Area of parallel plat capacitor

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SUMMARY

The discussion centers on calculating the plate area of a parallel-plate capacitor that matches the capacitance of a spherical capacitor with a capacitance of 12.4 pF and a plate separation of 0.012 m. The formula used is C = (ε * A) / d, where ε is the permittivity of free space (8.85 x 10^-12 F/m). The correct calculation yields an area A of 0.0168 m², which converts to 168 cm², not 1.68 cm², highlighting the importance of accurate unit conversion in capacitor calculations.

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  • Understanding of capacitor fundamentals and capacitance calculations
  • Familiarity with the formula C = (ε * A) / d
  • Knowledge of unit conversions between square meters and square centimeters
  • Basic grasp of spherical and parallel-plate capacitor configurations
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Students studying physics, particularly those focusing on electromagnetism and capacitor theory, as well as educators looking for examples of common calculation errors in capacitor problems.

juggalomike
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Homework Statement


The plates of a spherical capacitor have radii 31.0 mm and 43.0 mm.
What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance of 12.4pF

Homework Equations


C=(epsilon*A)/d

The Attempt at a Solution



12.4*10^-12=(8.85*10^-12*A)/(.012m)

so A=.0168m^2=1.68cm^2, which is incorrect?
 
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juggalomike said:
so A=.0168m^2=1.68cm^2, which is incorrect?

0.0168 m2 ≠ 1.68 cm2.

1 square meter does not contain 100 square centimeters. Rather it contains (100 [cm]) X (100 [cm]) = 10000 square centimeters.
 
collinsmark said:
0.0168 m2 ≠ 1.68 cm2.

1 square meter does not contain 100 square centimeters. Rather it contains (100 [cm]) X (100 [cm]) = 10000 square centimeters.

Yep lol, thanks, my answer was correct except for the conversion
 

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