Lets find electric field of cylindrical conductor:
λ - charge per unit length
From Gauss Law, electric flux over coaxial cylindrical surface with length L and radius a < r < b:
Φ=E2πrL=ε0Lλ Therefore,
E=2πε0rλ
Voltage difference between two conducting cylinders:
V=∫abE(r)dr=∫ab2πε0rλdr=2πε0λlogab By definition, capacitance per unit length is
C=Vλ=logab2πε0
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