Does Gauss' Law use line integrals or surface integrals?

[Albert Tran]

In my physics textbook, I see Gauss' Law as [PLAIN]https://upload.wikimedia.org/math/0/3/5/035b153014908c0431f00b5ddb60c999.png$\oint$$E dA$ but in other places I see it as [PLAIN]https://upload.wikimedia.org/math/0/3/5/035b153014908c0431f00b5ddb60c999.png[PLAIN]https://upload.wikimedia.org/wikipedia/commons/thumb/8/86/OiintLaTeX.svg/25px-OiintLaTeX.svg.png[PLAIN]https://upload.wikimedia.org/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png [PLAIN]https://upload.wikimedia.org/math/3/9/f/39f4ca19d0c263fd02c0e50cb8829239.png, which one is the right one?

 

[Incand]

The two expressions you wrote are the same, both are surface integrals as you can see from the area element $dA$, it's just different notation if you want to write out double integral signs or not.

The only difference is in the second one the dot product is used making it more general since we want the component of the $E$ field normal to the surface to get the flux. The first form assumes that $E$ is normal to the surface so we only need to care about the scalar value.

 

[beamie564]

Both are the same.. Some books write a single integral to make it less cumbersome.. If you see a "S" underneath the integral sign or the infinitesimal element is dA or dS it's understood to be a surface integral.