# Electric Flux **The net amount of [[electric field]] lines passing through a surface in a particular direction.** ![[ElectricFlux.svg|500]] *The electric flux of a surface can be visualised as the net total electric field lines through the surface in a particular direction; the surface shown is a sphere* > [!infobox] Electric Flux > | | | |:----------------- | -------------------------------------------------------:| | ***Symbol*** | $\Phi_{\mathbf{E}}$ | | ***SI unit*** | volt-meter, $\text{V m}$ | | ***SI base units*** | $\text{kg}\;\text{m}^{3}\;\text{s}^{-3}\;\text{A}^{-1}$ | > [!NOTE] Electric Flux > The *electric flux* $\Phi_{\mathbf{E}}$ of an electric field $\mathbf{E}$ through a surface $S$ is the net number of field lines passing through the surface in a given direction. That is, electric flux is the [[Surface Integral#Vector field|surface integral]] > $\Phi_{\text{E}}=\iint_{S}\mathbf{E}\cdot d\mathbf{A}$ > - $\mathbf{E}$ - the electric field, $\text{V}\;\text{m}^{-1}$ > - $d\mathbf{A}$ - an *infinitesimal vector area element*[^1], $\text{m}^{2}$ > If the electric field is constant, then the calculation for the magnetic flux passing through a surface can be simplified to a [[dot product]]. > $\Phi_{\mathbf{E}}=\mathbf{E}\cdot\mathbf{A}=EA\cos\theta$ Graphically, the electric flux of a field through the surface can be thought of as the *net number of field lines* passing through the surface in a *particular direction*. This direction is dictated by the vector area and the angle between the field lines and the [[normal]] to the surface in the formulas. Electric flux is used in the integral form of *[[Gauss's law]]*, one of [[Maxwell's equations]], which states that the total electric flux through a *closed surface* is *proportional* to the total charge enclosed by the surface. [^1]: The *vector area* of a finite orientable surface has a magnitude representing its area and a direction parallel to its normal.