Potential Energy Calculator with Solution

Electric Potential Energy Formula:

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

Potential Energy (U):

1. What is Electric Potential Energy?

Definition: Electric potential energy is the energy stored in a system of charged particles due to their positions relative to each other.

Purpose: This calculator helps determine the potential energy between two point charges, which is fundamental in electromagnetism and electrical engineering.

2. How Does the Calculator Work?

The calculator uses Coulomb's Law formula:

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

Where:

\( U \) — 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 potential energy is directly proportional to the product of the charges and inversely proportional to the distance between them.

3. Importance of Potential Energy Calculation

Details: Understanding potential energy is crucial for designing electrical systems, analyzing atomic interactions, and solving problems in electrostatics.

4. Using the Calculator

Tips: Enter the two charges in Coulombs (can be positive or negative) and the distance between them in meters. Distance must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What does a negative potential energy mean?
A: Negative potential energy indicates an attractive force between opposite charges, while positive indicates repulsion between like charges.

Q2: What's the value of Coulomb's constant?
A: Coulomb's constant \( k \) is approximately 8.99 × 10⁹ N·m²/C² in a vacuum.

Q3: Does this work for point charges only?
A: Yes, this formula is accurate for point charges or spherically symmetric charge distributions.

Q4: How does distance affect potential energy?
A: Potential energy decreases as distance increases (inverse relationship). Doubling the distance halves the potential energy.

Q5: What are typical charge values?
A: Elementary charge is ~1.6×10⁻¹⁹ C. Macroscopic objects might have charges in microcoulombs (µC) to millicoulombs (mC).