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Homework Help: Capacitors and Dielectrics

  1. Feb 11, 2004 #1
    I need some help with these problems:
    1) A parallel-plate vacuum capacitor has 7.36 J of energy stored in it. The separation between the plates is 3.64 mm. If the separation is decreased to 1.40 mm, what is the energy stored if the following events occur?
    a) the capacitor is disconnected from the potential source so the charge on the plates remains constant
    b) the capacitor remains connected to the potential source so the potential difference between the plates remains constant
    I have the equations U=.5CV^2=.5QV=(Q^2)/(2C)
    C=Epsilon_0(A)/d, V=Ed, u=.5Epsilon_0*E^2
    How do I apply them to this problem?

    2) A capacitor has parallel plates of area 20 square centimeters separated by 1.4 mm. The space between the plates is filled with polycarbonate (dielectric constant = 2.8, dielectric strength = 3*10^7)
    I correctly calculted the permittivity (2.479E-11) and maximum permissible voltage (42000). I need help finding the surface-charge density on each plate and the induced surface charge density on the surface of the dielectric. I really don't know where to start with this, so any help would be appreciated!

    Thanks for help with one or both questions,
  2. jcsd
  3. Feb 17, 2004 #2
    Energy of capacitor U = 1/2 CV^2. If voltage is constant and you bring the plates together, V stays put but C increases. So the energy increases.

    U = 1/2 Q^2/C. If u disconnect the power supply, Q stays put, but C increases. So U decreases. I think u can plug in and calculate the actual values.

    For the next problem, what voltage do u apply?
    I just take it as V volts.
    Ed = V
    E = Efree/k (Efree is the free charge and k is the dielectric constant)

    E = Efree - Einduced (Considering magnitudes only.. vectorially, they would add up).

    => Einduced = (1 - (1/k))Efree
    => sigma induced = (1-1/k) sigma free (sigma is surface charge density)

    Now u can calculate sigma free easily using C = Q/V and then dividing Q by surface area. Using that, calculate sigma induced.

    Hope it helped

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