two-point charges placed at a distance 'r' in air exert a force 'F'. The distance at which they exert same force when placed in a certain medium (dielectric constant K) is :-

To find the distance at which the two-point charges exert the same force when placed in a certain medium with a dielectric constant K, we can use Coulomb's law and the concept of electric field.

1. Let's denote the charge of the first point charge as q1 and the charge of the second point charge as q2.
2. In air, the force between the charges is given by Coulomb's law: F = (1/4πε₀) * (q1 * q2) / r², where ε₀ is the permittivity of free space and r is the distance between the charges.
3. In the medium with dielectric constant K, the force between the charges is modified due to the presence of the medium. The force is given by F' = (1/4πε₀K) * (q1 * q2) / r'², where r' is the new distance between the charges in the medium.
4. Since we want to find the distance at which the forces are the same, we can equate F and F': F = F'.
5. Substituting the expressions for F and F', we get (1/4πε₀) * (q1 * q2) / r² = (1/4πε₀K) * (q1 * q2) / r'².
6. Simplifying the equation, we find that r'² = K * r².
7. Taking the square root of both sides, we get r' = √(K * r²).
8. Therefore, the distance at which the two-point charges exert the same force in the medium with dielectric constant K is r' = √(K * r²).

In conclusion, the distance at which the two-point charges exert the same force when placed in a certain medium with a dielectric constant K is given by r' = √(K * r²).