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Question

# 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

A
ln(ba)2πσV0
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B
4πσln(ba)
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C
2πσln(ab)
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D
2πσln(ba)
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Solution

## The correct option is D 2πσln(ba)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)

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