Magnetic flux - wikipedia Magnetic flux This article is about magnetic flux. For the magnetic fields `` B '' ( magnetic flux density ) and `` H '', see Magnetic field. This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. Please help to improve this article by introducing more precise citations. ( July 2016 ) Electromagnetism Electricity Magnetism Electrostatics Electric charge Static electricity Electric field Conductor Insulator Triboelectricity Electrostatic discharge Induction Coulomb 's law Gauss 's law Electric flux / potential energy Electric dipole moment Polarization density Magnetostatics Ampère 's law Magnetic field Magnetization Magnetic flux Biot -- Savart law Magnetic dipole moment Gauss 's law for magnetism Electrodynamics Lorentz force law Electromagnetic induction Faraday 's law Lenz 's law Displacement current Magnetic potential Maxwell 's equations Electromagnetic field Electromagnetic pulse Electromagnetic radiation Maxwell tensor Poynting vector Liénard -- Wiechert potential Jefimenko 's equations Eddy current London equations Mathematical descriptions of the electromagnetic field Electrical network Electric current Electric potential Voltage Resistance Ohm 's law Series circuit Parallel circuit Direct current Alternating current Electromotive force Capacitance Inductance Impedance Resonant cavities Waveguides Covariant formulation Electromagnetic tensor ( stress -- energy tensor ) Four - current Electromagnetic four - potential Scientists Ampère Coulomb Faraday Gauss Heaviside Henry Hertz Lorentz Maxwell Tesla Volta Weber Ørsted In physics, specifically electromagnetism, the magnetic flux ( often denoted Φ or Φ ) through a surface is the surface integral of the normal component of the magnetic field B passing through that surface. The SI unit of magnetic flux is the weber ( Wb ) ( in derived units : volt - seconds ), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the magnetic flux. Contents 1 Description 2 Magnetic flux through a closed surface 3 Magnetic flux through an open surface 4 Changing magnetic flux 5 Comparison with electric flux 6 See also 7 References 8 External articles Description The magnetic flux through a surface -- when the magnetic field is variable -- relies on splitting the surface into small surface elements, over which the magnetic field can be considered to be locally constant. The total flux is then a formal summation of these surface elements ( see surface integration ). Each point on a surface is associated with a direction, called the surface normal ; the magnetic flux through a point is then the component of the magnetic field along this direction. The magnetic interaction is described in terms of a vector field, where each point in space ( and time ) is associated with a vector that determines what force a moving charge would experience at that point ( see Lorentz force ). Since a vector field is quite difficult to visualize at first, in elementary physics one may instead visualize this field with field lines. The magnetic flux through some surface, in this simplified picture, is proportional to the number of field lines passing through that surface ( in some contexts, the flux may be defined to be precisely the number of field lines passing through that surface ; although technically misleading, this distinction is not important ). Note that the magnetic flux is the net number of field lines passing through that surface ; that is, the number passing through in one direction minus the number passing through in the other direction ( see below for deciding in which direction the field lines carry a positive sign and in which they carry a negative sign ). In more advanced physics, the field line analogy is dropped and the magnetic flux is properly defined as the surface integral of the normal component of the magnetic field passing through a surface. If the magnetic field is constant, the magnetic flux passing through a surface of vector area S is Φ B = B ⋅ S = B S cos ⁡ θ, ( displaystyle Phi _ ( B ) = mathbf ( B ) cdot mathbf ( S ) = BS cos \theta, ) where B is the magnitude of the magnetic field ( the magnetic flux density ) having the unit of Wb / m ( tesla ), S is the area of the surface, and θ is the angle between the magnetic field lines and the normal ( perpendicular ) to S. For a varying magnetic field, we first consider the magnetic flux through an infinitesimal area element dS, where we may consider the field to be constant : d Φ B = B ⋅ d S. ( displaystyle d Phi _ ( B ) = mathbf ( B ) cdot d mathbf ( S ). ) A generic surface, S, can then be broken into infinitesimal elements and the total magnetic flux through the surface is then the surface integral Φ B = ∫∫ S B ⋅ d S. ( displaystyle Phi _ ( B ) = iint limits _ ( S ) mathbf ( B ) cdot d mathbf ( S ). ) From the definition of the magnetic vector potential A and the fundamental theorem of the curl the magnetic flux may also be defined as : Φ B = ∮ ∂ S A ⋅ d l, ( displaystyle Phi _ ( B ) = oint limits _ ( partial S ) mathbf ( A ) cdot d ( \boldsymbol ( ell ) ), ) where the line integral is taken over the boundary of the surface S, which is denoted ∂ S. Magnetic flux through a closed surface Some examples of closed surfaces ( left ) and open surfaces ( right ). Left : Surface of a sphere, surface of a torus, surface of a cube. Right : Disk surface, square surface, surface of a hemisphere. ( The surface is blue, the boundary is red. ) Main article : Gauss 's law for magnetism Gauss 's law for magnetism, which is one of the four Maxwell 's equations, states that the total magnetic flux through a closed surface is equal to zero. ( A `` closed surface '' is a surface that completely encloses a volume ( s ) with no holes. ) This law is a consequence of the empirical observation that magnetic monopoles have never been found. In other words, Gauss 's law for magnetism is the statement : Φ B = ( displaystyle Phi _ ( B ) = , ! ) S ( displaystyle scriptstyle S ) B ⋅ d S = 0 ( displaystyle mathbf ( B ) cdot d mathbf ( S ) = 0 ) for any closed surface S. Magnetic flux through an open surface For an open surface Σ, the electromotive force along the surface boundary, ∂ Σ, is a combination of the boundary 's motion, with velocity v, through a magnetic field B ( illustrated by the generic F field in the diagram ) and the induced electric field caused by the changing magnetic field. While the magnetic flux through a closed surface is always zero, the magnetic flux through an open surface need not be zero and is an important quantity in electromagnetism. Changing magnetic flux Main article : Faraday 's law of induction For example, a change in the magnetic flux passing through a loop of conductive wire will cause an electromotive force, and therefore an electric current, in the loop. The relationship is given by Faraday 's law : E = ∮ ∂ Σ ( E + v × B ) ⋅ d l = − d Φ B d t, ( displaystyle ( mathcal ( E ) ) = oint _ ( partial Sigma ) left ( mathbf ( E ) + mathbf ( v \times B ) \right ) cdot d ( \boldsymbol ( ell ) ) = - ( d Phi _ ( B ) over dt ), ) where E ( displaystyle ( mathcal ( E ) ) ) is the electromotive force ( EMF ), Φ is the magnetic flux through the open surface Σ, ∂ Σ is the boundary of the open surface Σ ; note that the surface, in general, may be in motion and deforming, and so is generally a function of time. The electromotive force is induced along this boundary. dl is an infinitesimal vector element of the contour ∂ Σ, v is the velocity of the boundary ∂ Σ, E is the electric field, B is the magnetic field. The two equations for the EMF are, firstly, the work per unit charge done against the Lorentz force in moving a test charge around the ( possibly moving ) surface boundary ∂ Σ and, secondly, as the change of magnetic flux through the open surface Σ. This equation is the principle behind an electrical generator. Area defined by an electric coil with three turns. Comparison with electric flux Main articles : Electric flux and Gauss 's law By way of contrast, Gauss 's law for electric fields, another of Maxwell 's equations, is Φ E = ( displaystyle Phi _ ( E ) = , ! ) S ( displaystyle scriptstyle S ) E ⋅ d S = Q ε 0 ( displaystyle mathbf ( E ) cdot d mathbf ( S ) = ( \frac ( Q ) ( epsilon _ ( 0 ) ) ) , ! ) where E is the electric field, S is any closed surface, Q is the total electric charge inside the surface S, ε is the electric constant ( a universal constant, also called the `` permittivity of free space '' ). Note that the flux of E through a closed surface is not always zero ; this indicates the presence of `` electric monopoles '', that is, free positive or negative charges. Part of a series on Magnetic circuits Conventional magnetic circuits Magnetomotive force F ( displaystyle ( mathcal ( F ) ) ) Magnetic flux Φ ( displaystyle Phi ) Magnetic reluctance R ( displaystyle ( mathcal ( R ) ) ) Phasor magnetic circuits Complex reluctance Z μ ( displaystyle Z_ ( mu ) ) Related concepts Magnetic permeability μ ( displaystyle mu ) Gyrator - capacitor model variables Magnetic impedance z M ( displaystyle z_ ( mathrm ( M ) ) ) Effective resistance r M ( displaystyle r_ ( mathrm ( M ) ) ) Magnetic inductivity L M ( displaystyle L_ ( mathrm ( M ) ) ) Magnetic capacitivity C M ( displaystyle C_ ( mathrm ( M ) ) ) Physics portal See also Electronics portal Magnetic circuit is a closed path in which magnetic flux flows Magnetic flux quantum is the quantum of magnetic flux passing through a superconductor. References Purcell, Edward and Morin, David ; Electricity and Magnetism 3rd Edition ; Cambridge University Press, New York, 2013. isbn 978 - 1 - 107 - 01402 - 2. Browne, Michael ; Physics for Engineering and Science 2nd Edition, McGraw - Hill / Schaum ; 2008 ; isbn 978 - 0 - 07 - 161399 - 6. External articles Patents Vicci, U.S. Patent 6,720,855, Magnetic - flux conduits Magnetic Flux through a Loop of Wire by Ernest Lee, Wolfram Demonstrations Project. Conversion Magnetic flux Φ in nWb per meter track width to flux level in dB - Tape Operating Levels and Tape Alignment Levels Jump up ^ Purcell, p278, Jump up ^ Browne, p235 Retrieved from `` https://en.wikipedia.org/w/index.php?title=Magnetic_flux&oldid=812135765 '' Categories : Physical quantities Magnetism Hidden categories : Articles lacking in - text citations from July 2016 All articles lacking in - text citations All articles with unsourced statements Articles with unsourced statements from December 2016 Pages containing citation needed template with deprecated parameters Talk Contents About Wikipedia Azərbaycanca Беларуская Беларуская ( тарашкевіца ) ‎ Български Boarisch Bosanski Català Čeština Deutsch Eesti Ελληνικά Español Esperanto Euskara فارسی Français Gaeilge Galego 한국어 Հայերեն हिन्दी Hrvatski Bahasa Indonesia Íslenska Italiano ಕನ್ನಡ ქართული Қазақша Latviešu Македонски मराठी Bahasa Melayu Монгол Nederlands 日本 語 Norsk Oʻzbekcha / ўзбекча Polski Português Română Русский Scots Shqip Simple English Slovenčina Slovenščina Српски / srpski Srpskohrvatski / српскохрватски Suomi Svenska தமிழ் Татарча / tatarça తెలుగు ไทย Türkçe Українська اردو Tiếng Việt 中文 Edit links This page was last edited on 26 November 2017, at 05 : 00. Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia ® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. About Wikipedia

Question: when is the magnetic flux on a section of a closed surface equal to zero
Answer: magnetic monopoles have never been found