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## Main Question or Discussion Point

I am taking a course in Electromagnetic Wave Theory, and the prescribed book for us is Engineering Electromagnetics by William Hayt. The book if excellent, till I reached the part about Gauss's Law. I will be describing my queries here, kindly help me out with them.

1) The book first states Faraday's experiments with charged sphere, and then says that "flux is proportional to charge. However, in SI units the constant of proportionality is 1, and hence flux equals charge." I didn't get this. The fact that charge is same as flux is then used throughout the chapter.

2) The book then introduces flux density (D), and proves the relation D=[tex]\epsilon[/tex]E, where E is the electric field. The proof seems alright, but again thats assuming that charge equals flux.

3) Finally, coming to Gauss's Law, the book states that total flux through any closed surface is equal to the charge enclosed. Mathematically, integral of D.ds over a closed surface equals volume integral of rho.dv (sorry I tried latex but I get a weird formatting bug), where D is the flux density, rho is the volumetric charge density and ds, dv have their usual meanings. I just cant seem to relate this with the Gauss's Law that I have learned, saying that the flux that the flux is equal to the charge enclosed upon the permittivity, the flux being the areal integral of of electric field and elemental area. I don't quite see how its the same thing, and I am really confused.

Even Gauss's law in differential form has the same thing. Also, I tried looking these things up over the internet, but apparently no one uses flux density with Gauss's Law.

Any help would be highly appreciated.

1) The book first states Faraday's experiments with charged sphere, and then says that "flux is proportional to charge. However, in SI units the constant of proportionality is 1, and hence flux equals charge." I didn't get this. The fact that charge is same as flux is then used throughout the chapter.

2) The book then introduces flux density (D), and proves the relation D=[tex]\epsilon[/tex]E, where E is the electric field. The proof seems alright, but again thats assuming that charge equals flux.

3) Finally, coming to Gauss's Law, the book states that total flux through any closed surface is equal to the charge enclosed. Mathematically, integral of D.ds over a closed surface equals volume integral of rho.dv (sorry I tried latex but I get a weird formatting bug), where D is the flux density, rho is the volumetric charge density and ds, dv have their usual meanings. I just cant seem to relate this with the Gauss's Law that I have learned, saying that the flux that the flux is equal to the charge enclosed upon the permittivity, the flux being the areal integral of of electric field and elemental area. I don't quite see how its the same thing, and I am really confused.

Even Gauss's law in differential form has the same thing. Also, I tried looking these things up over the internet, but apparently no one uses flux density with Gauss's Law.

Any help would be highly appreciated.