A variable air-filled capacitor of the type used in tuning radios
is shown. Alternate plates are connected together, one group
fixed in position (shown in dark grey), the other group capable
of rotation (shown in light gray). Consider a pile of n plates of
alternate polarity, each having an area A and separated from
adjacent plates by a distance d.
Show that this capacitor has a maximum capacitance of:
Picture for reference
2. The attempt at a solution
I'm pretty sure I am correct, but something about my approach seems.. too simple. My idea is that to find the capacitance you must simply add up the capacitance between every plate. Since if there n plates, there are n-1 separations and thus C=((n-1)ε0A)/d.
I can't logically find another way to calculate the capacitance, but it can't possibly be that easy?