Final answer:
Moving a negative charge closer to another negative charge increases the potential energy because work must be done against the repulsive force between the same types of charges.
Step-by-step explanation:
If we move a negative charge toward a second negative charge, the potential energy of the first charge increases. This occurs because both charges repel each other, and work must be done against the electric force to bring them closer together. Since negative charges repel, we have to do positive work on the system to overcome this repulsion. As a result, the energy of the system increases.
Considering the electrical potential energy, when the two charges are of the same sign, the potential energy is positive. This energy increases as the separation distance (r) between the two charges decreases, since potential energy is inversely proportional to the distance between the charges (1/r). Therefore, moving a negative charge closer to another negative charge increases the system's potential energy.