Good explantion of Gauss' Law but I have a question

[rockyshephear]

Here's the good explanation.
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A surface is an abstract mathematical tool that we can use to explore various phenomena. What a surface is, is a shell around a region of space. Consider a common inflatable ball, such as a soccer ball, or a basketball. The "ball" itself is just a rubberized shell around a pocket of air.

Like a ball, a surface is just a shape in space that encloses a certain volume. Like a ball, the surface cannot have any gaps in it (if a ball has gaps, air will escape, and the ball will deflate).

If the surface we have is a closed one, so it has no gaps, then you can imagine that in a river the same amount of water that enters the surface must also exit the surface. The only time that more water can be coming out of a surface is if there is a hose inside the surface. The only time more water can be entering the surface is if there is a drain inside the surface.

Or if we go back to Electric Field, the only time the flux in a surface is not zero, is when there is a charge inside that surface.


[Gauss' Law for Electric Fields (zero charge)]

\oint_S{\mathbf{E}\cdot d\mathbf{a}} = 0 ---

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The anaology is losing me a bit. I'm imaginging this surface (like a balloon submerged in water) I can see the surface as being the skin of the balloon. Water outside the balloon can somehow magically entere the balloon even though it's a closed surface (not going there). But the water that is reportedly entering the balloon that they say is equal to that entering is ending up INSIDE THE BALLOON. How is that supposed to be water leaving the surface?
I'm wondering why the suface has to be spherical. Maybe a sheet of paper is better for the analogy. Water enters one side and leaves the other. Then Gauss' Law states that the difference between the the volume of water entering the surface and leaving the surface is zero because there is no source or sink, no charge.

Or maybe they are saying without a 'charge' inside the balloon, water enters the balloon, fills the balloon and exits the other side of the balloon. I can buy that. Is that what they are saying?

 

[turin]

Think of a fine closed mesh, or closed netting, as the closed surface. Then, water can move in and out freely, and the surface can be any shape that you want. The purpose of the surface is not to keep things in or out, so you don't need an impermeable surface like a balloon. The purpose of the surface is simply to define some nonphysical boundary, and you don't want the nonphysical object to have any effect on the physical stuff (the water).