]].
== 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.|title=Electricity and magnetism|date=21 January 2013|isbn=978-1-107-01402-2|edition=Third|___location=Cambridge|pages=3–4|oclc=805015622}}</ref> The fundamental law that describes the gravitational force on a massive object in [[classical physics]] is [[Newton's law of gravity]]. Analogously, [[Coulomb's law]] is the fundamental law that describes the force that charged objects exert on one another. It is given by the formula
: <math>F=k_\text{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-|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 ==
[[File:VFPt_charges_plus_minus_thumb.svg|thumb|[[Field line|Electric field lines]] point from positive charges to negative charges.]]
{{Multiple image
| align =
| total_width = 450
| image1 = Force of an electric field on a positive charge.png
| alt1 =
| caption1 =
| image2 = Openstax college-physics 22.17 Lorentz-force-right-hand.jpg
| footer = The force exerted on a positive charge by an electric field (left) and a magnetic field (right) combine to give the [[Lorentz force]].
}}
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 display="block">F = qvB \sin\theta</math>
where ''F'' is the force on a charge ''q'' with speed ''v'' in a magnetic field ''B'' which is pointing in a direction of angle ''θ'' from the direction of motion of the charge.<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>
{{Multiple image
| align =
| total_width = 450
| image1 = GaussLaw2.svg
| alt1 =
| caption1 = If there is no charge enclosed by a closed surface, then the amount of electric field flowing into it must exactly cancel with the electric field flowing out of it.
| image2 = VFPt Earths Magnetic Field Confusion.svg
| caption2 = Because the flow of magnetic field out of a closed surface must cancel with the flow into it, magnets must have both North and South poles which cannot be separated into monopoles.
}}
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. |title=Electricity and magnetism|date=21 January 2013|isbn=978-1-107-01402-2|edition=Third|___location=Cambridge|pages=277|oclc=805015622}}</ref> [[Classical electromagnetism]] is fully described by the Lorentz force alongside a set of equations called [[Maxwell's equations]]. The first of these equations is known as [[Gauss's law]]. It describes the electric field produced by charged particles and by [[charge distribution]]s. According to Gauss's law, the [[flux]] (or flow) of electric field through any [[closed surface]] is proportional to the amount of charge that is enclosed by that surface.<ref name=":4">{{Cite book|last=Grant, I. S. (Ian S.) |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=17–22 |oclc=21447877}}</ref><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> This means that the greater the charge, the greater the electric field that is produced. It also has other important implications. For example, this law means that if there is no charge enclosed by the surface, then either there is no electric field at all or, if there is a charge near to but outside of the closed surface, the flow of electric field into the surface must exactly cancel with the flow out of the surface.<ref>{{Cite web|title=The Feynman Lectures on Physics Vol. II Ch. 4: Electrostatics, S5: The flux of E|url=https://feynmanlectures.caltech.edu/II_04.html#Ch4-S5|access-date=2020-11-27 |website=feynmanlectures.caltech.edu}}</ref> The second of Maxwell's equations is known as [[Gauss's law for magnetism]] and, similarly to the first Gauss's law, it describes flux, but instead of [[electric flux]], it describes [[magnetic flux]]. According to Gauss's law for magnetism, the flow of magnetic field through a closed surface is always zero. This means that if there is a magnetic field, the flow into the closed surface will always cancel out with the flow out of the closed surface. This law has also been called "no magnetic monopoles" because it means that any magnetic flux flowing out of a closed surface must flow back into it, meaning that positive and negative magnetic poles must come together as a [[magnetic dipole]] and can never be separated into [[magnetic monopole]]s.<ref name=":5">{{Cite book| last=Purcell | first = Edward M.| title=Electricity and magnetism |date=21 January 2013| isbn=978-1-107-01402-2| edition=Third|___location=Cambridge |pages=322 |oclc=805015622}}</ref> This is in contrast to electric charges which can exist as separate positive and negative charges.
{{Multiple image
| align =
| direction =
| total_width =
| image1 = Manoderecha.svg
| alt1 =
| caption1 =
| image2 = Coil right-hand rule.svg
| perrow =
| width1 = 235
| width2 = 200
| width3 = 245
| footer = The [[right-hand grip rule]] for a straight wire (left) and for a coiled wire (right). Electrical current passed through a wire coiled around an iron core can produce an [[electromagnet]].
}}
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.)|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> When electric currents are used to produce a [[magnet]] in this way, it is called an [[electromagnet]]. Electromagnets often use a wire curled up into [[solenoid]] around an iron core which strengthens the magnetic field produced because the iron core becomes magnetised.<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><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> Maxwell's extension to the law states that a time-varying electric field can also generate a magnetic field.<ref name=":5" /> Similarly, [[Faraday's law of induction]] states that a magnetic field can produce an electric current. For example, a magnet pushed in and out of a coil of wires can produce an electric current in the coils which is proportional to the strength of the magnet as well as the number of coils and the speed at which the magnet is inserted and extracted from the coils. This principle is essential for [[transformer]]s which are used to transform currents from high [[voltage]] to low voltage, and vice versa. They are needed to convert high voltage [[mains electricity]] into low voltage electricity which can be safely used in homes. Maxwell's formulation of the law is given in the [[Maxwell–Faraday equation]]—the fourth and final of Maxwell's equations—which states that a time-varying magnetic field produces an electric field.
[[File:EM Spectrum Properties (Amplitude Corrected).svg|thumb|440x440px|The [[electromagnetic spectrum]]]]
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 | first = Ian S. | 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 exactly equal to the speed of light led Maxwell to hypothesise 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..459M |doi=10.1098/rstl.1865.0008 |archive-url=https://web.archive.org/web/20110728140123/http://upload.wikimedia.org/wikipedia/commons/1/19/A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf|archive-date=28 July 2011|quote=Light and magnetism are affections of the same substance (p.499)|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]]s. The full [[electromagnetic spectrum]] (in order of increasing frequency) consists of radio waves, [[microwave]]s, [[Infrared|infrared radiation]], [[visible light]], [[Ultraviolet|ultraviolet light]], [[X-ray]]s and [[gamma ray]]s.<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>
{{Multiple image
| align =
| total_width = 450
| image1 = Relativistic electromagnetism fig5.svg
| alt1 =
| caption1 = The lab frame
| image2 = Relativistic electromagnetism fig6.svg
| caption2 = The electron's rest frame
}}
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 ==
=== 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.|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|date=10 April 2018 |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://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 [[solar cells]] 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 (electricity)|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.)|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=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 = \frac 1 2 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 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.|title=Electricity and magnetism|date=21 January 2013|isbn=978-1-107-01402-2|edition=Third|___location=Cambridge|pages=374|oclc=805015622}}</ref>
=== Other circuit components ===
{| class="wikitable"
!Component
!Main function
!Schematic symbol
|-
|[[Resistor]]
|Impedes the flow of current
|[[File:
|-
|[[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
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| image1 = Pierwsze prawo Kirchhoffa.svg
| alt1 =
| caption1 =
| image2 = KVL.png
| caption2 = Kirchhoff's junction rule (above):
I<sub>1</sub> + I<sub>2</sub> + I<sub>3</sub> = I<sub>4</sub> + I<sub>5</sub>
Kirchhoff'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.|title=Sears and Zemansky's University Physics with Modern Physics|publisher=[[Pearson PLC|Pearson]]|year=2016|isbn=978-0-321-97361-0|edition=14th|___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 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" />
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} = I_1 + I_2 + I_3 + \ldots</math>
== See also ==
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[[Category:Electromagnetism]]
[[Category:Introductory articles|electromagnetism ]]
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