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Charged concentric metal spheres

  1. Oct 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Two concentric metal spheres have radii R1 =10cm and R2=10.5cm. The inner sphere has a charge of Q=5 nC spread uniformly over its surface, and the outer sphere has charge −Q spread uniformly over its surface.

    Calculate the total energy stored in the electric field between the spheres. (Hint : the spheres can be treated as flat parallel slabs separated by 0.5cm)

    2. Relevant equations

    U = 0.5 x C x (V^2)
    =(Q x V)/2

    Energy Density=1/2 x epsilon_0 x E^2

    3. The attempt at a solution

    None, unless confused scribbles count. I know I can treat this as a parallel plate capacitor (from the hint), but that doesn't seem to help me.

    I've been looking though my textbooks for hours but I can't find a clear way to work this out. I tried using (Q x d) / (A x Permittivity of air) to work out the electric field strength (E), but I didn't know which area to use for A.

    If I can work out the energy density of the field, I can multiply it by the volume of the space between the spheres to find the energy stored, but again, I can't work out E.
     
    Last edited: Oct 26, 2009
  2. jcsd
  3. Oct 26, 2009 #2

    Andrew Mason

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    Homework Helper

    Use Gauss' law or Coulomb's law to calculate the field between the spheres:

    [tex]\int \vec{E}\cdot dA = \frac{q_{encl}}{\epsilon_0}[/tex]

    [tex]E = Q/4\pi \epsilon_0r^2[/tex]

    It is not quite, but approximately equal over the .5 cm distance between spheres.

    The potential difference between the spheres is V = Ed (in volts or joules/coulomb).

    Since potential difference is the energy in joules per coulomb of charge: U = QV

    AM
     
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