A thick-walled spherical shell of charge Q and uniform charge density ρ is bounded by radii...
A thick-walled spherical shell of charge Q and uniform charge density ρ is bounded by radii r1 and r2 > r1. With V = 0 at infinity, find the electric potential V as a function of distance r from the center of the distribution, considering the three regions:
(a) r > r2
(b) r2 > r > r1
(c) r < r1
Finally, comment on whether these solutions agree with each other at r = r1 and r = r2.
Homework Answers
(a) r > r2
potential V = Q/(4πε0r) = kQ/r
= ρ (4/3 π) (r2^3 - r1^3))/(4πε0r)
V = (ρ/(3ε0r))[(r2)3- (r1)3]
(b) r2 > r > r1
potential V = Q/(4πε0r)
= (ρ/(4πε0r)) (4/3 π) (r3 - r13)
V = (ρ/(3ε0r))((r)3- (r1)3)
(c) r < r1
potential V = V(r1) = 0
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