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Request Assistance with Gauss's Law- Surface charge of sphere

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data
    a 240nC point charge is placed at the center of an uncharged spherical consucting shell 20cm in radius. A) What is the surface charge density on the outer surface of the shell? B) What is the electric field strength at the shell's outer surface?

    2. Relevant equations
    A) Charge Density=surface charge/surface area.
    B) E=q/(4*pi*E*r^2)

    I am unsure if surface charge is the same as the "E" calculated in Part 'B". If it isn't, how do I calculate Surface charge.

    3. The attempt at a solution
    A) 107330c/m^2 (Doesn't seem correct)
    B) results are 53950n/C

    Thank you.
  2. jcsd
  3. Feb 7, 2009 #2
    Surface charge is simply the collective charge on the surface of the sphere (meaning q). The electric field around the surface is E = surface charge density/permittivity of free space.
  4. Feb 7, 2009 #3


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    Because the spherical shell is conducting, in the steady state the electric field in the interior of the shell must be zero. That means that there will be a sufficient surface charge on the interior of the shell to cancel the point charge [lace in the center. Since the conducting shell is neutral, there will be an equal and (opposite sign) surface charge on the outside surface of the shell. The magnitude of these surface charges will have something to do with the magnitude of the charge at the center. If you think about it a bit, you'll also be able to quickly figure out the magnitude of the electric field at the outer surface of the conducting shell.
  5. Feb 8, 2009 #4
    Ahhhh!!!! Thank you. I appreciate the guidance in the correct direction.

    My cognitive friction is a result of taking one or two college classes at a time, hence, many classes that are taken during the same semester for full time students are spread out by a few years for me. I have to recall or re-study certain principles, rules and/or methods.

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