So i've just learnt Gauss' Law a few days ago. I also worked out some applications of Gauss' Law. But I have a little confusion. In a couple of books that I referred, I found a statement that I don't quite understand. It says "Gauss' law works because the field due to a charge varies as $\frac{1}{r^2}$. Had the field not varied that way, it would have failed."

What does the statement actually mean? Why would it fail? And if it did fail, would there be an equivalent law in that case? I'm confused, please help!

So I've just learned Gauss' Law a few days ago. I also worked out some applications of Gauss' Law. But I have a little confusion. In a couple of books that I referred, I found a statement that I don't quite understand. It says "Gauss' law works because the field due to a charge varies as $\frac{1}{r^2}$. Had the field not varied that way, it would have failed."

What does the statement actually mean? Why would it fail? And if it did fail, would there be an equivalent law in that case? I'm confused, please help!