Two co-axial conducting cylinders of same length with radii 2 R and 2 R 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 =5 . Consider an imaginary plane of the same length at a distance R from the common axis of the cylinders. This plane is parallel to the axis of the cylin

Step-by-step solution

Here we are assuming that " " is very large just for the sake of symmetry. Outside cylinder will have zero electric field inside, so the flux generated on the plate will be due to inner cylinder only in sections AB and CD , as section be will be at that place where electric field is zero. flux through element will be aligned d & = E dS d & = 2 k dy ..... (1) aligned from figure we can say that aligned & = R r r = R & = y R y = R & dy = R ^2 ~d & ~d = 2 k R R ^2 ~d & ~d =2 k dq & ₀^ _ AB d =2 k _ / 4 ^ / 3 ~d & _ AB