A thick, conducting, spherical shell of inner radius a = 0.6 cm and outer radius

Question

A thick, conducting, spherical shell of inner radius a = 0.6 cm and outer radius b = 1.8 cm is uncharged. The shell surrounds a point charge +Q0 = 7.10mC at its center (see the figure).

1) What is the surface charge residing on the inner surface of the shell?

2) What charge resides on the outer surface?

3) What is the electric field in the region 0 < r< a, say r = 0.300 cm? ( V/m)

4) What is the electric field in the region a < r < b, say r= 1.20 cm?

5) What is the electric field in the region r > b, say r = 3.6 cm?

Explanation / Answer

inside conductor E = 0 so q enclosed = 0
(1)
so q inner surface = -Q = - 7.10 mC
(2)
so outersurface has Q = 7.10 mC

(3)
at r=0.300 q enclosed = 7.10

E = K*Q/r^2

E = (9*10^9*7.10*10^-3)/(0.30*10^-2)^2

= 7.1*10^12 V/m

(4)
in conducotr E = 0 so at r=1.15 cm E = 0

(5)
r>b q enclosed = 7.10*10^-3

so E = (9*10^9*7.10*10^-3)/(3.6*10^-2)^2

= 4.930*10^11 V/m

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