With regard to the "new" capacitor problem, it might have been
helpful to the student to have given them a few more "data" points and
having them plot the stored charge vs the potential difference across the
capacitor. Most of them probably would come to the conclusion that the
capacitance (defined as the stored charge divided by the potential
difference) does not change.
A much more instructive question to ask students, in my opinion,
is "Why is the relationship between stored charge and potential difference
for a capacitor linear?" If the students can answer that one they have a
good grasp of electrostatics.
Mark
Dr. Mark H. Shapiro
Physics Department
California State University, Fullerton
P.O. Box 6866
Fullerton, California 92834-6866