A conducting spherical shell with inner radius a and outer radius b has a positi

Question

A conducting spherical 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 from its surroundings (Figure 1) .

Part A

Derive the expression for the electric field magnitude in terms of the distance r from the center for the region r<a.

Express your answer in terms of some or all of the variables Q, a, b, and appropriate constants.

Part C

Derive the expression for the electric field magnitude in terms of the distance r from the center for the region a<r<b.

Express your answer in terms of some or all of the variables Q, a, b, and appropriate constants.

Part D

Derive the expression for the electric field magnitude in terms of the distance r from the center for the region r>b.

Express your answer in terms of some or all of the variables Q, a, b, and appropriate constants.

Part F

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

Express your answer in terms of some or all of the variables Q, a, b, and appropriate constants.

Part G

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

Express your answer in terms of some or all of the variables Q, a, b, and appropriate constants.

Explanation / Answer

Electric field = (1/4pi(epsilon0))*Qin/r^2

a) Qin = +Q

==> E = (1/4pi(epsilon0))*Q/r^2

c) Since the field inside the metal is Zero

==> E = 0

d) Qin = +Q-3Q = -2Q

==> E = -(1/4pi(epsilon0))*2Q/r^2

f) Charge in inner surface = -Q

==> Surface charge density = -Q/(4piR^2)

g) Charge in outer surface = -2Q

==> Surface charge density = -2Q/(4piR^2) = -Q/(2piR^2)

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