Ohm's Law - coaxial conducting cylinder, find resistance and surface charge density

  • #1

Homework Statement


Consider two coaxial conducting cylinders with radii a and 3a and length L. The region a<r<2a is filled with a material of conductivity σ1, and the region 2a<r<3a has conductivity σ2. (Assume ε12o.) The inner cylinder is held at potential V0 and the outer cylinder at V=0, so there is a radial current I.
(a) Determine the resistance.
(b) Determine the surface charge density on the boundary at r=2a.


Homework Equations


V=IR, R=pL/A, R=V/I=L/σA


The Attempt at a Solution


How do I do this? This probably is a simple problem, but I am having a hard time visualizing the path to the answer. Please help. :-)
 

Answers and Replies

  • #2
gneill
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If you're given the conductivity of a material then you also have the resistivity. Imagine adding thin cylindrical shells one at a time and adding up the total resistance (i.e. there's an integration involved).

What's the resistance of a thin shell? You can calculate the surface area, you have its thickness (dr -- I did say thin!). Add 'em up!
 

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