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[ElectroStatics]Question Regarding Charge within a Metal Sphere

  1. Dec 9, 2013 #1
    1. The problem statement, all variables and given/known data
    I have this question on a practice exam in preparation fora final exam, and I am questioning my solution here:

    A hollow spherical metal shell has an outer radius equal to 1.5 m and a
    shell thickness of 0.5 m. A +100 nC point charge is located in the hollow
    0.5 m from the centre. The metal has no net charge and is isolated from
    ground.

    a) Indicate with a clear drawing where charge density occurs on the
    surfaces or inside the metal. Indicate where the charge density is larger or
    smaller by using greater or lesser numbers of + or -
    signs.

    b) Determine the the electric field vector 2 m from the centre in the same
    direction as the charge.

    c) What is the total electric flux through a sphere 10 m in radius that
    encloses the metal sphere?

    2. Relevant equations

    flux=charge enclosed
    E=Q/(4*π*ε0*r^2)

    3. The attempt at a solution

    a)
    The outside of the inner cavity with the sphere will have a negative charge induced, with the density being greater at the portion closer to the point charge. I also said that since the net Electric field within the metal must be zero, the positive charge density on the outside must be uniform, as it is unaffected by the inner field. This is the part I am not sure of. I also concluded that the charge on the outside must be the same 100nC of the point charge inside, effectively making the sphere a mirror of the inner point charge.

    b)
    Assuming the logic in (a) was sound, I asserted that the electric field vector on the point 2m away from the centre must depend on the distance from the centre of the "point charge" sphere, which is 2m as stated. So using the formula I provided above (from a formula sheet we are provided) I computed the E field to be E=224.6888 N/C (or V/m) in the positive x direction.

    c)
    In our class, we define the flux to be equivalent to the charge enclosed. Which would clearly be 100nC.


    -----------

    Am I on the right track? Thank you very much in advance.

    EDIT: I attached a screenshot of the question.
     

    Attached Files:

    Last edited: Dec 9, 2013
  2. jcsd
  3. Dec 10, 2013 #2

    Simon Bridge

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    Well done. See the following p74
    http://ecee.colorado.edu/~ecen3400/Chapter%206%20-%20Conductors%20in%20the%20Electrostatic%20Field.pdf [Broken]

    (a) is correct.

    (b) Anyone outside the shell sees an image of the point charge somewhat displaced from it's actual position - in this case the charge appears to be at the center of the sphere.

    (c) You'd draw a gaussian surface - and this is correct: net flux is proportional to the charge enclosed.
     
    Last edited by a moderator: May 6, 2017
  4. Dec 10, 2013 #3
    Alright thanks for the confirmation.
     
  5. Dec 10, 2013 #4

    Simon Bridge

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    (b) is related to optics ... if it were a glass sphere and the charge were an object, the object would appear, from outside, to be displaced from it's actual position. Not too surprising since light is a form of electromagnetism.

    Notice, in the link, though that he field lines inside the sphere are curved?
    The field lines at a conducting surface must be normal to that surface.

    So I only had very small notes for you.
     
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