Final answer:
The electric potential energy of a system of two like charges increases as they are moved apart, and decreases when a positive and negative charge are moved closer together. For the system described with two 2.00 µC charges and one -1.00 µC charge, as the negative charge's y-coordinate increases, the potential energy increases and vice versa. Therefore, the answer is increases, decreases.
Step-by-step explanation:
When two charged particles are moved apart, the electric potential energy of the system generally depends on the nature of the charges present. If they are like charges (both positive or both negative), moving them apart increases the potential energy because work has to be done against the electrical repulsion. If the moving charges have opposite signs (one positive and one negative), the potential energy decreases since work is done by the system as it tends toward a lower energy configuration; essentially, the charges do work on their surroundings as they move closer together.
Considering the specific system given, a system of two 2.00 µC charges and one -1.00 µC charge, when the -1.00 μC charge, initially at (0, 70 cm), is moved further away (increasing y-coordinate), the potential energy increases because the separation between the negative charge and each of the positive charges increases.
Conversely, when the negative charge moves closer (decreasing y-coordinate), the potential energy decreases, since the negative charge is attracted to the positive ones and less work is required to move it closer to them. Based on this, the correct answer to the question of what happens to the potential energy as the y-coordinate of the -1.00 μC charge increases or decreases is option b: increases, decreases.
Applying this to electrostatic force principals, when two positive charges are brought closer from a distance of 1 m to 0.5 m, the strength of the electrostatic force between them increases and hence the potential energy also increases due to the inverse relationship between potential energy and separation distance. However, if the charges are of opposite signs, the potential energy becomes more negative and hence decreases with decreasing separation.