A proton has a positive charge. If two protons are brought near to one another, the potential energy of the system will

The correct option is Increase.

To understand why the potential energy increases, let us look at the behavior of electric charges and the work done on the system step-by-step:

1. Electrostatic Repulsion:
A proton carries a positive electric charge. According to the fundamental law of electrostatics, like charges repel each other. Therefore, when two protons are brought close together, they experience a repulsive electrostatic force that pushes them apart.

2. Work Done against the Repulsive Force:
To bring the two protons closer to each other, an external force must do work against this repulsive force. The work done by this external force is stored in the system as potential energy.

3. Mathematical Representation:
The electrostatic potential energy $U$ of two point charges $q_1$ and $q_2$ separated by a distance $r$ is given by Coulomb's potential energy formula:

$U=\frac{k·q_1·q_2}{r}$

where $k$ is Coulomb's constant. Since both protons have a positive charge, the product of their charges $q_1·q_2$ is positive. As the protons are brought nearer to one another, the separation distance $r$ decreases. As $r$ becomes smaller, the value of the fraction increases, which means the electrostatic potential energy $U$ of the system increases.