Two co-axial conducting cylinders of same length 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 =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 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 ( 0 is the permittivity of free space): [figure]
- Q30 0
- Q15 0
- Q60 0
- Q120 0
Answer
(3) Q60 0
Solution
Field exists only in the dielectric ( 2R<r<2R): E= Q2 0 r, radial (zero inside the inner conductor and outside the grounded outer one).
For a radial field from a line, flux through a strip = Q 0 2 , where is the angle the strip subtends at the axis.
Plane at distance R: it meets r= 2R at = 1 2 ( =45 ) and r=2R at = 12 ( =60 ).
Part inside the dielectric subtends 2 15 =30 = 6 in all.
= Q5 0 112= Q60 0
Answer: (C)