Magnetic flux

Magnetic flux, is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. 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. The Maxwell's equations in the absence of magnetic monopoles requires that the magnetic flux through a closed surface be zero. In symbols, this means:

\Phi_m \equiv \int \!\!\! \int \vec{B} \cdot \hat{n} \, da

We know from one of Maxwell's equations

\vec{\nabla} \cdot \vec{B}=0

in combination with the divergence theorem that

\oint \!\!\! \oint_{\partial V} \vec{B} \cdot \hat{n} \, da=\int \!\!\! \int \!\!\! \int_V \vec{\nabla} \cdot \vec{B} \, d\tau = 0

. In other words, the magnetic flux through any closed surface must be zero. By way of contrast, one of Maxwell's equations for electric fields is

\vec{\nabla} \cdot \vec{E} = {\rho \over \epsilon_0}

indicating the presence of electric monopoles. By the same token, there are no magnetic monopoles. The SI unit of magnetic flux is the Weber (Wb). The direction or vector of the magnetic flux 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 in a spool of electrical conductive wire called a solenoid will cause an electric current in the spool. This is the basis of the production of electricity. When turned around, that is, running a current through a spool, a magnetic flux will be produced in the spool. This is electromagnetism. The relationship is given by Faraday's law of induction:

\mathcal{E} = \oint \vec{E} \cdot d\vec{l} = -{d\Phi_m \over dt}

''Related concepts'': gauss, henry (inductance), Tesla (unit), maxwell, oersted, weber (Wb), volt, and B-Field. ==See also== *Magnetic flux quantum Physical quantity Magnetism

Magnetic flux

The given "proof" that the flux through a closed surface being zero seems backward. It starts from a vector potential A with curl A = B and then proves that div B = 0. In reality it is just the opposite. One of Maxwells laws states that div B = 0. As a consequence there is a vector potential A with curl A = B. −User:Woodstone 21:42, 2005 Apr 9 (UTC) :I added the reference to Maxwell's equations because of that, but it is still unsatisfying. Lemme see how it can be reworded. --User:Laurascudder 23:32, 9 Apr 2005 (UTC) ::I just removed the reference to the vector potential since it has no direct connection to discussion. --User:Laurascudder 23:43, 9 Apr 2005 (UTC)

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Words begining with Magnetic_flux:

Magnetic_flux
Magnetic_flux
Magnetic_flux_density
Magnetic_flux_quantum
Magnetic_flux_tube