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Thick spherical shell Question.

  1. Sep 15, 2014 #1
    1. The problem statement, all variables and given/known data
    A thick spherical shell with inner radius R and outer radius S has a uniform charge density d.(A) What is the total charge on the shell? Express your answer in terms of R, S, d, and π. (B) Express the electric field as a function of distance from the center of the sphere r, R, S, d, and the permitivity of free space p for each of the following regions: 0<r<R , R<r<S, S<r


    2. Relevant equations
    E = kQ/r2

    V=(4/3)πr3


    3. The attempt at a solution
    (For part A)
    Since its a thick shell the volume would be V = (4/3)π(S^3 - R^3)

    and dV = Qenc => d=Q/V

    so

    d = 3Q/(4π(S^3 - R^3))

    (For part B)
    0<r<R
    the electric field will be 0 because the electric field can't close on itself

    R< r< S
    E=kQenc/r2 = (4πkρ(r^3 - R^3))/3r^2

    S<r
    E = kQ/r2 because the sphere can be treated as a point charge and the electric field is symmetric on a sphere

    Is this correct?
     
  2. jcsd
  3. Sep 15, 2014 #2

    nrqed

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    Everything looks good. But note that for part A they want Q. And for the other problems, you must give the answer in terms of ##d , R, S ##
     
  4. Sep 15, 2014 #3
    So for part A would it be Q = dv --> Q = d * (4/3)π(S^3 - R^3)

    And for other problems what does it mean to give the answer in terms of d,R,S
     
  5. Sep 15, 2014 #4

    nrqed

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    That's correct.

    What it means is that your answer must contain only those parameters (your answer cannot contain Q).
     
  6. Sep 15, 2014 #5
    what does it mean to give the answer in terms of d,R,S?
     
  7. Sep 15, 2014 #6

    collinsmark

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    Hello twinpair,

    Welcome to Physics Forums! :smile:

    That's not technically wrong, but it doesn't answer the question. You are already given the density, d. The problem statement is asking you to solve for the total charge, Q.

    Correct. :approve:

    That's the first introduction of ρ, the Greek letter "rho." Is that supposed to be d?

    You're supposed to answer in terms of r, R, S, d and p.

    Whatever the case, rather than fiddle with substitutions, I suggest starting over. Use Gauss' law.

    This part of the problem is very straightforward if you start with Gauss' law; that way it doesn't require any fancy-schmancy substitutions.

    That's also correct, but is using the wrong set of variables. You could make the substitution of [itex] k = \frac{1}{4 \pi p} [/itex], but as it turns out, the solution is actually easier to come by if you apply Gauss' law from start to finish, solving for E as the final step*. :wink:

    *[Edit: although you can leverage the total charge found in part A.]
     
    Last edited: Sep 15, 2014
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