Final answer:
The ratio of the electric flux through two concentric spheres with charges Q and 2Q is 1:1 according to Gauss's law, meaning the fluxes are equal regardless of their radii. The introduction of a medium with a dielectric constant K in the space inside the outer sphere does not change the electric flux through the inner sphere, as the charge it encloses remains unchanged.
Step-by-step explanation:
To find the ratio of the electric flux through sphere S1 and S2, we can use Gauss's law. This law states that the electric flux through a closed surface is proportional to the charge enclosed within that surface, Ø = Q/ε₀, where Q is the charge enclosed and ε₀ is the permittivity of free space. Considering that S1 encloses a charge Q and S2 encloses a charge 2Q, the ratio of the electric flux Ø₁ through S1 to the electric flux Ø₂ through S2 is simply Ø₁/Q : Ø₂/(2Q), which simplifies to 1:1, indicating that the electric fluxes are the same regardless of the radius of the spheres.
When a medium with a dielectric constant K is introduced inside S2, the electric field within the medium is reduced by a factor of K. However, since S1 is entirely within this medium, the reduced electric field does not affect the electric flux through S1 because the charge enclosed by S1 remains Q. Therefore, the electric flux through sphere S1 does not change due to the introduction of a medium with dielectric constant K inside S2.