A coaxial cable contains an insulating material of conductivity σ .If the radius of the central wire is a and that of the sheet is b, then the conductance per unit length is
Consider the length of the coaxial cable as L
Let V0 be the potential difference between the inner and outer conductors so that,
V(ρ=a)=0
and V(ρ=b)=V0
→J=σ→E=−σV0ρlnba^ap
−→dS=−ρdϕdz^ap
I=∫→J.−→dS=∫2πΦ=0∫Lz=0V0σρlnbaρdϕdZ=2πLσV0lnba
Resistance per unit lengh , RL=V0I=ln(ba)2πσ
The conductance per unit length is,
G=1R=2πσln(ba)