Calculate The Electric Potential Energy Of The System Of Three Charges

Electric Potential Energy Equation:

\[ PE = \frac{k \cdot q_1 \cdot q_2}{r_{12}} + \frac{k \cdot q_1 \cdot q_3}{r_{13}} + \frac{k \cdot q_2 \cdot q_3}{r_{23}} \]

Charge 1 (q1):

Charge 2 (q2):

Charge 3 (q3):

Distance between q1 and q2 (r12):

Distance between q1 and q3 (r13):

Distance between q2 and q3 (r23):

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 infinity to their current positions.

2. How Does the Calculator Work?

The calculator uses the electric potential energy equation for three charges:

\[ PE = \frac{k \cdot q_1 \cdot q_2}{r_{12}} + \frac{k \cdot q_1 \cdot q_3}{r_{13}} + \frac{k \cdot q_2 \cdot q_3}{r_{23}} \]

Where:

\( PE \) — Electric potential energy (J)
\( k \) — Coulomb's constant (8.99 × 10⁹ N·m²/C²)
\( q_1, q_2, q_3 \) — Electric charges (C)
\( r_{12}, r_{13}, r_{23} \) — Distances between charges (m)

Explanation: The equation calculates the total potential energy by summing the pairwise interactions between all three charges.

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 all three charges in coulombs (C) and the distances between each pair of charges in meters (m). All distance values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is Coulomb's constant?
A: Coulomb's constant (k = 8.99 × 10⁹ N·m²/C²) is the proportionality constant in Coulomb's law that relates the electrostatic force between two charges to their magnitudes and distance.

Q2: Can the potential energy be negative?
A: Yes, potential energy can be negative when the charges have opposite signs, indicating an attractive interaction between them.

Q3: What units should I use for the inputs?
A: Charges should be in coulombs (C) and distances in meters (m). The result will be in joules (J).

Q4: Does the equation work for both positive and negative charges?
A: Yes, the equation works for both positive and negative charges. The sign of each charge affects the overall potential energy calculation.

Q5: What if two charges are at the same position?
A: If any distance becomes zero, the potential energy becomes infinite, which is physically impossible. All distances must be greater than zero.