# Flux through a sphere due to a charge outside of it [duplicate]

A point charge of $\rm+5.00 μC$ is located on the $x$-axis at $x=\rm5.00m$ , next to a spherical surface of radius $x=\rm4.00m$ centered at the origin.

According to Gauss's law, the net flux through the sphere is zero because it contains no charge. Yet the field due to the external charge is much stronger on the near side of the sphere (i.e., at $x=\rm4.00m$) than on the far side (at $x=\rm-4.00m$). How, then, can the flux into the sphere (on the near side) equal the flux out of it (on the far side)?

My Thoughts:

I know that the flux should be zero. I drew a picture, with the charge to the right of the sphere and drew lines radially from the point. However, I can't seem to wrap my head around why the net flux is zero. If I go through adding up all the $\rm\vec{E}.d\vec{A}$'s, does it have to do with the $\rm d\vec{A}$ being the opposite direction of the field on the close side to the particle, so flux is negative, but on the top, bottom, and left (front and back as well) sides of the sphere, the field is in a similar direction so flux would be positive?