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MightyMergz
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Homework Statement
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 \rho 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.
Homework Equations
current density J is defined as J \equiv \frac{I}{A}
current density related to the electric field: J = \sigma E
since \sigma = \frac{1}{\rho} therefore E = \rho J
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
J(r) = \frac{I}{2 \pi r^{2}}
and then E(r) = \frac{\rho I}{2 \pi r^{2}}
Thanks~
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