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Answer Check: Displacement Currents and Capacitors

  1. Nov 30, 2008 #1

    TFM

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    1. The problem statement, all variables and given/known data

    A fat wire, radius a, carries a constant current I, uniformly distributed over its cross section. A narrow gap in the wire, of width w << a, forms a parallel-plate capacitor, as shown in the figure above. Find the magnetic field in the gap, at a distance s < a from the axis.

    {Figure given below}

    2. Relevant equations

    [tex] displacement current, J_d = \epsilon_0 \frac{\partial E}{\partial t} [/tex] --- (1)

    [tex] \frac{\partial E}{\partial t} = \frac{1}{\epsilon_0 A}I [/tex] --- (2)

    [tex] B(r) = \frac{\mu_0 I}{2 \pi r} [/tex] --- (3)

    3. The attempt at a solution

    Okay so firstly, I have put together (1) and (2) to get:


    [tex] J_d = \epsilon_0 \frac{1}{\epsilon_0 A}I [/tex]

    I got this to cancel down into:

    [tex] J_d = \frac{I}{A} [/tex]

    I then made a very bold assumption that the current in B(r) = the displacement current J_d

    So I Inserted the values and got:

    [tex] B(r) = \frac{\mu_0 \left( \frac{I}{A}\right)}{2 \pi r} [/tex]

    This seems very quick and straight forwards, though...

    Does this look correct?

    TFM
     

    Attached Files:

  2. jcsd
  3. Dec 2, 2008 #2

    TFM

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    Does this look right?
     
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