Before revision: Coaxial characteristic impedance derivation Taking the characteristic impedance at high frequencies, By definition and getting the electric field by the formula of electric field of an infinite line, where is charge per unit length, is the permittivity of free space, is the radial distance and is the unit vector in the direction away from the axis.
After revision:  where is charge per unit length, is the permittivity of free space, is the radial distance and is the unit vector in the direction away from the axis.