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Find the dimension of capacitor given [phi]E and Id

  1. Mar 4, 2012 #1
    1. The problem statement, all variables and given/known data
    The electric field between two circular plates of a capacitor is changing at a rate of 1.5x10^6 V/m/s (ΦE). If displacement current at this instant is Id=0.80x10^-8A, find the dimensions of the plates.


    2. Relevant equations

    Id=ΔQ/Δt=εΔΦE/Δt
    Q=CV=(εA/d)(Ed)

    Q=εAE <-- need to solve for A but do not have E.

    3. The attempt at a solution

    Q=εΦE = (8.85x10^-12)(1.5x10^6)
    Q=1.33x10^-5

    Feel like I must be missing something, I've gone over this problem and relevant formulas for way too long and can't figure out how to determine A (area of the plates) from the information given. Would really appreciate a push in the right direction.
    Thanks
     
    Last edited: Mar 4, 2012
  2. jcsd
  3. Mar 4, 2012 #2

    gneill

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    Staff: Mentor

    What happens if you differentiate your formula Q = (εA/d)(Ed) with respect to time?
     
  4. Mar 4, 2012 #3
    Could you elaborate?

    I don't see how that helps to solve for A or E
     
  5. Mar 4, 2012 #4

    gneill

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    Staff: Mentor

    differentiate both sides w.r.t. time. (what varies on each side?). Does the result mesh with any other formula you've written?
     
  6. Mar 4, 2012 #5
    ΔQ/Δt = CV/Δt = εAE/Δt = Id


    Thanks for the reply, still not sure how to solve this. Even with respect to time I can't see how the formulas can be setup to find the plate dimensions (A) without having d, or E.
    :confused:
     
  7. Mar 4, 2012 #6

    gneill

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    Staff: Mentor

    So,

    ΔQ/Δt = εA ΔE/Δt by your differentiation

    and you're given:

    ΔQ/Δt = 0.80x10^-8A ; and ΔE/Δt = 1.5x10^6 V/m/s

    :rolleyes:
     
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