Question

Hello... if there`s someone who could answer, how do you define an open surface that Walter Lewis keeps talking about? Is it the same as in Calculus? (I mean, a surface without the borders) or is it something else? Like any surface attatched to the loop, or something like that...?

Answer 1

I think you're talking about Gaussian surfaces which you define in order to use Gauss' law.
Firstable, the Gaussian surfaces are imaginary, they don't exist in the reality, you just define them mathematically in order to use Gauss' law.
How do you define them? The first thing you have to know is that they are closed surfaces, they have no holes or singularities. Second of all, the system of reference and the surface is defined by you and you usually do it taking into account the symmetry of the problem.
After you do this then you can just use Gauss' law and if you choose it well you'll solve your problem,
The classic example of using a Gaussian surface is that when you want to find the electric field and the charge distribution is a sphere or a spherical shell. Then what you do is you choose a Gaussian surface that is a concentric sphere to the charge distribution and you decide which is the radius of the sphere and that allow you to know the electric field due to that charge distribution.
I hope the information help you.

Answer 2

An open surface is a surface with a border.

Any Gaussian surface is a closed surface (encompassing a volume)

Answer 3

Sorry, my bad... although Walter Lewis does not keep talking about open surfaces