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Spheres, Plates, and Gauss' Law

  1. Feb 3, 2007 #1
    1. The problem statement, all variables and given/known data

    A sphere of radius 8.0 cm carries a uniform volume charge density rho = 500*10^-9 C/m^3. What is the electric field at r = 3.0 cm?

    a.36.0 N/C

    b.230 N/C

    c.140 N/C

    d.565 N/C

    e.450 N/C




    2. Relevant equations

    E = (k*Q*r)/(R^3), where R = sphere’s radius and r is distance inside sphere

    3. The attempt at a solution
    V = (4/3)*pi*(0.08 m)^3 = 0.00214 m^3
    Q = p*V = (500*10^-9 C/m^3)*(0.00214 m^3) = 1.07*10^-9 C

    E = (k*Q*r)/(R^3), where R = sphere’s radius and r is distance inside sphere

    E = (8.988*10^9)*(1.07*10^-9 C)/(0.03 m^2) = 564.7 N/C




    1. The problem statement, all variables and given/known data

    A large, flat conducting plate has a surface charge density sigma = 8.0*10^-9 C/m^2 on one of its surfaces. What is the magnitude of the electric field 10 µm from this plate?


    a.72 N/C

    b.0.23 kN/C

    c.0.90 kN/C

    d.90 MN/C

    e.9.0 1012 N/C



    2. Relevant equations

    electric flux = Integral[E*A] = Q_enclosed/epsilon_0

    3. The attempt at a solution

    E*A_plate = q/epsilon_0
    E*A_plate = (sigma*A_plate)/(epsilon_0)

    E = sigma/epsilon_0 = (8.0*10^-9 C/m^2)/(8.85*10^-12) = 904 N/C

    Thanks.
     
  2. jcsd
  3. Feb 3, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    This isn't really a question. Is it?
     
  4. Feb 3, 2007 #3

    Astronuc

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    Staff: Mentor

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