I The integral form of Gauss' theorem

[BearY]

In many texts I have seen, Gauss theorem has the form of$$\frac{q}{\epsilon_0}=\oint\vec{E}d\vec{A}$$
Why a line integral symbol was used for this surface integral everywhere? The more I see it the more I believe there is something wrong with my understanding about this.
I didn't think too much of this problem earlier, I remember I simply dismissed this question with it somehow being an application of the Stokes theorem. but now I am revisiting this question.

 

[jtbell]

Why a line integral symbol was used for this surface integral everywhere?

An integral sign with a circle is commonly used (at least in physics textbooks) for both a line integral around a closed path, and a surface integral over a closed surface. The two kinds of integrals are usually distinguished by using something like $d \vec l$ for line integrals and $d \vec a$ for surface integrals.

 

[haushofer]

Maybe a better notation would be

$$\frac{q}{\epsilon_0}=\oiint\vec{E}d\vec{A}$$

(a double integral with the circle) but somehow here the \oiint code doesn't work. See e.g.

https://tex.stackexchange.com/questions/162771/xelatex-double-closed-path-integral

and

https://www.physicsforums.com/threads/closed-integral-in-latex.781932/

 

[BearY]

Maybe a better notation would be

$$\frac{q}{\epsilon_0}=\oiint\vec{E}d\vec{A}$$

(a double integral with the circle) but somehow here the \oiint code doesn't work. See e.g.

https://tex.stackexchange.com/questions/162771/xelatex-double-closed-path-integral

and

https://www.physicsforums.com/threads/closed-integral-in-latex.781932/

Heh maybe that's why $\oint$ is used
I am a sheeple and I am good as long as I know the convention is what I think it is.

 

[robphy]

<br /> \iint\hspace{-3.1ex}\bigcirc\ \vec E \cdot d\vec A<br />