Introduction:
The electric force between two point charges is given by Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. When the charges are placed in a medium, the force between them can change due to the presence of the medium's relative permittivity.

Explanation:
To determine the distance at which the charges should be placed in a medium of relative permittivity k so that the force remains the same, we need to consider the effect of the medium on the electric force.

Step 1: Understanding Relative Permittivity (k):
The relative permittivity (k) of a medium is a measure of how easily it can be polarized by an electric field. It is defined as the ratio of the electric field in vacuum to the electric field in the medium. Mathematically, it is given by k = ε/ε0, where ε is the permittivity of the medium and ε0 is the permittivity of vacuum.

Step 2: Analyzing the Force Equation:
According to Coulomb's Law, the electric force (F) between two point charges (q1 and q2) separated by a distance (r) in air is given by the equation F = (k * q1 * q2) / r^2, where k is the electrostatic constant.

Step 3: Keeping the Force Constant:
To keep the force constant when the charges are placed in a medium, we need to adjust the distance between them. Let's assume the new distance in the medium is x.

Step 4: Equating the Forces:
To find the new distance (x), we equate the force in air (F) with the force in the medium. So, we have F = (k * q1 * q2) / r^2 = (k' * q1 * q2) / x^2, where k' is the relative permittivity of the medium.

Step 5: Solving for x:
By rearranging the equation, we get x = r * sqrt(k / k'). This equation tells us that the new distance (x) in the medium is equal to the initial distance (r) multiplied by the square root of the ratio of the relative permittivities (k / k').

Conclusion:
In conclusion, to keep the electric force between two point charges the same when placed in a medium of relative permittivity k, the charges should be separated by a distance x = r * sqrt(k / k'), where r is the initial distance in air. This equation allows us to calculate the new distance required in the medium to maintain the same force.