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Two capacitive spheres separated by dielectric, ratio of radii for lowest electric fi

  1. Jul 17, 2012 #1
    1. The problem statement, all variables and given/known data

    It's desired to build a capacitor which has two concentric spheres separated by a dielectric of high permittivity, low loss, and high dielectric strength. Calculate the ratio of sphere b's radius to sphere a's radius which produces the lowest electric field between the spheres.

    Not sure how to start this one. Thank you for any help.
     
  2. jcsd
  3. Jul 18, 2012 #2

    CWatters

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  4. Jul 18, 2012 #3
    Re: Two capacitive spheres separated by dielectric, ratio of radii for lowest electri

    I do know, from Wikipedia, that concerning concentric spheres, Cap = 4 (pi) ε / ( (1 /a) - (1/b) )
     
  5. Jul 18, 2012 #4
    Re: Two capacitive spheres separated by dielectric, ratio of radii for lowest electri

    So what Ive done on this problem so far is
    C=[4pi(epsilon nought)][(ab)/(b-a)]
    and
    V=(Q/[4pi(epsilon nought)])(b-a)/(ab)
    and plug it in Q=CV
    i just get Q=Q

    Conceptually
    from E=kq/r^2 as the radius goes up the E field goes down
    so the ratio from B to a would approach infinity or
    A should be much less then A?
     
  6. Jul 18, 2012 #5

    CWatters

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    Re: Two capacitive spheres separated by dielectric, ratio of radii for lowest electri

    The electric field E = V/d where d is the distance between the plates.
     
  7. Jul 18, 2012 #6
    Re: Two capacitive spheres separated by dielectric, ratio of radii for lowest electri

    Alright, but you eventually get E = Q / (4 * pi * ε * a * b) ; so how would you get a ratio from that from b to a ?
     
  8. Jul 19, 2012 #7
    Re: Two capacitive spheres separated by dielectric, ratio of radii for lowest electri

    You failed me Physics Forums; here is the scanned answer from my professor's solution set given to us after the test; I hope that this will help someone else out there; Make of it what you will; his handwriting is kind of hard to read

    http://i633.photobucket.com/albums/uu57/Xinthose/scan0002.jpg

    http://i633.photobucket.com/albums/uu57/Xinthose/scan0003.jpg [Broken]

    or if you prefer to see it on the forum

    page 1
    scan0002.jpg
    page 2
    scan0003.jpg
     
    Last edited by a moderator: May 6, 2017
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