Electric Potential Energy Formula Calculator

Electric Potential Energy Formula:

\[ PE = k \cdot \frac{q_1 \cdot q_2}{r} \]

Coulomb's Constant (k):

N m²/C²

Charge 1 (q₁):

Charge 2 (q₂):

Distance (r):

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 done to assemble the charges from an infinite distance apart to their current configuration.

2. How Does the Calculator Work?

The calculator uses the electric potential energy formula:

\[ PE = k \cdot \frac{q_1 \cdot q_2}{r} \]

Where:

\( PE \) — Electric potential energy (Joules)
\( k \) — Coulomb's constant (8.99 × 10⁹ N m²/C²)
\( q_1, q_2 \) — Electric charges (Coulombs)
\( r \) — Distance between charges (meters)

Explanation: The formula calculates the potential energy between two point charges. Like charges produce positive potential energy (repulsive), while opposite charges produce negative potential energy (attractive).

3. Importance of Electric Potential Energy

Details: Understanding electric potential energy is crucial for analyzing electrostatic systems, designing electrical circuits, studying atomic and molecular interactions, and developing various technologies from capacitors to particle accelerators.

4. Using the Calculator

Tips: Enter Coulomb's constant (typically 9e9), both charges in Coulombs, and the distance in meters. All values must be valid (k > 0, r > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the sign in the result?
A: Positive result indicates repulsive force between like charges, negative result indicates attractive force between opposite charges.

Q2: Can this formula be used for multiple charges?
A: For multiple charges, the total potential energy is the sum of potential energies for all pairs of charges.

Q3: What are typical units used in this calculation?
A: Standard SI units are used: Newtons (N), meters (m), Coulombs (C), and Joules (J).

Q4: How does distance affect electric potential energy?
A: Potential energy is inversely proportional to distance - it decreases as distance increases.

Q5: What is the relationship between potential energy and electric force?
A: Electric force is the negative gradient of potential energy (F = -dU/dr), meaning force points in the direction of decreasing potential energy.