(adsbygoogle = window.adsbygoogle || []).push({}); 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]

Thanks~

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Current, Resistivity, and strange questions

**Physics Forums | Science Articles, Homework Help, Discussion**