Gauss's Law and nonconducting spherical shell

  • Thread starter Edasaur
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  • #1
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Homework Statement



A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere. Your answers should be in terms of ρ, R_1, R_2, r, ε_0, and π.

a) R_1 < r < R_2
b) r > R_2

Homework Equations


∫E dA = Q_enc/ε_0


The Attempt at a Solution



For a), I tried using Gauss's law to find it and I arrived at:

E = [ρ(R_1)^3]/[3(ε_0)(r^2)]

For b), I also used Gauss's law to find:

[ρ(R_1)^3 + ρ(R_2)^3]/[3(ε_0)(r^2)]


I'm not quite sure what I'm doing wrong...
 

Answers and Replies

  • #2
SammyS
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Homework Statement



A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere. Your answers should be in terms of ρ, R_1, R_2, r, ε_0, and π.

a) R_1 < r < R_2
b) r > R_2

Homework Equations


∫E dA = Q_enc/ε_0


The Attempt at a Solution



For a), I tried using Gauss's law to find it and I arrived at:

E = [ρ(R_1)^3]/[3(ε_0)(r^2)]

For b), I also used Gauss's law to find:

[ρ(R_1)^3 + ρ(R_2)^3]/[3(ε_0)(r^2)]

I'm not quite sure what I'm doing wrong...
It's difficult to say what you are doing wrong, without having you give more detail regarding your steps in arriving at those solutions.
 
  • #3
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A non-conducting spherical shell carries a non-uniform charge density ρ=ρ0r1/r. Determine the electric field in the regions:
A) 0<r<r1
B)r1<r<r0
C)r>r0

r1 is radius to inside of shell. r0 is radius to outside of shell.
 

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