University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 23 - Electric Potential - Problems - Exercises - Page 779: 23.36

Answer

(a) $E = 5.3 \times 10^{3} \mathrm{N} / \mathrm{C}$ (b) $V = 117 \mathrm{~V}$ (c) $E$ is the same while $V$ is doubled.

Work Step by Step

(a) The electric field between the two plates depends on the area of the plates and the charges on the plates in the form \begin{gather} E = \frac{Q}{A \epsilon_{o}}\\ E=\frac{\sigma}{ \epsilon_{o}}\\ E=\frac{47 \times 10^{-9}\mathrm{~C/m^2}}{8.85 \times 10^{-12}\,\text{F/m}}\\ \boxed{E =5.3 \times 10^{3} \mathrm{N} / \mathrm{C}} \end{gather} (b) The potential difference $V$ between the plates is related to the electric field by \begin{equation} V=Ed = (5.3 \times 10^{3} \mathrm{N} / \mathrm{C})(2.2 \times 10^{-2}\,\text{m})= \boxed{117 \mathrm{V}} \end{equation} (c) The electric field will be the $\textbf{same}$ as the surface charge density is the same. But the potential will be $\textbf{doubled}$ as it is directly proportional to the separated distance.
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