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Encyclopedia of Electrical Engineering
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Encyclopedia of Electrical Engineering
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Electric Flux

What is Electric Flux?

In electromagnetism, electric flux is the measure of the electric field through a given surface, although an electric field in itself cannot flow. It is a way of describing the electric field strength at any distance from the charge causing the field.
Electric flux is the rate of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a virtual surface.
Electric flux is denoted by upper case greek letter (Phi) $\phi$.
electric flux passing through a surface
Fig.no.1: Electric flux passing through area A.
electric flux passing through a surface
Fig.no.2: Electric flux passing through area A with different angles.
If the electric field is uniform, the electric flux passing through a surface of vector area A can be Mathematically written as; $$ \phi = E.A \cos \theta$$ $$ d\phi = E.dA \cos \theta$$ applying integration, $$ \int d\phi = \int E.dA \cos \theta$$
$$ \bbox[5px,border:1px solid red] {\color{blue}{\phi = \int E.dA \cos \theta}}$$Eq.(1)
$$ \bbox[5px,border:1px solid red] {\color{blue}{E = {d\phi \over dA}}}$$Eq.(2)
Equation 2 shows electric field is the rate of change of electric flux through a given area.
Electrical flux has SI units of volt meters (V.m), or, equivalently, newton meters squared per coulomb ($Nm^2/C$).