7.2 Electric flux

  Electrostatics

Electric flux is a measure of the number of electric field lines crossing a surface.

If the electric field lines pass through a surface then the surface is said to have flux linked with it. It is given by, $$d\phi = \overrightarrow E .\,d\overrightarrow S \quad ...(i)$$
where,

$\overrightarrow E :$ Electric field
$d\overrightarrow S :$ Area vector of the small area element.

The area vector of a closed surface is always in the direction of outward drawn normal.

So, the total flux lined with whole of the body is the closed integral of equation $(i)$,
$$\phi = \oint {\overrightarrow {E\,} .\,d\overrightarrow S } $$
where,

$\oint {} :$ Represents closed integral done for a closed surface.

Note:

• The SI unit of electric flux is $N{m^2}{C^{ - 1}}$.
  
  
• Dimensional formula of electric flux is $\left[ {M{L^3}{T^{ - 3}}{A^{ - 1}}} \right]$.
  
  
• Electric flux is a scalar quantity as it is a dot product of two vector quantity.
  
  
• Electric flux is zero for a surface when electric field $\left( {\overrightarrow E } \right)$ is perpendicular to the area vector $\left( {d\overrightarrow S } \right)$ or electric field is parallel to the surface.
  
  
  
  
  
  
• Electric flux can be negative if the angle between the electric field and the area vector is more than $\frac{\pi }{2}$.