S1  and  S2 are two hollow concentric spheres with charge q and 2q. Space between  S1  and  S2 is filled with a dielectric of dielectric constant K =5. The ratio of flux through S2 and flux through  S1 is K'.  Then find the value of   9K' 11.

With air in the space, between  S1 and  S2.  ϕS1=qε0  and  ϕS2=2qε0When a medium of K = 5 is filled in space ϕ S1'=QKε0=ϕS15=q5ε0And in this case, flux through S2 ϕ S2'=flux  of  S1+flux  of  charge  2q=q5ε0+2qε0=q+10q5ε0=11q5ε0So, ratio ϕS1'ϕS2'=11=K'So, 9K'11=9