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Wondering why my method of finding charge doesn't work?

  1. Oct 21, 2011 #1
    1. The problem statement, all variables and given/known data
    A parallel plate capacitor has a capacitance of C=5.00pF when there is air between the plates. The separation between the plates is 1.50mm. What is the maximum magnitude of charge Q that can be placed on each plate if the electric field in the region between the plates is not to exceed 3.00 x 10^4 V/m?


    2. Relevant equations
    Equations my professor used:
    Vmax=Emax*d
    Qmax=CVmax

    Equations I used:
    E=σ/ε

    3. The attempt at a solution
    So the way my professor solved which is probably the easiest way and the right way is first he solved for the maximum potential:
    Vmax=Emaxd
    = (3.00 x 10^4 V/m)(1.50 x 10^-3m)= 45V
    Then you can solve for the charge:
    Qmax=CVmax
    = (5pF)(45.0V)= 225pC

    So the way I did it was that since we have parallel plates, we know the electric field between them is E=σ/ε. So:
    3.00 x 10^4 V/m= σ/(8.85 x 10^-12 C^/Nm^2)
    σ=2.655 x 10^-7

    And since σ=Q/L
    Q=σL
    =(2.655 x 1-^-7)(1.50 x 10^-3 M)
    =3.98 x 10^-10 C A different answer than my professor.

    I know that my units are all messed up. But I just get confused because there are so many different ways to solve for the electric field..so shouldn't they all equal the same thing? Or is this different because it is a capacitor? Any help would be appreciated. Thanks!
     
  2. jcsd
  3. Oct 21, 2011 #2

    Doc Al

    User Avatar

    Staff: Mentor

    σ = Q/Area (not Q/L)

    You need to make use of the given capacitance to find the charge.
     
  4. Oct 21, 2011 #3
    ohhh ok I feel stupid now. So if we know the are then we could use this way. My professor however on a different problem used A=2∏r^2 for the area of the parallel capacitors. That doesn't really make sense to me since they are rectangles..
     
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