# Maximum potential (coaxial cable)

1. ### weesiang_loke

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.

Last edited: Mar 23, 2011
2. ### weesiang_loke

33
Anyone pls help ......