Electric flux|What is Electric flux ?|Definition

Electric flux : The term flux implies some kind of flow. Flux is the property of any vector field.

The electric flux is a property of electric field.

The electric flux through a given area held inside electric field is the measure of the total number of electric lines of force passing normally through that area.

As shown in Fig, if an electric field \displaystyle \vec{E}

  passes normally through an area element \displaystyle \Delta S , then the electric flux through this area is

\displaystyle \Delta \Phi _{E}=E\Delta S

Electric Flux through normal area
fig. 1 Electric Flux through normal area

As shown in Fig. 1, if the normal drawn to the area element \displaystyle \Delta S

makes an angle \displaystyle \Theta with the uniform field \displaystyle \vec{E} , then the component of \displaystyle \vec{E}  normal to \displaystyle \Delta S will be \displaystyle E\ cos\Theta , so that the electric flux is

\displaystyle \Delta \Phi _{E}= Normal\ component\ of\ E\times Surface\ area

=\displaystyle E\ cos\Theta\ \times \Delta S

or, \displaystyle \Delta \Phi _{E}=E\Delta S\ cos\Theta =\vec{E}.\vec{\Delta S}

In case the field \displaystyle \vec{E}

  is non-uniform, we consider a closed surface S lying inside the field, as shown in Fig. We can divide the surface S into small area elements : \displaystyle \vec{\Delta S_{1}} ,\displaystyle \vec{\Delta S_{2}} ,\displaystyle \vec{\Delta S_{3}} ,…\displaystyle \vec{\Delta S_{N}}. Let the corresponding electric fields at these elements be \displaystyle \vec{E_{1}} ,\displaystyle \vec{E_{2}} ,\displaystyle \vec{E_{3}} …,\displaystyle \vec{E_{N}} ..

Then the electric flux through the surface Swill be

\displaystyle \Delta \Phi _{E}=\vec{E_{1}}.\vec{\Delta S_{1}}+\vec{E_{2}}.\vec{\Delta S_{2}}+\vec{E_{3}}.\vec{\Delta S_{3}}+...+\vec{E_{N}}.\vec{\Delta S_{N}}

\displaystyle \Delta \Phi _{E}=\sum_{i=1}^{N}\vec{E_{i}}.\vec{\Delta S_{i}}

When the number of area elements becomes infinitely large (N → 0) and AS →0, the above sum approaches a surface integral taken over the closed surface. Thus

\displaystyle \Delta \Phi _{E}=\lim_{{N\rightarrow \propto ,\Delta S\rightarrow 0}}\sum_{i=1}^{N}\vec{E_{i}}.\vec{\Delta S_{i}}=\oint_{S}^{}\vec{E}.\vec{\Delta S}

Thus the electric flux through any surface S, open or closed, is equal to the surface integral of the electric field E taken over the surface S.

Electric flux is a scalar quantity.

Unit of \displaystyle \Delta \Phi _{E}

= Unit of E and unit of S .

SI unit of \displaystyle \Delta \Phi _{E}=NC^{-1}.m^{2}=Nm^{2}C^{-1}

Equivalently, SI unit of \displaystyle \Delta \Phi _{E}=Vm^{-1}.m^{2}=Vm

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