Suppose the nonconducting sphere of Example 22-4 has a spherical cavity of radiu

Question

Suppose the nonconducting sphere of Example 22-4 has a spherical cavity of radius r1 centered at the sphere's center (see the figure). Assuming the charge Q is distributed uniformly in the "shell" (between r = r1 and r = r0), determine the electric field as a function of r for the following conditions. (Use r0 for r0, r1 for r1, epsilon_0 for ?0, r, and Q, as necessary.)

Suppose the nonconducting sphere of Example 22-4 has a spherical cavity of radius r1 centered at the sphere's center (see the figure). Assuming the charge Q is distributed uniformly in the "shell" (between r = r1 and r = r0), determine the electric field as a function of r for the following conditions. (Use r0 for r0, r1 for r1, epsilon_0 for ?0, r, and Q, as necessary.) (a) 0

Explanation / Answer

a)

E = 0

b)

q = Q (4/3 pi (r^3 - r1^3))/(4/3 pi (r0^3 - r1^3))

==> q = Q (r^3 - r1^3)/(r0^3 - r1^3)

E = q/(4 pi epsilon_0 r^2)

E = (Q (r^3 - r1^3)/(r0^3 - r1^3))/(4 pi epsilon_0 r^2)

E = (Q (r^3 - r1^3))/(4 pi epsilon_0 (r0^3 - r1^3) r^2)

c)

E = Q/(4 pi epsilon_0 r^2)

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