Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 29 - Potential and Field - Exercises and Problems - Page 863: 32

Answer

$8.94\times 10^{-11}\;\rm F$

Work Step by Step

We know that the capacitance of a parallel plate capacitor is given by $$C=\kappa C_0=\dfrac{\kappa \epsilon_0 A}{d} $$ where $\kappa$ is the dielectric constant. The area of the capacitor is the area of the cell surface, which is the area of a sphere's surface, A=$4\pi R_{\rm cell}^2$. $$C= \dfrac{ 4\pi \kappa_{\rm cell} \epsilon_0 R_{\rm cell}^2}{d} $$ Plug the known; $$C=\dfrac{4\pi(9)(8.85\times 10^{-12})(25\times 10^{-6})^2}{(7\times 10^{-9})}$$ $$C=\color{red}{\bf 8.94\times 10^{-11}}\;\rm F$$
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