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.

1. Calculate $U_E$ for each pair of charges using the formula $U_{E} = k frac{q_1 q_2}{r}$. 2. Add all the individual potential energies together.

Identify all the charges in the system and their positions.

Determine the distance between each pair of charges.

Calculate the electric potential energy for each pair of charges using the formula $U_{E} = k frac{q_1 q_2}{r}$.

Sum the electric potential energies for all pairs to find the total electric potential energy of the system.

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