Why does a Charge Outside a Surface Produce No Net Flux?

[patrickbotros]

My textbook says "the net flux is zero through a closed surface that does not contain any net charge," and justifies it by saying that everything flowing in has an equal thing flowing out. This makes ABSOLUTELY NO sense to me.

 

[Vanadium 50]

Nonetheless it is true.

If you saw it work in 2-D would you believe it in 3-D? Draw a source with field lines coming out of it. You can draw the field lines any way you want, provided that they do not cross. Now, draw a closed shape that does not include the source anywhere on the paper. Any closed shape. Count the lines going in and count the lines going out.

 

[Pierce610]

In a surface that contains a source, for example a positive charged particle, the flux is determined by only outcoming field lines from it, while in a surface that doesn't contain any source, the field lines passing through it, generated by an external field , enter but also go out, and so the net flux is zero.