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The value of electric current on a sinking conductor

  1. May 15, 2016 #1
    1. The problem statement, all variables and given/known data
    A flat capacitor formed by two square plates of side 0.3 m which are 2 mm apart. Source keeps voltage 250 V on the plates. What current flows between the plates and the source if the condenser is immersing in kerosene at velocity of 5 mm / s? The relative permittivity of kerosene is 2.

    2. Relevant equations
    -

    3. The attempt at a solution
    Here is a pic
    7TQE70j.png


    I=Q/t

    Because of the fact that immersing cunductor can be understood as two parallel conductors the capacity of an immersed conductor (the depth x = v*t) is C =(ε0*(a-x)*a)/d + (ε0εr*a*x)/d

    My question is how do I compute the time in the x = v*t? And sorry for my english.
     
  2. jcsd
  3. May 15, 2016 #2

    vela

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    The simple answer is you don't. Just assume you know it and hope it cancels out in the end.
     
  4. May 15, 2016 #3
    But it doesn't cancel in the end because of the plus and minus in the equation
     
  5. May 15, 2016 #4

    vela

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    What equation? Remember your ultimate goal is to find the current.
     
  6. May 15, 2016 #5
    I think I get it now...

    I put the "v*t" instead the "x" in the equation for capacity, multiply it by the voltage (U) and then derivate it following I=dQ/dt

    Or am I wrong?

    Anyways thank you for your clear explanation, it helped me a lot
     
    Last edited: May 15, 2016
  7. May 15, 2016 #6

    vela

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    That's right. Or you could just leave it as ##x##, and when you differentiate with respect to time, you'll get ##v## in its place.
     
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