A conducting shell with inner radius a and outer radius b has a positive point c

Question

A conducting shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is -3Q, and it is insulated form its surroundings.

(a) Derive expressions for the electric-field magnitude in terms of the distance r from the center for the regions r<a, a<r<b, and r>b.

(b) What is the surface charge density on the inner surface of the conducting shell?

(c) What is the surface charge density on the outer surface of the conducting shell?

(d) Sketch the electric field lines and the location of all charges.

(e) Graph the elctric-field magnitude as a function of r.

Figure:

http://session.masteringphysics.com/problemAsset/1009107/7/yf_Figure_22_38.jpg

Explanation / Answer

a) r<a
now qenc = Q

so E = k Q/r^2

for a<r<b, you are inside conductor so E = 0

r> b qenc = -3q +q = -2q

so E = - 2kQ/r^2

b)

if E inside = 0, q enc = 0

so q inside = -Q

so density = -Q/(4 pi a^2)

c) this means q outside = -2Q

so density = -2Q/(4 pi b^2)

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