Maximum potential (coaxial cable)

[weesiang_loke]

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.

 

[weesiang_loke]

Anyone pls help ...