An insulating sphere of radius 2 cm and charge -4 ? C is surrounded by a spheric

Question

An insulating sphere of radius 2 cm and charge -4 ?C is surrounded by a spherical metallic shell of inner radius 4 cm and outer radius 6 cm. The outer shell has a net charge of 3 ?C . The insulating sphere has a uniform volume charge density

1. What is the electric field at 5 cm?

2. What is the electric field at 9.0 cm?

3. What is the electric field at 15.0 cm?

4. Pick ALL of the valid charge densities from the list below for the system described. Please be very careful about the wording of the choices that you choose and only pick descriptions that are appropriate.

Area charge density for the outer surface of the outer shell.

Linear charge density for the outer shell.

Linear charge density for the inner cylinder. Area charge density for the inner cylinder. Volume charge density for the inner cylinder. Linear charge density for the inner surface of the outer shell. Area charge density for the inner surface of the outer shell. Volume charge density for the outer shell. Linear charge density for the outer surface of the outer shell.

Area charge density for the outer surface of the outer shell.

Linear charge density for the outer shell.

Explanation / Answer

a)

here

From Gass´ Law we have

E * (4 * pie * r^2) = Qen / e0

E = Qen / (4 * pie * e0 * r^2)

for r= 5 cm

e0 = 8.854 * 10^-12

E = ( 4 * 10^-6) / (4 * pie * 8.854 * 10^-12 * ( 5 * 10^-2)^2) = 1.43 * 10^7 N/C

b)

for r = 9 cm

E = (3 * 10^-6 - 4 * 10^-6 ) / (4 * pie * 8.854 *10^-12 * ( 9 * 10^-2)^2) = - 1.109 * 10^6 N/C

c)

for r = 15cm

E = (3 * 10^-6 - 4 * 10^-6 ) / (4 * pie * 8.854 *10^-12 * ( 15 * 10^-2)^2) = -4 * 10^5 N/C

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