Problem $1$

Find the capacitance per unit length for a very long coaxial cable with the cross section shown in figure, where the inner conductor radius $\backslash (=$a $\backslash ),$ the outer conductor inner radius $\backslash (=$b $\backslash ),$ the dielectric between the two conductors is divided into two cylindrical layers with relative permittivity $\backslash (\backslash$varepsilon$\_\{$r $1\}\backslash )$ and $\backslash (\backslash$varepsilon$\_\{$r $2\}\backslash )$ and the boundary between the two layers is at radius $\backslash (=$c $\backslash )$