Introduction:
When considering the interaction between two parallel beams of positrons moving in the same direction, we need to analyze the properties of positrons and their charged nature. Positrons are the antiparticles of electrons, carrying a positive charge. The interaction between charged particles follows the laws of electromagnetism, specifically Coulomb's law, which governs the behavior of electric charges.

Positron Interaction:
When two parallel beams of positrons move in the same direction, their interaction can be described in terms of their electric charges. Since positrons carry a positive charge, they will repel other positrons due to the similar charge. This repulsion arises because like charges repel each other according to Coulomb's law.

Coulomb's Law:
Coulomb's law states that the force between two charged particles is directly proportional to the magnitude of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

F = k * (q1 * q2) / r^2

Where F is the force between the charges, q1 and q2 are the magnitudes of the charges, r is the distance between them, and k is the electrostatic constant.

Repulsion between Parallel Positron Beams:
Considering two parallel beams of positrons moving in the same direction, the positrons in each beam will have similar charges, resulting in repulsion between them. The repulsive force will tend to push the positrons away from each other, causing the beams to diverge.

Explanation:
- The positrons in the two parallel beams, being positively charged, will repel each other.
- This repulsion arises due to the interaction between the electric fields generated by the positrons.
- The electric fields extend around each positron and influence other charged particles in their vicinity.
- As the positrons in the beams move closer to each other, the repulsive force between them increases.
- This force creates a divergence in the beams, causing them to spread apart.
- The magnitude of the repulsive force depends on the charge of the positrons and the distance between them.
- As the distance between the beams increases, the force of repulsion decreases according to the inverse square law.
- Therefore, the parallel beams of positrons moving in the same direction will repel each other.

Conclusion:
Two parallel beams of positrons moving in the same direction will repel each other due to their positive charges. This repulsion arises from the interaction between the electric fields generated by the positrons. Coulomb's law governs the behavior of the repulsive force, which increases as the positrons get closer to each other and causes the beams to diverge.