In electromagnetism, electric flux is the measure of the electric field through a given surface, although an electric field in itself cannot flow.
The electric field E can exert a force on an electric charge at any point in space. The electric field is the gradient of the potential.
An electric charge, such as a single electron in space, has an electric field surrounding it. In pictorial form, this electric field is shown as a dot, the charge, radiating "lines of flux". These are called Gauss lines. 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 proportional to the total number of electric field lines going 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 of vector area S is
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 dΦE through a small surface area dS is given by
(the electric field, E, multiplied by the component of area perpendicular to the field). The electric flux over a surface S is therefore given by the surface integral:
where E is the electric field and dS 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:
where
E is the electric field,
S is any closed surface,
Q is the total electric charge inside the surface S,
ε0 is the electric constant (a universal constant, also called the "permittivity of free space") (ε0 ≈ 8.854187817e-12F/m)
This relation is known as Gauss' law for electric fields in its integral form and it is one of Maxwell's equations.
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Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface.
In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it states that the flux of the electric field out of an arbitrary closed surface is proportional to the electric charge enclosed by the surface, irrespective of how that charge is distributed.
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ε (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor.
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