In the figure a sphere, of radius a = 15.6 cm and charge q = 6.0010 -6 C uniform

Question

In the figure a sphere, of radius a = 15.6 cm  and charge  q = 6.0010-6 C uniformly distributed throughout its volume, is concentric with a spherical conducting shell of inner radius b = 29.6 cm  and outer radius c = 31.6 cm .  This shell has a net charge of -q.

1. Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r < a). Evaluate for r = 7.8 cm.

2. 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=22.6 cm.

3. Find expressions for the electric field, as a function of the radius r,  inside the shell (b < r < c). Evaluate for r =   30.6 cm.

4. Find expressions for the electric field, as a function of the radius r, outside the shell (r > c). Evaluate for r = 32.6 cm

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

In the figure a sphere, of radius a = 15.6 cm and charge q = 6.00 times 10-6 C uniformly distributed throughout its volume, is concentric with a spherical conducting shell of inner radius b = 29.6 cm and outer radius c = 31.6 cm. This shell has a net charge of -q. Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r

Explanation / Answer

a)

Qnet = ((4/3)*r^3/((4/3)a^3))q = q (r/a)^3

E = Qnet/A = q (r/a)^3/(4r^2) = q r/(4a^3)

E(r=7.8cm) = 6*10^-6*0.078*9*10^9/(0.156^3) = 1.11*10^6 N/C

b)

E = q/(4r^2)

E(21.1 cm) = 6*10^-6*9*10^9/(0.211^2) = 1.21*10^6 N/C

c)

E = 0 (everywhere)

E(27.5 cm) = 0.

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