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How to find energy stored between two spheres?

  1. Sep 23, 2011 #1
    1. The problem statement, all variables and given/known data
    A spherical conductor of radius 7.00 mm carries a surface charge density of 9.00 μC/mm2. A second hollow, concentric, spherical conductor has an inner radius of 7.09 mm. How much stored energy is there between the spheres?


    2. Relevant equations
    C=Q/V
    A=4pi(r^2)
    C=4(pi)(Epsilon_0)((R_a*R_b)/(R_a-R_b))
    surface charge density = Q/A
    U=.5*Q^2/C=.5*C*V^2=.5QV


    3. The attempt at a solution
    I keep getting 2.5o4e^-4 kJ but it isnt one of the answer choices. There is a 250 kJ, but that makes me off by a factor of 1 million...
    Here are the answer choices:
    A) 16kJ B) 1000kJ C) 6.4kJ D) 250kJ
    Thank you very much!
     
  2. jcsd
  3. Sep 23, 2011 #2
    Your charge density is in charge/mm^2 and the dimensions of the sphere are in mm. Do you have Epsilon_0 in the right units or did you convert mm above to m?
     
  4. Sep 23, 2011 #3
    Yes, I did convert everything to standard units.
    R_a=.00709m
    R_b=.007m
    σ=.009 coulombs/m^2

    C=Q/V_ba=4(pi)(Epsilon_0)((R_a*R_b)/R_a-R_b))=6.1327e-11F

    Surface area of inner sphere =4(pi)(.007^2)=6.1575e-4m2
    σ=Q/A so Q=5.5418e-6

    U=.5(Q^2/C)=.5((5.5418e-6)^2)/6.1327e-11)=2.504e-4 kJ
    in kJ because that's what the answer choices are in.
     
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