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 28 - The Electric Potential - Exercises and Problems - Page 836: 61

Answer

a) $8.33\;\rm \mu C$ b) $3.32\;\rm MV/m$

Work Step by Step

$$\color{blue}{\bf [a]}$$ We know that the electric potential of a charged sphere on its surface is given by $$V =\dfrac{1}{4\pi \epsilon_0}\dfrac{Q}{R}$$ So $$Q=(4\pi \epsilon_0)RV$$ Plugging the known $$Q=\dfrac{(15\times 10^{-2})(500,000)}{9\times 10^9}$$ $$Q=\color{red}{\bf 8.33}\;\rm \mu C$$ $$\color{blue}{\bf [b]}$$ We know that the electric field strength outside a charged sphere is given by $$E=\dfrac{Q}{A\epsilon_0}=\dfrac{Q}{4\pi r^2\epsilon_0}$$ where just outside the surface of the sphere means when $r=R$, $$E=\dfrac{Q}{4\pi R^2\epsilon_0}$$ $$E=\dfrac{8.33\times 10^{-6}}{4\pi (0.15)^2((8.85\times 10^{-12})}$$ $$E=\color{red}{\bf 3.32\times 10^6}\;\rm V/m$$
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