A long cylindrical capacitor of length \(L\) consists of a solid inner conducting cylinder of radius \(a\) and a concentric outer conducting cylindrical shell of inner radius \(c\) and outer radius \(d\). The space between the conductors is filled with two concentric layers of dielectric material. Layer 1 fills the region \(a < r < b\) and has a dielectric constant \(\kappa_1\). Layer 2 fills the region \(b < r < c\) and has a dielectric constant \(\kappa_2\). It is given that \(\kappa_1 > \kappa_2\). The total length \(L\) is much greater than \(d\). The inner cylinder has a net positive charge \(+Q\) and the outer shell has a net negative charge \(-Q\).