I'm confused about electric flux?

Question

In a previous physics class, I learned that the electric flux was $vec{E}cdotvec{A}$ (dot product), and hence the unit is $Nm^2/C$. But in my electromagnetics book, it says the unit is Coulomb, and that flux density is $C/m^2$. I'm really lost.

Rodney Dunning · Answer

In your previous physics class, electric flux was defined as

$$Phi = oint_S vec{E} cdot dvec{S},$$

which has SI units of V-m or $textrm{N-m}^2textrm{-C}^{-1}$. Hayt and Buck are defining flux in terms of the electric flux density $vec{D}$, given by $vec{D} = epsilon_{textrm{o}}vec{E}$ with the SI unit being $textrm{C-m}^2$:

$$Psi = oint_S vec{D} cdot dvec{S},$$

which has SI units of C. So $Psi = epsilon_{textrm{o}}Phi$, and Gauss' law can be written as

$$Psi = oint_S vec{D} cdot dvec{S} = Q,$$

where $Q$ is the charge enclosed by the surface $S$.

I'm confused about electric flux?

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