Editing Electromagnetic induction (section)

===Faraday's law of induction and Lenz's law===
{{main|Faraday's law of induction}}
[[File:Solenoid-1.png|right|thumb|upright=1.3|A solenoid]]
[[File:VFPt_Solenoid_correct2.svg|right|thumb|upright=1.3|The longitudinal cross section of a solenoid with a constant electrical current running through it. The magnetic field lines are indicated, with their direction shown by arrows. The magnetic flux corresponds to the 'density of field lines'. The magnetic flux is thus densest in the middle of the solenoid, and weakest outside of it.]]

Faraday's law of induction makes use of the [[magnetic flux]] Φ<sub>B</sub> through a region of space enclosed by a wire loop. The magnetic flux is defined by a [[surface integral]]:<ref>
{{cite book
 |last=Good |first=R. H.
 |year=1999
 |title=Classical Electromagnetism
 |page=107
 |publisher=[[Saunders College Publishing]]
 |isbn=0-03-022353-9
}}</ref>
<math display="block"> \Phi_\mathrm{B} = \int_{\Sigma} \mathbf{B} \cdot d \mathbf{A}\, , </math>
where ''d'''''A''' is an element of the surface Σ enclosed by the wire loop, '''B''' is the magnetic field. The [[dot product]] '''B'''·''d'''''A''' corresponds to an infinitesimal amount of magnetic flux. In more visual terms, the magnetic flux through the wire loop is proportional to the number of [[field line|magnetic field lines]] that pass through the loop.

When the flux through the surface changes, [[Faraday's law of induction]] says that the wire loop acquires an [[electromotive force]] (emf).{{refn|group=note|The EMF is the voltage that would be measured by cutting the wire to create an [[Open-circuit voltage|open circuit]], and attaching a [[voltmeter]] to the leads. Mathematically, <math>\mathcal{E}</math> is defined as the energy available from a unit charge that has traveled once around the wire loop.<ref name=Feynman>
{{cite book
 |last1=Feynman |first1=R. P.
 |last2=Leighton |first2=R. B.
 |last3=Sands |first3=M. L.
 |year=2006
 |title=The Feynman Lectures on Physics, Volume 2
 |url=https://feynmanlectures.caltech.edu/II_17.html#Ch17-S2
 |page=17{{hyphen}}2
 |publisher=[[Pearson Education|Pearson]]/[[Addison-Wesley]]
 |isbn=0-8053-9049-9 
}}</ref><ref name=Griffiths2>
{{cite book
 |last=Griffiths
 |first=D. J.
 |year=1999
 |title=Introduction to Electrodynamics
 |url=https://archive.org/details/introductiontoel00grif_0/page/301
 |edition=3rd
 |pages=[https://archive.org/details/introductiontoel00grif_0/page/301 301–303]
 |publisher=[[Prentice Hall]]
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 }}</ref><ref>
{{cite book
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 |last2=Mosca |first2=G.
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 |url=https://books.google.com/books?id=R2Nuh3Ux1AwC&pg=PA795
 |publisher=[[W.H. Freeman]]
 |isbn=978-0716708100
}}</ref>}} The most widespread version of this law states that the induced electromotive force in any closed circuit is equal to the [[time derivative|rate of change]] of the [[magnetic flux]] enclosed by the circuit:<ref name="Jordan & Balmain (1968)">
{{cite book
 |last1=Jordan |first1=E.
 |last2=Balmain |first2=K. G.
 |year=1968
 |title=Electromagnetic Waves and Radiating Systems
 |url=https://archive.org/details/electromagneticw00jord_157 |url-access=limited |page=[https://archive.org/details/electromagneticw00jord_157/page/n113 100]
 |edition=2nd
 |publisher=[[Prentice-Hall]]
|isbn=978-0132499958
 }}</ref><ref name="Hayt (1989)">
{{cite book
 |last=Hayt
 |first=W.
 |year=1989
 |title=Engineering Electromagnetics
 |page=[https://archive.org/details/engineeringelect5thhayt/page/312 312]
 |edition=5th
 |publisher=[[McGraw-Hill]]
 |isbn=0-07-027406-1
 |url=https://archive.org/details/engineeringelect5thhayt/page/312
 }}</ref>
<math display="block">\mathcal{E} = -\frac{d\Phi_\mathrm{B}}{dt} \, , </math>
where <math>\mathcal{E}</math> is the emf and Φ<sub>B</sub> is the [[magnetic flux]]. The direction of the electromotive force is given by [[Lenz's law]] which states that an induced current will flow in the direction that will oppose the change which produced it.<ref>
{{cite book
 |last=Schmitt |first=R.
 |year=2002
 |title=Electromagnetics Explained
 |publisher=Newnes |url=https://archive.org/details/electromagnetics0000schm
 |url-access=registration |page=[https://archive.org/details/electromagnetics0000schm/page/75 75]
 |isbn=978-0750674034
}}</ref> This is due to the negative sign in the previous equation. To increase the generated emf, a common approach is to exploit [[flux linkage]] by creating a tightly wound [[inductor|coil of wire]], composed of ''N'' identical turns, each with the same magnetic flux going through them. The resulting emf is then ''N'' times that of one single wire.<ref>
{{cite book
 |last1=Whelan |first1=P. M.
 |last2=Hodgeson |first2=M. J.
 |year=1978
 |title=Essential Principles of Physics
 |edition=2nd
 |publisher=[[John Murray (publishing house)|John Murray]]
 |isbn=0-7195-3382-1
}}</ref><ref>
{{cite web
 |last=Nave |first=C. R.
 |title=Faraday's Law
 |url=http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html
 |work=[[HyperPhysics]]
 |publisher=[[Georgia State University]]
 |access-date=2011-08-29
}}</ref>
<math display="block"> \mathcal{E} = -N \frac{d\Phi_\mathrm{B}}{dt} </math>

Generating an emf through a variation of the magnetic flux through the surface of a wire loop can be achieved in several ways:
# the magnetic field '''B''' changes (e.g. an alternating magnetic field, or moving a wire loop towards a bar magnet where the B field is stronger),
# the wire loop is deformed and the surface Σ changes,
# the orientation of the surface ''d'''''A''' changes (e.g. spinning a wire loop into a fixed magnetic field),
# any combination of the above