Two point charges placed in air separated by distance R exert a force F on each other. Now the space between those charges is filled with dielectric constant K . At distance R₁ between the charges, the same force is exerted as F . Then

Step-by-step solution

Force between two point charges in air separated by distance R is given by: F = 1 4 ₀ q₁ q₂ R^2 When the space is filled with a dielectric of constant K , the force at distance R₁ is: F' = 1 4 ₀ K q₁ q₂ R₁^2 Given that the force remains the same, F = F' : 1 4 ₀ q₁ q₂ R^2 = 1 4 ₀ K q₁ q₂ R₁^2 1 R^2 = 1 K R₁^2 R₁^2 = R^2 K R₁ = R K Answer: R₁ = R K