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Physics Question on Electric Field

  1. May 19, 2013 #1
    1. The problem statement, all variables and given/known data

    A solid conducting sphere of radius r1 has a total charge of +3Q. It is placed inside (and concentric with) a conducting spherical shell of inner radius r2 and outer radius r3. Find the electric field in these regions:
    r < r1
    r1 < r < r2
    r2 < r < r3
    r > r3

    2. Relevant equations

    E = F / q
    E = kq / R (for a point charge)

    3. The attempt at a solution

    Because it's a conductor, I know that the electric field for r < r1 should be 0 (I also forgot the reasoning for this. I think it's because the charges are moving and somehow they cancel each other out?)

    I'm confused on the other parts, though. For r1 < r < r2, I said that the electric field is 3kQ/r because the electric field from the sphere could be felt from that point. For r2 < r < r3, I said that the electric field was 0 for the same reasoning as r < r1, and I'm not even sure if that makes sense. Finally, for r > r3, I said it was 3kQ / r.
     
  2. jcsd
  3. May 19, 2013 #2

    Doc Al

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    Staff: Mentor

    Careful. That formula is not quite right.

    Except for that, your answers are fine. For electrostatic equilibrium, the field inside a conductor must be zero, otherwise charges would move until they canceled the field.
     
  4. May 19, 2013 #3
    Oops, that should be R2 haha. So my answers were correct then?

    And also, if both the sphere and the shell were insulators, would the answers be the opposite? Like for r < r1, the answer would be 3kQ/(r12)?
     
  5. May 19, 2013 #4

    Doc Al

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    Staff: Mentor

    Yes, except as noted.

    Not exactly. If the sphere were a uniformly charged insulator, then the field at any point within the sphere (say at r = ra, where ra < r1) would only depend on the charge within the region 0 < r < ra.
     
  6. May 19, 2013 #5
    Are you sure that E = kq / R (for a point charge) is correct?
     
  7. May 19, 2013 #6
    So it would have to be 3kQ/(r2) then.
     
  8. May 19, 2013 #7

    Doc Al

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    Staff: Mentor

    No. 3Q is the total charge of the sphere. All you want is the charge within r.
     
  9. May 19, 2013 #8
    Since r is an arbitrary length that is less than r1, how would we determine what the charge would be?
     
  10. May 19, 2013 #9

    Doc Al

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    Staff: Mentor

    If the sphere were uniformly charged, then the charge would be proportional to the volume.
     
  11. May 19, 2013 #10

    CAF123

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    Gold Member

    To find the charge contained within a sphere with radius less than ##r_1##, you will need to use the volume charge density of the sphere, where ##dq = \rho dV##
     
  12. May 19, 2013 #11
    That makes sense. Thanks for the help everybody!
     
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