Electric flux

Yesterday I watched some of the videos of Walter Lewin lectures on Electricity and Magnetism. He is really amazing especially when he is doing experiments. Thought the concepts are a familiar one it gave me a good time pass. I spend a little time on thinking about Electrostatics.

We need to know that Electric field lines are not real. It is just a simple representation invented by Michael Faraday to visualize Electric field. We should not simply accept it as the real fact.

Electric flux is the measure of the number of field lines passing through the surface that is chosen. But it is not the number of the absolute number of field lines.

The electric flux “ϕ” over a surface S is therefore given by the surface integral:

ϕ = ∬ E. ds

       s

where “E” is the electric field and “ds” is a differential area on the surface S with the normally outward facing direction.

And the electric flux around the closed surface “S” is given by:

ϕ = ∯ E. ds = q / ϵ

But be careful that it is not absolute that, there is exactly 

“q / ϵ” electric flux around a point charge “q” [In SI unit system].

Electric flux is not really the measurement of the number of field lines around a charge. It is just a calculating tool of Electric strength on the basis of proportionality arguments.

We know that we can draw infinitely many electric field lines as much as we want. But for the sake of simplicity in our calculations, we can’t use “infinite” as a number.

[Note: We need to be very careful that “∞” is not a number. It is just a symbol given for concepts.

It is like instead of saying “Newton’s Laws of Motion”, if I made a code “£” in a book, it says that where ever I use the symbol “£” it really means “Newton’s laws of Motion”.

In the same manner, the symbol “∞” is also used just to represent a Mathematical and Physical concept. The “∞” symbol just says that “it gets bigger and bigger where there is no end”. Simply it means “no limit or end”.]  

So we made a proportionality factor that is related with the number of field lines. Though the number of lines is infinite it is a proportional and dependent quantity.  

It was defined the Electric flux as it is proportional to the number of field lines.

It is already known from the definition that charge “q” is also proportional to the number of field lines.

Therefore we made calculations from the conclusion; Electric flux is proportional to “q”

It is first formulated by Carl Freidrich Gauss that is

The net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed within that closed surface.

If the number of field lines was found out to be increasing that implies the charge “q” inside the closed surface is increased.

In SI units the proportionality constant is taken to be “1/ϵ” and so the electric flux  

Thus we are just finding the proportional increase in Electric flux from “q/ϵ” but it is not the measure of the absolute electric flux around the space of the charge “q”.