Coulomb potential energy for two point charges separated by distance r is:
U = (k · q₁ · q₂) / (εᵣ · r)
- U is potential energy in joules (J).
- q₁ and q₂ are charges in coulombs (C).
- r is separation in meters (m).
- εᵣ models the medium (dimensionless).
- k is the Coulomb constant (N·m^2/C^2).
Sign matters: like charges yield positive U, unlike charges yield negative U.
- Enter q₁ and choose its unit.
- Enter q₂ and choose its unit.
- Enter the separation distance r and select its unit.
- Set εᵣ for the material between the charges.
- Pick a preferred output unit, then press Calculate.
- Use the export buttons to download CSV or PDF.
| # | q₁ (µC) | q₂ (µC) | r (cm) | εᵣ | U (J) | U (eV) |
|---|---|---|---|---|---|---|
| 1 | 2.0 | 3.0 | 10 | 1.0 | 0.539253 | 3.365e+18 |
| 2 | 5.0 | -2.0 | 15 | 2.5 | -0.239801 | -1.497e+18 |
| 3 | -1.5 | -4.0 | 8 | 1.0 | 0.842582 | 5.258e+18 |
Example values are illustrative for learning and validation.
1) What this calculation represents
Coulomb potential energy describes the stored electrostatic energy of two point charges separated by a distance. It is the work required to bring the charges from very far apart to a specific separation without changing their speed. The calculator evaluates this energy with unit handling and medium effects.
2) Interpreting the sign of energy
The sign of U is determined by the product q₁·q₂. Like charges make U positive, indicating repulsion and a higher-energy configuration. Unlike charges make U negative, meaning the system is bound and energy is released as they approach.
3) Distance sensitivity
Energy varies inversely with distance: U ∝ 1/r. Halving r doubles the magnitude of U. This strong dependence makes careful distance measurement important in laboratory setups, charged-particle problems, and sensor spacing analysis. The tool converts common length units to meters before computing.
4) Charge magnitude and scaling
Because U ∝ q₁·q₂, doubling either charge doubles the energy magnitude, and doubling both charges multiplies the magnitude by four. Small charges are often expressed in microcoulombs or nanocoulombs; the calculator converts these to coulombs internally for consistent physics.
5) Medium effects through relative permittivity
Real materials reduce electrostatic interaction by a factor of εᵣ. For many gases, εᵣ is close to 1. Common liquids and solids can be much larger. For quick reference: air ≈ 1.0006, water ≈ 80, glass often 4–10, and plastics commonly 2–4. Increasing εᵣ lowers the energy magnitude proportionally.
6) Units: joules and electronvolts
Joule (J) is the standard SI energy unit, useful for macroscopic work and lab reporting. Electronvolt (eV) is convenient for microscopic scales, where even tiny joule values correspond to large eV counts. The calculator displays both to support physics coursework and particle-level reasoning.
7) Typical data ranges and checks
For microcoulomb charges separated by centimeters in air, energies are often fractions of a joule. For nanocoulomb charges at millimeter spacing, values may be millijoules or microjoules. A quick check: if your inputs are large and r is very small, energy can grow rapidly, so confirm units before exporting.
8) Accuracy and limitations
The formula assumes point charges and electrostatic conditions. Extended objects, nearby conductors, strong polarization, and changing fields can alter the true energy. Use this tool as a clean baseline model, then refine with geometry or field methods when needed.
1) Why can the potential energy be negative?
Negative energy occurs for opposite charges. The system is bound, and energy would be released if the charges move closer from the chosen reference at infinity.
2) What value should I use for εᵣ?
Use εᵣ = 1 for vacuum and near‑air conditions. For materials, use a typical dielectric constant from references or datasheets. Higher εᵣ reduces the energy magnitude.
3) Does the calculator handle charge sign correctly?
Yes. Enter positive or negative charges. Like signs produce positive U, while opposite signs produce negative U, matching the physical interpretation of repulsive or attractive interactions.
4) When should I prefer eV instead of joules?
Use eV for microscopic or particle‑scale problems. Use joules for lab work, engineering estimates, or when combining energies with other SI quantities like watts or newtons.
5) What happens if I halve the distance?
The magnitude of U doubles because U varies as 1/r. Small distance changes can strongly affect the result, so ensure your distance unit selection is correct.
6) Can I use this for extended charged objects?
This tool assumes point charges. For spheres, rods, plates, or distributions, the correct energy may require integration or field methods. Use this result as an approximation when size is small versus distance.
7) What is included in CSV and PDF exports?
Exports include your raw inputs, the converted SI values, and energy results in multiple units. This helps document assumptions and supports reporting for coursework or lab notebooks.