Electric Potential Energy

Overview

Electric Potential Energy ($U_e$) is a scalar quantity representing the energy stored in a system of charges due to their positions relative to each other. It is a conservative form of energy, meaning the work done by the electric field depends only on the initial and final positions, not the path taken.

Mathematical Formula

For two point charges, $q_1$ and $q_2$, separated by a distance $r$, the energy is calculated using: [math]\displaystyle{ U_e = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r} }[/math]

Key Properties

• Units: Measured in Joules (J).
• Scalar Quantity: It has magnitude but no direction.
• Signage:
  • Positive ($+$) for like charges (energy is required to push them together).
  • Negative ($-$) for opposite charges (the system is naturally bound).
• Relationship to Work: The change in potential energy is the negative of the work done by the field: $\Delta U = -W_{field}$.

To Be Added

• [ ] Diagram showing the distance between two charges.
• [ ] Example calculation.
• [ ] Embedded PhET simulation for "Charges and Fields".