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Consider a non-perfect conductor of re- sistivity p and shaped like a slice of pineap- ple. Its inner radius is R1, its outer radius R2, and its thickness is h. Two perfectly conducting terminals are attached to it: one covers the entire in- Rz ner cylinder and the other covers the entire outer cylinder. The disk-shaped top and bottom of the slice are covered in perfectly isolating material. Determine the resistance, with the help of the following hints: 1. Work in cylindrical coordinates (z, r, ø), with the z-axis placed along the conduc- tor's central axis. 2. Assume that the electric potential V inside the non-perfect conductor depends on r only, and not on z and not on ø (this can be proven, but we don't do that here).

Consider a non-perfect conductor of re- sistivity p and shaped like a slice of pineap- ple. Its inner radius is R1, its outer radius R2, and its thickness is h. Two perfectly conducting terminals are attached to it: one covers the entire in- Rz ner cylinder and the other covers the entire outer cylinder. The disk-shaped top and bottom of the slice are covered in perfectly isolating material. Determine the resistance, with the help of the following hints: 1. Work in cylindrical coordinates (z, r, ø), with the z-axis placed along the conduc- tor's central axis. 2. Assume that the electric potential V inside the non-perfect conductor depends on r only, and not on z and not on ø (this can be proven, but we don't do that here).

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Consider a non-perfect conductor of re- sistivity p and shaped like a slice of pineap- ple. Its inner radius is R1, its outer radius R2, and its thickness is h. Two perfectly conducting terminals are attached to it: one covers the entire in- ner cylinder and the other covers the entire outer cylinder. The disk-shaped top and bottom of the Rg R2 slice are covered in perfectly isolating material. Determine the resistance, with the help of the following hints: 1. Work in cylindrical coordinates (z,r, ø), with the z-axis placed along the conduc- tor's central axis. 2. Assume that the electric potential V inside the non-perfect conductor depends on r only, and not on z and not on ø (this can be proven, but we don't do that here).
Transcribed Image Text:Consider a non-perfect conductor of re- sistivity p and shaped like a slice of pineap- ple. Its inner radius is R1, its outer radius R2, and its thickness is h. Two perfectly conducting terminals are attached to it: one covers the entire in- ner cylinder and the other covers the entire outer cylinder. The disk-shaped top and bottom of the Rg R2 slice are covered in perfectly isolating material. Determine the resistance, with the help of the following hints: 1. Work in cylindrical coordinates (z,r, ø), with the z-axis placed along the conduc- tor's central axis. 2. Assume that the electric potential V inside the non-perfect conductor depends on r only, and not on z and not on ø (this can be proven, but we don't do that here).
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