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A parallel-plate capacitor has a plate area of 200 cm^2 and a plate separation of 10 micrometers, giving a measured capacitance of 4.12 microfarads. Using kappa = C d / (epsilon_0 A), which material from the dielectric constant table is between its plates?
ASheet of nylon
BStrontium titanate
COrdinary tap water
DPyrex glass sheet
Answer & Solution
Correct answer: B. Strontium titanate
1. Rearranging C = kappa epsilon_0 A / d for kappa gives kappa = C d / (epsilon_0 A).
2. Convert units: area = 200 cm^2 = 200 x 10^-4 m^2, and d = 10 micrometers = 1.0 x 10^-5 m.
3. kappa = (4.12 x 10^-6 F)(1.0 x 10^-5 m) / [(8.85 x 10^-12 F/m)(200 x 10^-4 m^2)] = 233.
4. Checking the dielectric constant table, a kappa near 233 clearly matches strontium titanate rather than water (about 80), Pyrex glass (about 5.6), or nylon (about 3.4).
_Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section Dielectrics_
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