Where:

• \( PE \) — Electric potential energy (joules)
• \( \varepsilon_0 \) — Vacuum permittivity (8.85 × 10⁻¹² F/m)
• \( q_i, q_j \) — Electric charges (coulombs)
• \( r_{ij} \) — Distance between charges i and j (meters)
• The sum is taken over all unique pairs of charges (i < j)

Explanation: The formula calculates the total work required to bring all charges from infinity to their current positions, considering all pairwise interactions.

3. Importance of Electric Potential Energy Calculation

Details: Calculating electric potential energy is essential for understanding electrostatic systems, designing electrical circuits, analyzing atomic and molecular structures, and solving problems in electrostatics and electromagnetism.

4. Using the Calculator

Tips: Enter the number of charges, then provide the values for each charge in coulombs and the distances between each pair of charges in meters. All values must be valid (distances > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of electric potential energy?
A: It represents the capacity of a system of charges to do work due to their configuration. Positive PE means work is needed to assemble the system, negative PE means energy is released.

Q2: How does distance affect electric potential energy?
A: PE is inversely proportional to distance between charges. As distance increases, PE decreases (becomes less positive or more negative).

Q3: What is the value of ε₀ (epsilon naught)?
A: ε₀ = 8.8541878128 × 10⁻¹² F/m, which is the electric constant or vacuum permittivity.

Q4: Can this calculator handle both positive and negative charges?
A: Yes, the calculator accepts both positive and negative charge values, and correctly calculates the resulting potential energy.

Q5: What are typical units for electric potential energy?
A: Electric potential energy is measured in joules (J), the same as other forms of energy.