Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 23 - Gauss' Law - Questions - Page 678: 4b

Answer

We can rank the magnitudes of the electric fields on the surfaces: $a \gt b \gt c \gt d$ The electric field is uniform on Gaussian surfaces $a$ and $c$ The electric field is variable on Gaussian surfaces $b$ and $d$

Work Step by Step

We can write an expression for the electric field due to the enclosed charge $+q$: $E = \frac{1}{4\pi~\epsilon_0}~\frac{q}{r^2}$, where $r$ is the distance from the charge Therefore, the magnitude of the electric field will be greater on Gaussian surfaces that are closer to the charge. We can rank the magnitudes of the electric fields on the surfaces: $a \gt b \gt c \gt d$ Each point on a sphere is the same distance from the charge $+q$, so the electric field is uniform on Gaussian surfaces $a$ and $c$ The points on a cube are not the same distance from the charge $+q$, so the electric field is variable on Gaussian surfaces $b$ and $d$
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