Capacitance Problem; somewhat solved, but units are off

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Homework Help Overview

The problem involves calculating the capacitance of an air-filled spherical capacitor with specified inner and outer shell radii, as well as determining the potential difference that results in a given charge on the capacitor. The subject area is primarily focused on capacitance and electric potential in electrostatics.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculations for capacitance and potential difference, with some noting discrepancies between their results and the book's answers. There is an emphasis on unit conversion and potential calculation errors.

Discussion Status

Some participants have confirmed that the capacitance calculation matches the book's answer, while others have identified a calculation error in determining the potential difference. There appears to be a productive exchange regarding the accuracy of the calculations.

Contextual Notes

Participants express uncertainty about unit conversions and the correctness of their calculations, indicating a need for clarification on these aspects.

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Homework Statement



An air-filled spherical capacitor is constructed with inner and outer shell radii of 7.00 and 14.0 cm, respectively. (a) Calculate the capacitance of the device. (b) What potential difference between the spheres results in a charge of 4.00 microC on the capacitor?

Homework Equations



C = ab / Ke(b-a)
C = Q/V

The Attempt at a Solution



(a) C = ab/Ke(b-a) = (.07m * .14m) / (8.9875*10^9N*m^2/C^2 * .07m) = 1.558*10^-11
(b) C = Q/V
V = Q/C = (4*10^-6C) / (1.558*10^-11) = 2.56*10^17

Book's Answers: (a) 15.6 pF (b) 256 kV


I'm pretty sure I messed up somewhere with units and converting, as I'm not sure what units I ended up with, and these answers are much bigger than the book answers. I'm not sure where I went wrong though.
 
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Your answer and book's matches for (a). But for (b), there is some calculation error. The working is all right, though.
 
Ah, I see. I put it back into my calculator and came up with the correct answer. 256739 which is equivalent to 256 kV I think.
 
Yep that's right.
 

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