If the plate spacing increases by 1.25 mm for each full turn of a knob, by what amount does the spacing change in millimeters (mm) when the knob goes through half a turn?

Physics case study
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Preliminary Questions
Note: You will receive full credit for each prediction made in this preliminary section whether or not it matches conclusions you reach in the next section. As part of the learning process it is important to compare your predictions with your results. Do not change your predictions!
As you proceed with this assignment, you’ll be working with a short video clip entitled . It shows the spacing between a pair of parallel plates increasing by a known amount each time a knob is twisted by a half turn. The potential difference between the plates is measured with both an electrometer and voltage probes connected to a computer (see Fig. 1) so data can be recorded with the Logger software. Before proceeding, you should view the video clip.
(a) Use Equations 1 and 2 to derive an equation that describes how the voltage across a parallel plate capacitor depends on the plate spacing, d, and area, A. Show your work.
(b) If the plate spacing increases by 1.25 mm for each full turn of a knob, by what amount does the spacing change in millimeters (mm) when the knob goes through half a turn?
(c) You should have noticed in frame 5 of the movie that only one plate of the capacitor is being charged positively. The other plate is “grounded.” The right-hand plate and the left-hand plate are separated by only one-half of a turn of the dial. How can we claim this set up is actually a capacitor and thus has equal and opposite excess charges on both plates? Hint: What happens immediately after the first plate is charged? Is induction possible?
(d) What do you expect will happen to the capacitor system as the spacing between the plates increases? Hint: Refer to the equation you derived in section 1(a).
(e) When the potential difference is large the capacitor system is storing more energy than when it is small. Where does the additional energy “come from” as the plate spacing increases?
(f) If the two plates behave like an ideal capacitor, sketch the shape of a graph of voltage vs. spacing you might expect to measure and explain your reasoning.

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