Maximum potential (coaxial cable)

AI Thread Summary
The discussion focuses on proving that the maximum potential in a coaxial cable occurs when the inner conductor's radius a equals b/e, where b is the outer conductor's radius and e is the base of the natural logarithm. The user applies Gauss's Law to derive the electric field E between the conductors and calculates the potential difference V as a function of the radii. They express V in terms of the logarithm of the ratio of the outer to inner radius. The user seeks assistance in differentiating V with respect to a to find the maximum potential condition. Clarification on this differentiation process is requested to complete the proof.
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Homework Statement


Given a coaxial cable with outer conductor of radius b, and inner conductor of radius a. Prove that maximum potential is obtained when a = b /e, e is base of natural log.

Homework Equations


gauss law, ...

The Attempt at a Solution


By using Gauss Law,
for a < r < b,
i have E = 2*k*\lambda / r, where \lambda = Q/L

then the potential difference, V= \int E dr
V = 2*k*\lambda ln (b/a),

but i am not sure how to continue by differentiating V wrt a.
Help me pls...
Thank you.
 
Last edited:
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