Introduction:
In this problem, we have two charged particles labeled as M and m. Particle M has charge Q, while particle m has charge -q. These particles are placed in a uniform electric field and are released. After the release, the particles stay at a constant distance from each other. We need to determine this distance, denoted as L, neglecting the gravitational interaction between the particles.

Explanation:
To solve this problem, we need to consider the forces acting on the charged particles and find the equilibrium condition where the net force on each particle is zero.

1. Electric Force:
The electric force between two charged particles is given by Coulomb's Law:
F = k * |Q * q| / r^2
where F is the electric force, Q and q are the charges on the particles, r is the distance between them, and k is the electrostatic constant.

2. Net Force:
Since the particles stay at a constant distance from each other, the net force on each particle must be zero. Therefore, the electric forces acting on the particles must be equal in magnitude and opposite in direction.

3. Equation:
Using the above conditions, we can write the equation for the electric forces as:
k * |Q * q| / L^2 = k * |Q * q| / L^2
where L is the distance between the particles.

4. Simplification:
We can cancel out the common terms and simplify the equation to:
L^2 = L^2

5. Solution:
From the equation, we can see that the distance between the particles, L, is the same on both sides. Therefore, the distance between the particles remains constant, and we can't determine its value from the given information.

Conclusion:
In conclusion, the distance (L) between the charged particles (M, Q) and (m, -q) remains constant in a uniform electric field. However, without additional information, we cannot determine the exact value of this distance. This analysis is based on the assumption that the gravitational interaction between the particles is negligible.