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Updated On : 2017-02-19 at : 12:00:00

What is the Meaning of Electric Flux - How is it defined ?

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 -

ΦE.SE 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 dΦE through an infinitesimaly small surface area dS is calculated by following formula-

dΦ= E.dS

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 . dS

where E is the electric field and dS 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 -

Gauss Theorem

where

E is the electric field,
S is any closed surface,

Unit of Electric Flux

 

Electrical flux has SI units of volt metres (V m), or, equivalently, newton metres squared per coulomb (N m2C-1). Thus, the SI base units of electric flux are kg-m3-s-3-A-1 .

Its dimensional formula is [ L3MT-3I-1 ].

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