Two point charges 4e and e each, at a separation r in air, exert force of magnitude F. They are immersed in a medium of dielectric constant 16. What should be the separation between the charges so that the force between them remains unchanged.

Explanation

To solve the problem, we need to find the new separation between the two point charges when they are immersed in a medium with a dielectric constant of 16, such that the force between them remains unchanged.

### Step-by-Step Solution:

1. **Identify the Initial Force**:
The initial force \( F \) between two point charges \( q_1 = 4e \) and \( q_2 = e \) separated by a distance \( r \) in air can be expressed using Coulomb's law:
\[
F = \frac{1}{4 \pi \epsilon_0} \cdot \frac{q_1 q_2}{r^2}
...