`S_1` and `S_2` are two hollow concentric spheres enclosing charges `Q` and `2Q`, respectively, as shown in figure.
i. What is the ratio of the electric flux through `S_1` and `S_2`?
ii. How will the electric flux through sphere `S_1` change if a medium of dielectric constant 5 is introduced in the space inside `S_1` in place of air.
.

Explanation

i. Flux through `S_1` is
`phi_1 = Q/epsilon_1`
Flux through `S_2` is
`phi_2 = (Q+2Q)/epsilon_0 = (3Q)/epsilon_0`
Thus,
`phi_1/phi_2 = (Q//epsilon_0)/(3Q//epsilon_0) = 1/3 = 1:3`
ii. As `E_m = E/epsilon_r and epsilon_r = 5, so E_m = E/5`
`phi`_1` (changed flux through `S_1`)
`= oint vecE_m * vec(d) S = oint vecE * vec(d) S`
`=1/5 phi_1 (as oint vecE * vec(d) S = phi_1)`
`= Q/(5epsilon_0) (as phi_1 = Q/epsilon_0)` .