In the figure a sphere, of radius a = 11.4 cm and charge q = 6.00*10^-6 C unifor

Question

In the figure a sphere, of radius a = 11.4 cm and charge q = 6.00*10^-6 C uniformly distributed throughout its volume, is concentric with a spherical conducting shell of inner radius b = 23.9 cm and outer radius c = 25.9 cm . This shell has a net charge of -q.

a.Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r < a). Evaluate for r = 5.7 cm.

b.Find expressions for the electric field, as a function of the radius r, between the sphere and the shell (a < r < b). Evaluate for r=17.7 cm.

c.Find expressions for the electric field, as a function of the radius r, inside the shell (b < r < c). Evaluate for r = 24.9 cm.

d.Find expressions for the electric field, as a function of the radius r, outside the shell (r > c). Evaluate for r = 26.9 cm.

e.What is the charge on the outer surface of the shell?

Explanation / Answer

a) portion of q enclosed at .057 m = (.057 / .114)^3 * q
E = k (.057 / .114)^3 * q / .057^2 = k * .057 * q / .114^3
b) E = k * q / .177^2
c) No field exists within the shell otherwise a current would flow.
d) No field exists outside the shell because a Gaussian surface encloses no net charge.
e) No charge exists on the outer surface of the shell because the central charge q
induces a charge of -q on the inner surface of the shell.

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