Electric flux

Electromagnetism

Electricity Magnetism
Electrostatics Electric charge Static electricity Electric field Conductor Insulator Triboelectricity Electrostatic discharge Induction Coulomb's law Gauss's law Electric flux / potential energy Electric dipole moment Polarization density
Magnetostatics Ampère's law Magnetic field Magnetization Magnetic flux Biot–Savart law Magnetic dipole moment Gauss's law for magnetism
Electrodynamics Lorentz force law Electromagnetic induction Faraday's law Lenz's law Displacement current Magnetic potential Maxwell's equations Electromagnetic field Electromagnetic radiation Maxwell tensor Poynting vector Liénard–Wiechert potential Jefimenko's equations Eddy current London equations
Electrical network Electric current Electric potential Voltage Resistance Ohm's law Series circuit Parallel circuit Direct current Alternating current Charged current Neutral current Electromotive force Capacitance Inductance Impedance Resonant cavities Waveguides
Covariant formulation Electromagnetic tensor (stress–energy tensor) Four-current Electromagnetic four-potential
Scientists Ampère Coulomb Faraday Gauss Heaviside Henry Hertz Lorentz Maxwell Tesla Volta Weber Ørsted

In electromagnetism, electric flux is the measure of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface. If the electric field is uniform, the electric flux passing through a surface of vector area $S$ is

\Phi_E = \mathbf{E} \cdot \mathbf{S} = ES \cos \theta,

where $E$ is the electric field (having units of $V/m$ ), $E$ is its magnitude, $S$ is the area of the surface, and $θ$ is the angle between the electric field lines and the normal (perpendicular) to $S$ .

For a non-uniform electric field, the electric flux $d Φ E$ through a small surface area $d S$ is given by

d\Phi_E = \mathbf{E} \cdot d\mathbf{S}

(the electric field, $E$ , multiplied by the component of area parallel to the field). The electric flux over a surface $S$ is therefore given by the surface integral:

\Phi_E = \iint_S \mathbf{E} \cdot d\mathbf{S}

where $E$ is the electric field and $d S$ is a differential area on the closed surface $S$ with an outward facing surface normal defining its direction.

For a closed Gaussian surface, electric flux is given by:

\Phi_E =\,\!

$\oiint$

\scriptstyle S

\mathbf{E}\cdot d\mathbf{S} = \frac{Q}{\varepsilon_0}\,\!

where

E

is the electric field,

S

is any closed surface,

Q

is the total electric charge inside the surface

S

ε 0

is the electric constant (a universal constant, also called the "permittivity of free space") (ε₀ ≈ 8.854 187 817... x 10⁻¹² farads per meter (F·m⁻¹)).

This relation is known as Gauss' law for electric field in its integral form and it is one of the four Maxwell's equations.

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

Electrical flux has SI units of volt metres ( $V m$ ), or, equivalently, newton metres squared per coulomb ( $N m 2 C -1$ ). Thus, the SI base units of electric flux are $kg\cdotm 3 \cdots -3 \cdotA -1$ .

Its dimensional formula is $[L 3 MT -3 I -1]$ .

External links

Electric flux — HyperPhysics

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Electric flux

See also

External links