Electric flux

Common symbols	ΦE
SI unit	Volt-meter(V m)
InSI base units	kg⋅m3⋅s−3⋅A−1
Dimension	ML3T−3I−1

Inelectromagnetism,electric fluxis the measure of theelectric fieldthrough a given surface,^[1]although an electric field in itself cannot flow.

The electric fieldEcan exert a force on an electric charge at any point in space. The electric field is thegradientof the potential.

Overview[edit]

An electric charge, such as a singleelectronin space, has an electric field surrounding it. In pictorial form, this electric field is shown as "lines of flux" being radiated from a dot (the charge). These are called Gauss lines.^[2]Note that field lines are a graphic illustration of field strength and direction and have no physical meaning. The density of these lines corresponds to the electric field strength, which could also be called the electric flux density: the number of "lines" per unit area. Electric flux is directly proportional to the total number of electricfield linesgoing through a surface. For simplicity in calculations it is often convenient to consider a surface perpendicular to the flux lines. If the electric field is uniform, the electric flux passing through a surface ofvector area $A$ is $\Phi _{E}=\mathbf {E} \cdot \mathbf {A} =EA\cos \theta,$ where $E$ is the electric field (having units of $V/m$ ), $E$ is its magnitude, $A$ is the area of the surface, and $θ$ is the angle between the electric field lines and the normal (perpendicular) to $A$ .

For a non-uniform electric field, the electric flux $dΦ E$ through a small surface area $d A$ is given by ${\textrm {d}}\Phi _{E}=\mathbf {E} \cdot {\textrm {d}}\mathbf {A}$ (the electric field, $E$ ,multiplied by the component of area perpendicular to the field). The electric flux over a surface is therefore given by thesurface integral: $\Phi _{E}=\iint _{S}\mathbf {E} \cdot {\textrm {d}}\mathbf {A}$ where $E$ is the electric field and $d A$ is an infinitesimal area on the surface with an outward facingsurface normaldefining its direction.

For a closedGaussian surface,electric flux is given by:

\Phi _{E}=\,\!

$\oiint$

\scriptstyle S

\mathbf {E} \cdot {\textrm {d}}\mathbf {A} ={\frac {Q}{\varepsilon _{0}}}\,\!

where

$E$ is theelectric field,
$d A$ is an infinitesimal area on theclosed surface,
$Q$ is the totalelectric chargeinside the surface,
$ε 0$ is theelectric constant(a universal constant, also called the "permittivityof free space ") ( $ε 0 \approx 8.854 187817 \times 10 -12 F / m$ )

This relation is known asGauss's lawfor electric fields in itsintegralform and it is one ofMaxwell's equations.

While the electric flux is not affected by charges that are not within the closed surface, the net electric field, $E$ can be affected by charges that lie outside the closed surface. While Gauss's law holds for all situations, it is most useful for "by hand" calculations when high degrees of symmetry exist in the electric field. Examples include spherical and cylindrical symmetry.

The [SI] unit of electric flux is the volt-meter ( $V\cdotm$ ), or Dimension is m⁰t‐¹a‐¹, or, equivalently,newton-meter squared percoulomb( $N\cdotm 2 \cdotC -1$ ). Thus, the unit of electric flux expressed in terms ofSIbase units is $kg\cdotm 3 \cdots -3 \cdotA -1$ .Its dimensional formula is ${\mathsf {L}}^{3}{\mathsf {MT}}^{-3}{\mathsf {I}}^{-1}$ .

Citations[edit]

^Purcell, pp. 22–26
^Purcell, pp. 5–6.

References[edit]

Purcell, Edward, Morin, David; Electricity and Magnetism, 3rd Edition; Cambridge University Press, New York. 2013ISBN 9781107014022.
Browne, Michael, PhD; Physics for Engineering and Science, 2nd Edition; McGraw Hill/Schaum, New York; 2010.ISBN 0071613994

External links[edit]

Electric flux–HyperPhysics

[1] Purcell, pp. 22–26

[2] Purcell, pp. 5–6.

[1]

[2]

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