How is electric potential energy defined?

Electric potential energy is defined as the work done to move a charge within an electric field. When a charge is influenced by an electric field, work must be done either to move it against the field (where work is done on the charge) or by the field (which allows the charge to move freely within it). This work results in potential energy associated with the position of the charge in the electric field. The further you move a charge against the electric field, the more work is done, leading to an increase in electric potential energy. Similarly, if the charge moves in the direction of the electric field, it loses potential energy.

This concept is foundational in electrostatics and helps to explain the behavior of charges in electric fields, as well as the principles governing capacitors and battery operation. Understanding this definition is crucial for analyzing electric circuits and energy storage systems in physics.