Calculator inputs
Choose a model, enter values, then submit to see the potential above.
Formulas used
- k = 1/(4π ε0 εr), with ε0 ≈ 8.8541878128×10⁻¹² F/m.
- Point charge: V = k·q / r.
- Multiple charges: V = Σ(k·qi / ri).
- Ring on axis: V = k·Q / √(R² + x²).
- Uniform sphere (r ≥ R): V = k·Q / r.
- Uniform sphere (r < R): V = k·Q·(3R² − r²)/(2R³).
- Dipole on axis: V(x) = k·q·(1/|x − d/2| − 1/|x + d/2|).
- These models reference zero potential at infinity.
How to use this calculator
- Select a model that matches your geometry.
- Pick charge and length units that match your inputs.
- Set εr to match your medium, then enter values.
- For multiple charges, add rows and fill q, x, y, z.
- Press Submit to view the result above the form.
- Use the download buttons to export CSV or PDF.
Example data table
Sample inputs and outputs for quick validation.
| Example | Model | Inputs (units shown) | Expected behavior |
|---|---|---|---|
| #1 | Point Charge | q = 2 µC, r = 10 cm, εr = 1 | Positive potential, decreases as r increases. |
| #2 | Multiple Charges | q = +1 µC at (-5,0,0) cm and -1 µC at (5,0,0) cm, P=(0,0,0) cm | Contributions cancel by symmetry, near zero potential. |
| #3 | Ring on Axis | Q = 5 µC, R = 7 cm, x = 4 cm, εr = 1 | Finite potential, smooth along the axis. |
| #4 | Uniform Sphere | Q = 3 µC, R = 6 cm, r = 3 cm | Inside potential is finite and varies with r². |
FAQs
It is the electric potential energy per unit charge at a point. This tool computes V relative to infinity for idealized charge distributions.
Materials reduce electric interactions. Using εr adjusts the Coulomb constant, scaling the computed potential to match your medium.
The math is exact for the chosen ideal models. Real-world accuracy depends on how closely your setup matches the geometry and assumptions.
For point charges, the model becomes singular at r = 0. The calculator blocks zero-distance cases to avoid infinite values.
Yes. Use the multiple point charges model, add rows, and enter positions and charges. The tool sums each contribution at your field point.
Use any units provided in the menus. The calculator converts everything to SI internally, then reports potential in volts.
The distances to each charge must be positive. Absolute values ensure the denominator is the magnitude of separation from each charge.
After a successful calculation, the export buttons download your latest result. Run a new calculation to refresh what gets exported.