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Homework Help: Spherical Capacitor half filled with dielectric.

  1. Mar 28, 2010 #1
    If anyone can help with this problem it would be greatly appreciated. I think I know what I'm doing, but am not sure of a couple things.
    An isolated spherical capacitor has charge +Q on its inner conductor of radius r1 and charge -Q on its outer conductor of radius r2. half of the volume between the two conductors is then filled with a liquid dielectric of constant K.
    a) find the capacitance of the capacitor.
    b) find the magnitude of (electric field) E in the volume between the two conductors as a function of the distance r from the center of the capacitor. give answers for both the upper and lower halves of this volume.
    c) find the surface density of free charge on the upper and lower halves of the inner and outer conductors.
    d) what is the surface density of bound charge on the inner and outer surfaces of the dielectric.

    So far I have attempted to calculate the capacitance using
    C = 4*pi*epsilon*(r1*r2/r2 - r1)
    for both the upper and lower halve of the sphere. This gives
    c(upper) = 4*pi*epsilon_0*(r1*r2/r2 - r1)
    c(lower) = 4*pi*k*(r1*r2/r2 - r1)
    However I am not sure how to combine these.

    for b) E_upper = Q/(4*pi*epsilon_0*r-sub-b^2)
    E_lower = Q/(4*pi*k*epsilon_0*r-sub-b^2)

    for c) D = epsilon_0*E
    and this can be used to find surface density of free charge, but not sure how exactly.

    for d) total charge density = Q/area
    Can I take free charge density from total charge density to get bound charge density?

    Thanks in advance for any help you can give.
  2. jcsd
  3. Mar 28, 2010 #2


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    The potential difference V between the two conductors is the same for both the top and bottom halves, so think of the two halves as being two capacitors in parallel.
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