electric flux

Electric flux measures how much electric field pokes through a surface, like counting how many field lines pierce a hoop you hold up. Think of the field as a wind and the surface as a window: the flux is how much wind blows through. Hold the window face-on to the wind and lots gets through; turn it edge-on and almost none does.

For a flat surface of area A in a uniform field E, the electric flux is Phi_E = E A cos theta, where theta is the angle between the field and the line sticking straight out of the surface (its normal). When the field is perpendicular to the surface (theta = 0) the flux is largest, E A; when the field skims parallel to the surface (theta = 90 degrees) the flux is zero. Its SI unit is the newton-metre-squared per coulomb (N m^2/C). For curved surfaces or changing fields you add up the flux over tiny patches, an integral.

Flux matters because of what it reveals about the charge inside a closed surface. The number of field lines threading out of a closed bag depends only on how much charge is trapped inside, an idea made exact by Gauss's law. Electric flux is therefore the bridge between the field you can measure on a surface and the charge hidden within it.