Grounded spherical shell with uniform space charge. Suppose a hollow conducting sphere of radius a contains a uniform volume charge density p(r)= po in the region 0

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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Grounded spherical shell with uniform space charge. Suppose a hollow conducting sphere
of radius a contains a uniform volume charge density p(r)= po in
the region 0<r<a. The sphere is grounded such that Þ(a)=0 Volts.
Find the field and potential inside by a direct integration of Poisson's
equation. Once the potential is found, find the induced charge
density on the inner surface of the shell. Note: the r in this problem
is interpreted as the radial distance in spherical coordinates.
+
+
+
+
-p(r)
Transcribed Image Text:Grounded spherical shell with uniform space charge. Suppose a hollow conducting sphere of radius a contains a uniform volume charge density p(r)= po in the region 0<r<a. The sphere is grounded such that Þ(a)=0 Volts. Find the field and potential inside by a direct integration of Poisson's equation. Once the potential is found, find the induced charge density on the inner surface of the shell. Note: the r in this problem is interpreted as the radial distance in spherical coordinates. + + + + -p(r)
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