**Electric Flux - Definition :**
**Electric flux** gives the measure of flow of the **electric field** through a given area. We may define electric flux as-
“ **Electric flux** is proportional to the number of **electric field lines** passing normally through a surface.”
If the electric field is uniform, the electric flux passing through a surface of vector area **S** is calculated by following formula -
**Φ**_{E }= **E.S**= *E S *cosθ
where - **E** is the electric field (measured in 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*.
Now if we are dealing with a non-uniform electric field, then electric flux *d*Φ_{E} through an infinitesimaly small surface area *d***S** is calculated by following formula-
*d*Φ_{E }= E.*d*S
The scalar product of electric field and area vector (Oh! off course area is not a vector, however in some case treating it as vector simplifies our situation without affecting the result). The total electric flux over a surface *S* is therefore given by the surface integral -
**Φ**_{E }= ∫∫_{S }E . dS
where **E** is the electric field and *d***S** is a differential element of the surface S, with an outward facing surface normal defining its direction.
Now for a closed surface, electric flux is given by -
where
**E** is the electric field,*S* is any closed surface,
## Unit of Electric Flux
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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-m^{3}-s^{-3}-A^{-1} .
Its dimensional formula is **[ L**^{3}MT^{-3}I^{-1} ]. |