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Capacitor with radius finding the energy density

  1. Apr 25, 2008 #1
    A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 12.5 cm , and the outer sphere has radius 16.5 cm . A potential difference of 100 V is applied to the capacitor.



    What is the energy density at r = 12.6 cm , just outside the inner sphere?

    What is the energy density at r = 16.4 cm , just inside the outer sphere?

    Equations:
    U= 1/2 CV^2/Ad
    U= 1/2 Eo E^2
    C= EoA/d
    V= Ed

    C= 8.85*10^-12 *pi * .126^2/.04 =1.11*10^-11
    so next i solved for U, U= .5 *1.11*10^-11 *100^2/pi*.126^2*.04=2.78*10^-5 which is not correct, Help PLease!
     
  2. jcsd
  3. Apr 25, 2008 #2

    Astronuc

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    Staff: Mentor

  4. Apr 25, 2008 #3

    alphysicist

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    Homework Helper

    Hi sonrie,

    I believe you are using a wrong formula here. The expression

    [tex]
    C=\epsilon_0 \frac{A}{d}
    [/tex]

    applies to a parallel plate capacitor. The spherical capacitor has a different formula.

    The formula energy density = (1/2) CV^2/(Ad) is also normally used for the constant field of a parallel plate capacitor. The other one (energy density = (1/2) [itex]\epsilon_0[/itex] E^2) applies to any capacitor problem.

    (You might also find that the formula C=Q/V is helpful.)
     
  5. May 5, 2008 #4
    Thanks!
     
  6. Jul 18, 2009 #5
    How do I find E, which I need to find the energy density? Then what do I do?
     
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