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Concept
Electric flux
Summary
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.
Official source
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