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Homework Help: Energy Density in the Electric Field of a Charged Sphere

  1. Oct 12, 2008 #1
    1. The problem statement, all variables and given/known data
    A charged isolated metal sphere of diameter 10cm has a potential of 8000V relative to V=0 at infinity. Calculate the energy density in the electric field near the surface of the sphere

    2. Relevant equations
    u=1/2[tex]\(epsilon x E^2)

    3. The attempt at a solution
    I have tried this like an example given in my book, which gives the q value, but since q=CV, cant i find C of the sphere, solve for q, put that into E, and subsequently solve for u? The answer in my book is .11 J/m^3, but when i use the above strategy, I get around .028. Could someone point me in the right direction?
  2. jcsd
  3. Oct 12, 2008 #2
    Express V in terms of q and r, then solve for q. It's a slightly roundabout way to calculate the energy density this way, but since you want to find q, this will work.
    Last edited: Oct 12, 2008
  4. Oct 13, 2008 #3
    I tried that using V=kq/r and put q into E=kq/r^2. I also got E using V=Ed and got about 80000 V/m or N/C both times. I still get around .028 J/m^3 for my answer when i put that into the density formula.
  5. Oct 13, 2008 #4
    Oh, you probably just confused diameter and radius.
  6. Oct 14, 2008 #5
    Thats exactly what i did wrong. I corrected and got .11J/m^3. thanks
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