Consider a charged, hollow metal sphere. Hovering inside at the center is a char

Question

Consider a charged, hollow metal sphere. Hovering inside at the center is a charged solid metal sphere. The image below is a cross section of this structure, where the dark parts are metal. The inner sphere has a total charge Q1 and the outer sphere has a total charge Q2.
a. Using Gauss’s law and your knowledge of conductors, find an expression for the electric field in terms of the distance from the center of the spheres, r, for each of the following locations:
i. inside the inner sphere
ii. between the two spheres
iii. inside the metal of the outer sphere, and
iv. outside the entire structure.
b. If the inner sphere has a total charge of +30 nC and a radius of 1.5 cm and the outer sphere has a total charge of +15 nC and a radius of 3.5 cm, what is the magnitude of the electric field at 2.5 cm from the center of the structure?

Explanation / Answer

here,

a)

1)

using Gauss law

flux = Qenclosed /e0

for inside inner surface

E * 4 * pi * r^2 = 0/e0

E = 0

2)

using Gauss law

flux = Qenclosed /e0

between the two spheres

E * 4 * pi * r^2 = Q1/e0

E = Q1/( 4 * pi* r^2 * e0 )

3)

the charge enclosed inside the metal of the outer sphere is zero

4)

using Gauss law

flux = Qenclosed /e0

between the two spheres

E * 4 * pi * r^2 = (Q1 + Q2)/e0

E = (Q1 + Q2) /( 4 * pi* r^2 * e0 )

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