Final answer:
The system with the most positive potential energy is option (B) Three negative charges very close together, as like charges repel, and bringing them very close together requires the most work, resulting in the highest potential energy.
Step-by-step explanation:
According to the principles of electric potential energy, the system that would have the most positive potential energy would be the one that consists of like charges being forced to be close together. So, when deciding between options (A), (B), (C), (D), and (E), we need to determine which configuration requires the most work to be done in order to bring the charges into proximity.
The electrical potential energy is positive if the charges are the same type (either both positive or negative) and inversely proportional to the distance between them (1/r). Hence, bringing two like charges very close together requires significant positive work to overcome the repulsion between them, thereby increasing their potential energy. With this understanding, (A) Two positive charges very close together would indeed have a high potential energy, and (B) Three negative charges very close together would also have high potential energy because both scenarios involve like charges in close proximity.
However, (B) with three like charges would have more positive potential energy than (A) with only two, due to the additional repulsion from the third charge. On the contrary, (C) Two oppositely charged particles very close together would have negative potential energy because they attract each other. For (D) and (E), the potential energy would be lower as the charges are far apart, and the potential energy decreases with increasing distance.
Therefore, the correct answer is (B) Three negative charges very close together, as this configuration represents the most concentrated amount of like-charges within close proximity, resulting in the highest positive potential energy.