# Current, Resistivity, and strange questions

1. Nov 14, 2007

### MightyMergz

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 $$\rho$$ 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.

2. Relevant 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 $$E = \rho J$$

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
$$J(r) = \frac{I}{2 \pi r^{2}}$$
and then $$E(r) = \frac{\rho I}{2 \pi r^{2}}$$
Thanks~

Last edited: Nov 15, 2007
2. Nov 15, 2007

### Supernats

Are you giving the whole problem? What is b?

Edit: My mistake. Sorry.