Electric flux density. The number of electric lines of force passing normally per unit area about any point, is called electric flux density about that point. It is also called electric intensity. It is a vector quantity represented by \(\vec E\). Its units is NC-1.
Electric Flux. The surface integral of electric field over a surface is called electric flux linked with the surface. Thus total numbers of electric lines of force passing through a surface in a direction normal to the surface when the surface is placed inside an electric field is called electric flux. It is denoted by Φ.
Consider a small area element d \(\vec S\) of a closed surface S. Let \(\vec E\) be electric field at area element. Thus, electric flux through area.element is \(d\ \vec S\) given by
dΦ = \(\vec E.d\ \vec S\)
(where area vector \(d\ \vec S\) is a vector whose magnitude represents the area of the element and direction is normal to the element)
If θ is the angle between the direction of area element and the electric field, then,
dΦ = E dS cos θ = (E cos θ) dS
Now, E cos θ is normal component of the electric field (component of the electric field along normal to area element) and is denoted by En.
Therefore,
dΦ = \(\vec E.\vec {ds}\)
Total electric flux lined with a surface S is given by
Φ = \(∫\vec E.\vec {ds}\)
If the surface S is closed. then total electric flux linked with the closed surface is given by
Φ = \(∮\vec E.\vec {ds}\)
