Electrostatics

Two co-axial conducting cylinders of same length ℓ with radii √2R 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 κ=5. Consider an imaginary plane of the same length ℓ 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 ( ε0 is the permittivity of free space):