Can You Resist The Donut?

You are given a disk of thickness hh with inner and outer radii r1r_1 and r2r_2, respectively. If the resistivity of the disk varies as ρ=ρ0secφ\rho = \rho_0 \left|\sec \varphi\right|, where φ\varphi is the polar angle, find the resistance between the points AA and BB.

Give your answer to 3 decimal places.

Details and Assumptions:

  • The inner and outer rims are metal rings with zero resistance.
  • Take r2r1=e27.389\dfrac {r_2}{r_1} = e^2 \approx 7.389, ρ0=10 Ωm\rho_0 = \SI{10}{\ohm \meter}, and h=3 cmh= \SI{3}{\centi \meter}.

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