Positive $U_E$: Like charges, repulsive force. Negative $U_E$: Opposite charges, attractive force.

At distance 'r': $U_E = k frac{q_1 q_2}{r}$. At distance '2r': $U_E = k frac{q_1 q_2}{2r}$. Doubling the distance halves the potential energy.

Electric potential energy: Energy per system of charges. Electric potential (voltage): Electric potential energy per unit charge.

Two-charge system: Direct calculation using $U_{E} = k frac{q_1 q_2}{r}$. Multi-charge system: Superposition principle, summing $U_E$ for all pairs.

Scalar: Magnitude only. Vector: Magnitude and direction

Increases the electric potential energy of the system (positive $U_E$).

The electric potential energy becomes less negative (increases).

Stored energy is released (like a book falling).

The potential energy is halved.

The electric potential energy stored in the system increases.

Energy stored in a system of charges due to their positions and interactions.

k is Coulomb's constant ($8.99 imes 10^9 frac{\text{N} cdot \text{m}^2}{\text{C}^2}$).

Electric potential energy per unit charge. $V = U/q$

Electric potential energy (in Joules, J)

For more than two charges, you calculate the potential energy for every pair of charges and add them up.