Capacitance Problem; somewhat solved, but units are off

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The discussion revolves around calculating the capacitance of an air-filled spherical capacitor with specified inner and outer shell radii. The capacitance was calculated using the formula C = ab / Ke(b-a), yielding a result of approximately 15.6 pF, which matches the book's answer. For the potential difference resulting in a charge of 4.00 microC, the initial calculation produced an incorrect value, but upon re-evaluation, the correct potential difference of 256 kV was confirmed. The main issue identified was a unit conversion error in the initial calculations. The final results align with the textbook answers after correcting the calculations.
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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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