Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 23 - The Electric Field - Exercises and Problems: 24

Answer

To create a spark, $2.7\times 10^{11}$ electrons must be transferred from one disk to the other.

Work Step by Step

We can use the expression for the electric field strength in a plate capacitor to find the required charge on each disk. $E = \frac{\sigma}{\epsilon_0}$ $E = \frac{Q}{A~\epsilon_0}$ $Q = E~A~\epsilon_0$ $Q = (3.0\times 10^6~N/C)(0.040~m)(0.040~m)(8.85\times 10^{-12}~C^2/N~m^2)$ $Q = 4.25\times 10^{-8}~C$ We can find the number of electrons which must be transferred. $N = \frac{4.25\times 10^{-8}~C}{1.6\times 10^{-19}~C}$ $N = 2.7\times 10^{11}~electrons$ To create a spark, $2.7\times 10^{11}$ electrons must be transferred from one disk to the other.
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