Problem $1$:

Electric Flux and Gauss's Law: A spherical shell sits next to a charge $q_1>0$ :

$($a$)$ The net flux through the spherical shell should be zero $-$ explain why. $($That is$,$ what formula $/$ rule says this should be true?$)$

$($b$)$ Even though the net flux is zero, there is an electric field piercing through the shell $($the electric field from $q_1).$ On the above diagram, show what portion of the sphere has negative flux going through it$,$ and what portion has positive flux.

$($c$)$ Your answer to part $($b$)$ should show that more of the area of the sphere has positive flux. How do you reconcile this with the statement in part $($a$)?$