One system consists of two like charges (q₁ and q₂) separated by a distance r. A second system consists of two charges that are oppositely charged but that have the same magnitudes as q₁ and q₂, and they also separated by a distance r. Compare the electric potential energy of the two systems.

 

Electric potential energy exists only when we move a charge from infinity to a measurable distance. For both systems, that has not happened, so both systems have zero potential energy.

When two like charges are brought together at a distance r, they repel and move away from each other, having no electric potential energy. Conversely, two unlike charges brought together at a distance r would attract and move towards each other, gaining electric potential energy.

Two like charges at a distance r have negative potential energy, and conversely, two unlike charges at the same distance r have positive potential energy. The magnitude of potential energy is the same in both instances.

The electric potential energy is the same for both systems because energy is a scalar quantity and signs do not matter.

Two like charges at a distance r have positive potential energy, and conversely, two opposite charges at the same distance r have negative potential energy. The magnitude of potential energy is the same for both systems.

 

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