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(ba) 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)?
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(ba) 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)?
College Physics
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a-d
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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