College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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a-d

Problem 3
A capacitor is constructed using concentric conducting spheres. The inner sphere has radius a, the
outer sphere (a thin-walled shell) has radius b.
(a) Show that the capacitance is
ab
k(b-a)
when the space between the inner and outer spheres is empty. Start with our result from Gauss's
law for the field outside a spherical charge distribution - you do not have to re-derive that, but
please DO derive the potential difference between the spheres.
PHY 205 Homework 6. Due March 1, 2023
3
(b) What is the capacitance if a = 0.1 m and b = 0.103 m?
(c) What would the capacitance be if we filled the gap with Aluminum Oxide (and again, make
a = 0.1 m and b = 0.103)?
(d) Consider the limit when a and b are approximately equal (the shell wall is extremely thin.)
What happens to the capacitance, mathematically? What is a physics explanation for this?
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Transcribed Image Text:Problem 3 A capacitor is constructed using concentric conducting spheres. The inner sphere has radius a, the outer sphere (a thin-walled shell) has radius b. (a) Show that the capacitance is ab k(b-a) when the space between the inner and outer spheres is empty. Start with our result from Gauss's law for the field outside a spherical charge distribution - you do not have to re-derive that, but please DO derive the potential difference between the spheres. PHY 205 Homework 6. Due March 1, 2023 3 (b) What is the capacitance if a = 0.1 m and b = 0.103 m? (c) What would the capacitance be if we filled the gap with Aluminum Oxide (and again, make a = 0.1 m and b = 0.103)? (d) Consider the limit when a and b are approximately equal (the shell wall is extremely thin.) What happens to the capacitance, mathematically? What is a physics explanation for this?
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