Problem 1

1.) (10 points) A point A is located a distance d away from an infinite sheet of charge. Another point B is located a distance 2d from the same sheet of charge. What is the ratio of the electric field at point A to that at point B due to the infinite sheet of charge? Explain why this result makes sense physically.
 
A formula you may or may not find useful... 

$\oint \vec{E} \cdot d\vec{A} = \frac{Q_{enclosed}}{\epsilon_{0}}$

Answer:
The electric field away from an infinite sheet of charge is given by
$(E)(A) = \frac{Q}{\epsilon_{0}}$
$E = \frac{Q}{A \epsilon_{0}}$
There is no radial dependence in this formula. Therefore, the electric field at point A is the same as that at point B.
I also accepted arguments on how the components of electric field vectors contribute to the electric field. That says that if a point is close to a sheet of charge, only the few electric field lines that are generated from right next to the point contribute to the electric field that is normal to the surface. For a point further away, although individual field vectors contribute less, there are more of them that contribute in the direction normal to the sheet of charge.
Another argument is that the electric flux, or density of electric field lines doesn't change as you move further away from the sheet of charge.
The ratio was 1:1.