Example Data Table
| Case |
Grid Values |
dx |
dy |
Charge Unit |
Use |
| Dipole sheet |
0,0,0,0 / 0,1,-1,0 / 0,1,-1,0 / 0,0,0,0 |
1 m |
1 m |
µC/m² |
Checks positive and negative charge regions. |
| Single region |
0,0,0,0 / 0,2,2,0 / 0,0,0,0 / 0,0,0,0 |
0.5 m |
0.5 m |
µC/m² |
Reviews one charged patch. |
| Balanced pattern |
1,-1,1,-1 / -1,1,-1,1 / 1,-1,1,-1 / -1,1,-1,1 |
2 cm |
2 cm |
nC/m² |
Tests alternating surfaces. |
Formula Used
The calculator solves a discrete version of Poisson’s equation in two dimensions.
Poisson relation: ∇²φ = -ρ / ε
Spectral solution: φ̂(kx, ky) = ρ̂(kx, ky) / [ε(kx² + ky²)]
Wave numbers: kx = 2πnx / Lx and ky = 2πny / Ly
Permittivity: ε = ε0 × εr
Electric field: Ex = -∂φ/∂x and Ey = -∂φ/∂y
The zero frequency term is set to zero. Then the reference potential is added after the inverse transform.
How To Use This Calculator
- Enter the charge density grid. Keep every row the same length.
- Select the charge density unit used by the grid values.
- Enter dx and dy spacing between neighboring samples.
- Select the length unit for spacing values.
- Enter the relative permittivity of the medium.
- Set a reference voltage if you need an offset.
- Choose a report point by row and column.
- Press Calculate, or export CSV and PDF files.
Electric Potential From Grid Data
Electric potential mapping is useful when charge distribution is known on a regular grid. A direct spatial solution can become slow as the grid grows. This calculator uses a spectral method to estimate the potential from sampled charge density. It treats the grid as periodic, then solves Poisson’s equation in frequency space. That approach is fast for power of two grids and clear for design review.
Why Frequency Space Helps
In physical space, each cell interacts with many other cells. In frequency space, the Laplacian becomes a simple multiplier. Each Fourier mode has a wave number. The calculator divides each charge mode by permittivity and wave number squared. The zero frequency mode is set to zero. This removes the undefined absolute average level. You may add a reference potential after the inverse transform.
Electrical Design Uses
The tool helps compare shielding layers, plate charge patterns, sensor surfaces, and educational electrostatic models. It also reports electric field components from the calculated potential. These values are estimated with central differences. The maximum field is useful for checking stress points. The RMS field gives a compact view of the whole map. The stored energy estimate gives another helpful design metric.
Input Quality Matters
Good results need consistent units. Grid spacing should match the physical distance between samples. Charge density should use the selected unit. Relative permittivity should match the medium. A larger value lowers the voltage response. A smaller value raises it. Padding may reduce edge pressure, but it also changes the numerical domain. Keep notes about every assumption.
Reading The Result
The potential table shows voltage at each grid cell. Positive values indicate higher potential relative to the chosen reference. Negative values indicate lower potential. For periodic spectral solving, opposite edges are connected mathematically. This is important when interpreting borders. Use the example table first. Then replace it with measured or simulated charge data. Export CSV for spreadsheet checks. Export PDF for a quick report.
Best Practice
Start with small grids before large studies. Check symmetry against the charge pattern. Compare two spacing values when accuracy matters. Avoid mixing volume and surface density units. Document the reference voltage. Keep exported files with calculations for safe later verification.
FAQs
1. What does this calculator estimate?
It estimates electric potential from a two dimensional charge density grid. It also calculates electric field components, field magnitude, voltage range, and average energy density.
2. Does the method use periodic boundaries?
Yes. The spectral method treats opposite grid edges as connected. This is common in FFT based solving. Interpret border values with that assumption in mind.
3. Why is the zero frequency mode removed?
The average potential level is undefined in this Poisson setup. The calculator sets it to zero. Your reference potential is then added as a controlled offset.
4. What grid sizes work best?
Power of two sizes work best, such as 4, 8, 16, or 32. The padding option can expand other grid sizes automatically.
5. What unit should charge density use?
Use the unit selected in the form. The calculator converts values to C/m² before solving. Do not mix different units in one grid.
6. How is electric field calculated?
The field is calculated from the negative gradient of potential. The page uses finite differences on the final voltage grid.
7. Can I export the full grid?
Yes. The CSV download includes row, column, charge density, potential, field components, and field magnitude for every original grid cell.
8. Is this a replacement for full simulation software?
No. It is a fast engineering calculator for grid based study. Use detailed solvers for complex boundaries, materials, conductors, and safety critical design.