Is it precisely true that gauss' law states that the total no. of lines of force crossing any closed surface in the outward direction is proportional to net positive charge enclosed within the surface?

Answer 1

As soon as you ask "Is it precisely true ...", we know immediately that it must

not be, and we know that our task is to search your version of the statement

for the hidden gotchas.

I don't think Gauss stated his "Law of Electricity" in terms of 'lines of force'.

Seems to me more likely that he stated it in terms of the surface integral over

the closed surface.

But even if you want to state it in terms of 'lines', then there are a couple of

small problems with the way it's stated in the question above:

1). Instead of the "total" number of lines, it would have to be the "net" number

of lines, and it would have to say something about the lines crossing the closed

surface in the direction normal to it, in case the closed surface isn't a sphere.

2). Gauss talked about just plain charge, without regard for positive or negative

as quoted here. And corresponding to that item, he wouldn't have mentioned the

"outward direction" either.