Does Gauss's Law hold true for a point charge near a sphere?

[ehabmozart]

Consider a point charge on the x-axis at x=4. And a sphere with radius 3cm is kept beside the point charge centered at the origin. Consider the near end (x=3) and the far end (x=-3) ... We will find that E from the point charge is much bigger in the close end than E at the far end. So if we calculate inward and outward flux to get the net, this would not be zero since they strike the same area. Does this vilate with Gauss's Law??

 

[CompuChip]

When in doubt, do the math. You will (hopefully) find that Gauss's law also applies in this case.

 

[DimReg]

The intuition behind this case is as follows:

We think of the electric field as a bunch of arrows (field lines), with the density of them telling you the strength of the field. But they also tell you the flux through a surface, the more arrows, the more flux. If you think about the situation you came up with, how many arrows enter the sphere, and how many leave? (if you have a hard time thinking about this, "follow" a single arrow from the point charge, towards the sphere, and out to infinity. What does it do?) Does this violate gauss' law?