Editing Flux (section)

==== Magnetic flux ====
The magnetic flux density ([[magnetic field]]) having the unit Wb/m<sup>2</sup> ([[Tesla (unit)|Tesla]]) is denoted by '''B''', and [[magnetic flux]] is defined analogously:<ref name="Electromagnetism 2008"/><ref name="Electrodynamics 2007"/>
<math display=block>\Phi_B=\iint_A\mathbf{B}\cdot\mathrm{d}\mathbf{A}</math>
with the same notation above.  The quantity arises in [[Faraday's law of induction]], where the magnetic flux is time-dependent either because the boundary is time-dependent or magnetic field is time-dependent. In integral form:
<math display=block>- \frac{{\rm d} \Phi_B}{ {\rm d} t} = 
\oint_{\partial A} \mathbf{E} \cdot d \boldsymbol{\ell}</math>
where ''d'''''{{ell}}''' is an infinitesimal vector [[line element]] of the [[closed curve]] <math>\partial A</math>, with [[Magnitude (vector)|magnitude]] equal to the length of the [[infinitesimal]] line element, and [[Direction (geometry)|direction]] given by the tangent to the curve <math>\partial A</math>, with the sign determined by the integration direction.

The time-rate of change of the magnetic flux through a loop of wire is minus the [[electromotive force]] created in that wire. The direction is such that if current is allowed to pass through the wire, the electromotive force will cause a current which "opposes" the change in magnetic field by itself producing a magnetic field opposite to the change.  This is the basis for [[inductor]]s and many [[electric generator]]s.