Question:
Two coaxial non-conducting cylinders of radius \(a\) and \(b\) are separated by a material of conductivity \(\sigma\) and a constant potential difference \(V\) is maintained between them by a battery. The current per unit length flowing from one cylinder to the other is:
Two coaxial non-conducting cylinders of radius \(a\) and \(b\) are separated by a material of conductivity \(\sigma\) and a constant potential difference \(V\) is maintained between them by a battery. The current per unit length flowing from one cylinder to the other is:
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For cylindrical symmetry, always use logarithmic potential variation.
Updated On: Mar 24, 2026
- \(\dfrac{4\pi\sigma V}{\ln(b/a)}\)
- \(\dfrac{4\pi\sigma V}{b+a}\)
- \(\dfrac{2\pi\sigma V}{\ln(b/a)}\)
- \(\dfrac{2\pi\sigma V}{b+a}\)
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The Correct Option is C
Solution and Explanation
Step 1: Electric field between coaxial cylinders: \[ E = \frac{V}{r\ln(b/a)} \]
Step 2: Current density: \[ J = \sigma E \]
Step 3: Current per unit length: \[ I = \int J\, dA = 2\pi r J \] \[ I = \frac{2\pi\sigma V}{\ln(b/a)} \]
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