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: 30

Answer

a) $1.5\times 10^{-10}\;\rm F$ b) $12\;\rm kV$

Work Step by Step

$$\color{blue}{\bf [a]}$$ 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. Plug the known; $$C= \dfrac{\kappa_{\rm Teflon} \epsilon_0 A}{d} =\dfrac{(2.1)(8.85\times 10^{-12})(0.04)^2}{(0.20\times 10^{-3})}$$ $$C=\color{red}{\bf 1.5\times 10^{-10}}\;\rm F$$ $$\color{blue}{\bf [b]}$$ The maximum potential difference between the plates is given by $$E_{\rm max}=\dfrac{(\Delta V)_{\rm max}}{d}$$ where $E_{\rm max}$ is the maximum possible electric field in the capacitor before breakdown for the Teflon. $$(\Delta V)_{\rm max}=E_{\rm max}d$$ Plug the known; $$(\Delta V)_{\rm max}=(60\times 10^6)(0.2\times 10^{-3})$$ $$(\Delta V)_{\rm max}=\color{red}{\bf 12}\;\rm kV$$
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