Magnetic flux, 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, and the unit of magnetic flux density is the weber per square meter, or tesla.

Description

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The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field density and the area element. More generally, magnetic flux is defined by a scalar product of the magnetic field density 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 measureable.

In symbols, this means:

$\backslash Phi\_m\; \backslash equiv\; \backslash int\; \backslash !\backslash !\backslash !\; \backslash int\; \backslash mathbf\{B\}\; \backslash cdot\; d\backslash mathbf\; S\backslash ,$

where $\backslash Phi\_m\; \backslash$ is the magnetic flux and B is the magnetic flux density.

We know from Gauss's law for magnetism that

$\backslash nabla\; \backslash cdot\; \backslash mathbf\{B\}=0.\backslash ,$

This equation, in combination with the divergence theorem, provides the following result:

$\backslash oint\; \backslash !\backslash !\backslash !\; \backslash oint\_\{\backslash partial\; V\}\; \backslash mathbf\{B\}\; \backslash cdot\; d\backslash mathbf\{S\}=\backslash int\; \backslash !\backslash !\backslash !\; \backslash int\; \backslash !\backslash !\backslash !\; \backslash int\_V\; \backslash nabla\; \backslash cdot\; \backslash mathbf\{B\}\; \backslash ,\; d\backslash tau\; =\; 0.$

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

By way of contrast, Gauss's law for electric fields, another of Maxwell's equations, is

$\backslash nabla\; \backslash cdot\; \backslash mathbf\{E\}\; =\; \{\backslash rho\; \backslash over\; \backslash epsilon\_0\},$

where E is the electric field intensity, $\backslash rho$ is the free electric charge density, (not including dipole charges bound in a material), and $\backslash epsilon\_0$ is the permittivity of free space.

Note that this indicates the presence of electric monopoles, that is, free positive or negative charges.

The direction of the magnetic-flux-density vector $\backslash mathbf\{B\}$ 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:

$\backslash mathcal\{E\}\; =\; \backslash oint\; \backslash mathbf\{E\}\; \backslash cdot\; d\backslash mathbf\{s\}\; =\; -\{d\backslash Phi\_m\; \backslash over\; dt\}.$

This is the principle behind an electric generator.

See also

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• Magnetic flux density, otherwise known as magnetic field density, is essentially what the layman knows as a magnetic field — akin to a gravitational or electric 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.

External articles

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Patents

• Vicci, , Magnetic-flux conduits

Physical quantity | Magnetism

Magnetický tok | שטף | تدفق مغناطيسي | Магнитен поток | Magnetischer Fluss | Flujo magnético | Flux du champ magnétique | 자속 | Magnetische flux | 磁束 | Strumień indukcji magnetycznej | Magneettivuo