(8c23p51) In the figure a sphere, of radius a = 10.0 cm and charge q = 9.00?10-6

Question

(8c23p51) In the figure a sphere, of radius a = 10.0 cm and charge q = 9.00?10-6 C uniformly distributed throughout its volume, is concentric with a spherical conducting shell of inner radius b = 28.0 cm and outer radius c = 30.0 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 < a). Evaluate for r = 5.0 cm.

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=19.0 cm.

Find expressions for the electric field, as a function of the radius r, inside the shell (b < r < c). Evaluate for r = 29.0 cm.

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

Explanation / Answer

Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r < a). Evaluate for r = 5.0 cm.

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=5cm) = 9e-6*0.05/(4*3.1416*8.85e-12*0.1*0.1*0.1) = 4.05e6 N/C

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=19.0 cm.

E = q/(4r^2)

E(19cm) = 9e-6/(4*3.1416*8.85e-12*0.19*0.19) = 2.24e6 N/C

Find expressions for the electric field, as a function of the radius r, inside the shell (b < r < c). Evaluate for r = 29.0 cm.

E = 0

E(29cm) = 0

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

Q = 0 C

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