Can You Resist The Donut?

You are given a disk of thickness \(h\) with inner and outer radii \(r_1\) and \(r_2\), respectively. If the resistivity of the disk varies as \(\rho = \rho_0 \left|\sec \varphi\right|\), where \(\varphi\) is the polar angle, find the resistance between the points \(A\) and \(B\).

Give your answer to 3 decimal places.

Details and Assumptions:

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

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