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Current, Resistivity, and strange questions

  1. Nov 14, 2007 #1
    1. The problem statement, all variables and given/known data
    A sheet of aluminum is 1 um thick. A thick copper ring of radius b is placed on the film, and a (smaller) copper disk, of radius a, is placed on the film at the centre of the ring. The disk and ring are connected to the terminals of a battery, so that current I flows through the film from the ring to the disk. Derive, in terms of I, a, b, and the thickness t and resistivity [tex]\rho[/tex] of the film, expression for the current density and electric field in the film as functions of the distance r from the centre of the disk and ring. Evaluate the resistance between the disk and ring if b = 10 mm, a = 5mm, t = 1 um.

    2. Relevant equations
    current density J is defined as [tex]J \equiv \frac{I}{A}[/tex]
    current density related to the electric field: [tex]J = \sigma E[/tex]
    since [tex]\sigma = \frac{1}{\rho}[/tex] therefore [tex]E = \rho J[/tex]

    3. The attempt at a solution
    The further out away from the centre, the lower the current density will be, since there will be the same amount of charge flowing over a greater area.

    I'm can't think of a way that needs a, b, or thickness. I don't know how the copper is affecting the current, since current is given. All I can think of right now is
    [tex]J(r) = \frac{I}{2 \pi r^{2}}[/tex]
    and then [tex]E(r) = \frac{\rho I}{2 \pi r^{2}}[/tex]
    Last edited: Nov 15, 2007
  2. jcsd
  3. Nov 15, 2007 #2
    Are you giving the whole problem? What is b?

    Edit: My mistake. Sorry.
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