To determine which action will increase the electric potential energy between the two negatively charged balloons, we need to consider that electric potential energy increases when like charges (which they are, since both are negatively charged) are brought closer together or when work is done against the repulsive force between them.
Let's evaluate the options:
A. Adding two inches to the length of both strings - This action would not increase the electric potential energy; it would rather allow the balloons to be separated further, which decreases the potential energy.
B. Separating the two balloons - This action increases the distance between them, which decreases the electric potential energy since like charges repel.
C. Bringing the two balloons closer together - This action brings the balloons closer, decreasing the distance between them, which causes an increase in the electric potential energy due to the repulsive force trying to push them apart.
D. Releasing both balloons into the air - This action doesn't inherently increase electric potential energy; they may drift apart or oscillate depending on the air currents, but their electric potential energy will not be specifically increased by just being released.
Based on the analysis, the action that will increase the electric potential energy between the two balloons is:
C. Bringing the two balloons closer together.