Two points charges are kept in air with a separation between them. The force between them is F₁ , if half of the space between the charges is filled with a dielectric constant 4 and the force between them is F₂ . If 1 3 rd of the space between the charges is filled with dielectric of dielectric constant 9. Then F₁ F₂ is

Step-by-step solution

When dielectric of thickness t is introduced in two charges at distance r , the effective force between the charges is given by F= q₁ q₂ 4 ₀[r-t+t K ]^2 where, K= dielectric constant of medium In first case, t=r / 2 and K=4 F₁= q₁ q₂ 4 ₀ [r-r / 2+ r 2 4 ]^2 = q₁ q₂ 4 ₀ 9 4 r^2 = q₁ q₂ 9 ₀ r^2 In second case, t=r / 3 and K=9 aligned & F₂=q₁ q₂ / 4 ₀ [r- r 3 + r 3 3 ]^2= q₁ q₂ 4 ₀ ( 25 9 ) r^2 & F₁ F₂ = q₁ q₂ 9 ₀ r^2 4 ₀ ( 25 9 ) r^2 q₁ q₂ = 100 81 aligned