Two co-axial conducting cylinders of same length $$\ell$$ with radii $$\sqrt{2}R$$ and $$2R$$ are kept, as shown in Fig. 1. The charge on the inner cylinder is $$Q$$ and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant $$\kappa = 5$$. Consider an imaginary plane of the same length $$\ell$$ at a distance $$R$$ from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross-sectional view of this arrangement is shown in Fig. 2. Ignoring edge effects, the flux of the electric field through the plane is ($$\epsilon_0$$ is the permittivity of free space):