I'm reading the Feynman lectures on electromagnetism and in Vol II, Chapter 1.4 Vol. II, Chapter 1-4 he talks about the flux of the electric field and says that flux of $E$ through and closed surface is equal to the net charge inside divided by $\epsilon_0$.
If there are no charges inside the surface, even though there are charges nearby outside the surface, the average normal component of $E$ is zero, so there is no net flux through the surface
I cannot see why the net flux is zero here. Say we have a closed unit sphere at the origin with no charge inside it and at the point $(2, 0, 0)$ we have some charge $q$.
Well doesn't this charge then define the electric field $E$ for the system and it will flow into the unit sphere on the right hand side, and out of the unit sphere on the left hand side?
Furthermore, as the strength of the electric field decreases with distance from $q$ won't we have more flux going into the right hand side which is closer to the charge $q$, and less flux leaving through the left hand side as it is further away - and hence we should have a non-zero flux?
Can someone please explain what I am misinterpreting here?