A thick-walled, non-conducting spherical shell has a positive uniform volume cha

Question

A thick-walled, non-conducting spherical shell has a positive uniform volume charge density p bounded by radii r1 and r2>r1. With V=0 at infinity, find the electric potential V and electric field E as a function of distance r from the center of the charge distribution.

a) Find the net charge of the shell. Put your answer in terms of p, r1, r2, and physical constants.

b) Determine the electric field for r<r1, r1<r<r2, and r>r2. Put your answer in terms of p, r1, r2, r, and physical constants.

c) Determine the electric potential for r>r2. Put your answer in terms of p, r1, r2, r, and physical constants. Let V=0 at infinity.

d) Determine the electric potential for r1<r<r2. Put your answer in terms of p, r1, r2, r, and physical constants. Let V=0 at infinity.

e) Determine the electric potential for r<r1. Put your answer in terms of p, r1, r2, r, and physical constants. Let V=0 at infinity.

Explanation / Answer

a) 4/3 pi p (r2^3-r1^3) b) 0, pr*.037*10^12, (9* 10^9* 4/3 pi p (r2^3-r1^3))/r^2 c) (9* 10^9* 4/3 pi p (r2^3-r1^3))/r d) p*.0188*10^12(3r2^2-r^2) e) (9* 10^9* 4/3 pi p (r2^3-r1^3))/r2

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