Calculate The Electric Potential Energy Of The System Of Charges

Electric Potential Energy Formula:

\[ PE = \sum \frac{k \times q_i \times q_j}{r_{ij}} \]

Coulomb's Constant (k):

N·m²/C²

Charges (q₁, q₂, ...):

Distances (r₁₂, r₁₃, ...):

Electric Potential Energy (PE):

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1. What is Electric Potential Energy?

Electric potential energy is the energy stored in a system of charged particles due to their positions relative to each other. It represents the work that must be done to assemble the system of charges.

2. How Does the Calculator Work?

The calculator uses the electric potential energy formula:

\[ PE = \sum \frac{k \times q_i \times q_j}{r_{ij}} \]

Where:

\( PE \) — Electric potential energy (J)
\( k \) — Coulomb's constant (8.99 × 10⁹ N·m²/C²)
\( q_i, q_j \) — Electric charges (C)
\( r_{ij} \) — Distance between charges i and j (m)

Explanation: The formula calculates the total potential energy by summing the pairwise interactions between all charges in the system.

3. Importance of Electric Potential Energy Calculation

Details: Calculating electric potential energy is fundamental in electromagnetism, helping understand electrostatic systems, capacitor design, and molecular interactions in chemistry.

4. Using the Calculator

Tips: Enter Coulomb's constant, charges separated by commas, and distances between charge pairs separated by commas. For 3 charges, provide 3 distances (r₁₂, r₁₃, r₂₃).

5. Frequently Asked Questions (FAQ)

Q1: Why is the potential energy negative for opposite charges?
A: Opposite charges attract, so work is released when they come together, resulting in negative potential energy.

Q2: How does distance affect potential energy?
A: Potential energy is inversely proportional to distance - it decreases as charges move farther apart.

Q3: What is the reference point for zero potential energy?
A: Typically, potential energy is defined as zero when charges are infinitely far apart.

Q4: Can this calculator handle more than two charges?
A: Yes, the calculator can handle multiple charges by summing all pairwise interactions.

Q5: What are typical units used in these calculations?
A: Charges are in Coulombs (C), distances in meters (m), and energy in Joules (J).