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Displacement and electric field

  1. Jan 7, 2014 #1
    1. The problem statement, all variables and given/known data

    displacement and electric field related by D=εE where dielectric constant depends on volume and temperature. Express dD in terms of dV, dT and dE

    (this is just a part of a question but want to make sure I have it right else the rest of the 'showing' and proofs are never going to work out)


    3. The attempt at a solution

    so taking D=εE

    Then dD = εdV (because it is volume dependent) + εdT (temperature dependent)

    what happens to the E, is it Edε + edE aswell as the above
    although it can't be dε because it says express in terms of dT dV and dE, no dε mentioned?

    is any of that on the right lines?

    any help appreciated
     
  2. jcsd
  3. Jan 7, 2014 #2

    haruspex

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    We can write that predicate statement as ε = ε(V, T).
    Based on that, you need to find an expression for dε in terms of dV and dT.
    What would be the change in ε if T stays constant and V increases by dV?
     
  4. Jan 7, 2014 #3

    rude man

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  5. Jan 7, 2014 #4
    as in like this?

    dε = (∂ε/∂V)dV + (∂ε/∂T)dT

    where does dD =
    come into this?
     
  6. Jan 7, 2014 #5
     
  7. Jan 7, 2014 #6
    come up with this

    dD = E∂ε + εdE

    where

    dε = (∂ε/∂V)dV + (∂ε/∂T)dT

    overall

    dD = E [(∂ε/∂V)dV + (∂ε/∂T)dT] + εdE

    is that what I should be getting?
     
  8. Jan 7, 2014 #7

    rude man

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    Excellent!
     
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