There is an infinite slab of charge, and a (Gaussian surface) cylinder whose ends are both outside of the slab.
$\phi_A$ is the flux through this cylinder, by symmetry the component of the flux through the top end is $\frac{ \phi_A}{2}$.
Now, lift bottom end of the cylinder until it is inside the slab. The net flux is now $ \phi_B$.
Proposition 1: The component of the flux through the top end is unaffected by the position of the bottom end (even though the total flux is), as the electric field and area at and of the top end are both unaffected by the movement of the bottom end.Thus the flux through the top end is still $\frac{ \phi_A}{2}$.
Proposition 2: Therefore the flux through the bottom part is all the flux that is remaining (that is, $\phi_B-\frac{ \phi_A}{2}$).
This must be balderdash, as with by extension of my logic, the flux through the bottom in the second case is$\phi_B-(\phi_B-\frac{ \phi_A}{2})=\frac{ \phi_A}{2}$: that is, the net flux is unaffected as the top and bottom flux add up to $ \phi_A $, in contradiction with $\phi=\frac{Q}{\epsilon_0}$. What is incorrect with propostion 1, both physically and mathematically?
