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Encyclopedia > Magnetic flux
Electrostatics Electromagnetism Electricity · Magnetism Electric charge Coulomb's law Electric field Gauss's law Electric potential Electric dipole moment Ampère's Circuital law Magnetic field Magnetic flux Biot-Savart law Magnetic dipole moment Electric current Lorentz force law Electromotive force (EM) Electromagnetic induction Faraday-Lenz law Displacement current Maxwell's equations (EMF) Electromagnetic field (EM) Electromagnetic radiation Electrical conduction Electrical resistance Capacitance Inductance Impedance Resonant cavities Waveguides This box: view • talk • edit

The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field and the area element. More generally, magnetic flux is defined by a scalar product of the magnetic field and the area element vector. 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 zero. This law is a consequence of the empirical observation that magnetic monopoles do not exist or are not measurable. flux in science and mathematics. ... Area is a physical quantity expressing the size of a part of a surface. ... Fig. ... This template is misplaced. ... Area is a physical quantity expressing the size of a part of a surface. ... In mathematics, the dot product (also known as the scalar product and the inner product) is a function (·) : V × V &#8594; F, where V is a vector space and F its underlying field. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... In physics, a magnetic monopole is a hypothetical particle that may be loosely described as a magnet with only one pole (see electromagnetic theory for more on magnetic poles). ...

The magnetic flux is defined as the integral of the magnetic field over an area: In calculus, the integral of a function is an extension of the concept of a sum. ...

$Phi_m = int !!! int mathbf{B} cdot dmathbf S,$

where

$Phi_m$ is the magnetic flux
B is the magnetic field
S is the area.

We know from Gauss's law for magnetism that

$nabla cdot mathbf{B}=0.,$

The volume integral of this equation, in combination with the divergence theorem, provides the following result: In mathematics â€” in particular, in multivariable calculus â€” a volume integral refers to an integral over a 3-dimensional domain. ... In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Ostrogradskyâ€“Gauss theorem is a result that links the divergence of a vector field to the value of surface integrals of the flow defined by the field. ...

$int !!! int !!! int_V nabla cdot mathbf{B} , dtau = oint !!! oint_{partial V} mathbf{B} cdot dmathbf{S}=0.$

In other words, the magnetic flux through any closed surface must be zero; there are no "magnetic charges".

By way of contrast, Gauss's law for electric fields, another of Maxwell's equations, is In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ...

$nabla cdot mathbf{E} = {rho over epsilon_0},$

where

E is the electric field,
ρ is the free electric charge density, (not including dipole charges bound in a material),
ε0 is the permittivity of free space.

Note that this indicates the presence of electric monopoles, that is, free positive or negative charges. It has been suggested that optical field be merged into this article or section. ... Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ...

The direction of the magnetic field vector $mathbf{B}$ is by definition from the south to the north pole of a magnet (within the magnet). Outside of the magnet, the field lines will go from north to south.

A change of magnetic flux through a loop of conductive wire will cause an emf, and therefore an electric current, in the loop. The relationship is given by Faraday's law: Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ...

$mathcal{E} = oint mathbf{E} cdot dmathbf{s} = -{dPhi_m over dt}.$

This is the principle behind an electrical generator. â€œDynamoâ€ redirects here. ...

 Electronics Portal
• Magnetic field
• Maxwell's equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter.
• Gauss's law gives the relation between the electric flux flowing out a closed surface and the electric charge enclosed in the surface.
• Magnetic monopole is a hypothetical particle that may be loosely described as "a magnet with only one pole".
• Magnetic flux quantum is the quantum of magnetic flux passing through a superconductor.
• Karl Friedrich Gauss developed a fruitful collaboration with the physics professor Wilhelm Weber; it led to new knowledge in the field of magnetism.
• James Clerk Maxwell demonstrated that electric and magnetic forces are two complementary aspects of electromagnetism.

Image File history File links Nuvola_apps_ksim. ... This template is misplaced. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ... In physics, a magnetic monopole is a hypothetical particle that may be loosely described as a magnet with only one pole (see electromagnetic theory for more on magnetic poles). ... The magnetic flux quantum Î¦0 is the quantum of magnetic flux passing through a superconductor. ... Johann Carl Friedrich Gauss Johann Carl Friedrich Gauss (Gauß) (April 30, 1777 - February 23, 1855) was a legendary German mathematician, astronomer and physicist with a very wide range of contributions; he is considered to be one of the greatest mathematicians of all time. ... James Clerk Maxwell (13 June 1831 â€“ 5 November 1879) was a Scottish mathematician and theoretical physicist. ...

## External articles

Patents
• Vicci, U.S. Patent 6,720,855 , Magnetic-flux conduits

Results from FactBites:

 Magnetic flux - definition of Magnetic flux in Encyclopedia (247 words) Magnetic flux, usually denoted by Greek letter Φ, is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. The SI unit of magnetic flux is the weber. The direction or vector of the magnetic flux is by definition from the south to the north pole of a magnet (within the magnet).
More results at FactBites »

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