# Maximum potential (coaxial cable)

by weesiang_loke
Tags: cable, coaxial, maximum, potential
 P: 33 1. The problem statement, all variables and given/known data 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. 2. Relevant equations gauss law, ... 3. 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.