Formula Used
For a point charge q, the electric field magnitude at distance r in a medium with relative permittivity εr is:
E = (1 / (4π ε0 εr)) · q / r²
In coordinate form, let ⃗r = (x−xq, y−yq, z−zq) and r = |⃗r|. The vector field is:
⃗E = (1 / (4π ε0 εr)) · q · ⃗r / r³
How to Use This Calculator
- Select Distance mode for field magnitude from r.
- Select Coordinate mode for Ex, Ey, Ez components.
- Enter the charge value and unit, including negative sign if needed.
- Set εr to model different materials and dielectrics.
- Provide distance or coordinates, then press Calculate.
- Use the CSV and PDF buttons to export the computed results.
Example Data Table
Sample results for q = +2 µC, εr = 1.
| Distance r (m) | |E| (N/C) | |E| (kV/m) |
|---|---|---|
| 0.1 | 1797510.4 | 1797.5104 |
| 0.25 | 287601.66 | 287.60166 |
| 0.5 | 71900.414 | 71.900414 |
| 1 | 17975.104 | 17.975104 |
Electric Field of a Point Charge: Practical Notes
1) What this calculator measures
The electric field E represents force per unit charge, reported in N/C (equivalently V/m). This tool evaluates the field created by a single point charge and returns either a scalar magnitude (distance mode) or a full vector (Ex, Ey, Ez) in coordinate mode.
2) Core constants and typical values
The vacuum permittivity is ε0 = 8.8541878128×10⁻¹² F/m. From it, the Coulomb constant is k = 1/(4π ε0) ≈ 8.9876×10⁹ N·m²/C² when εr = 1. In materials, the effective constant becomes k/εr, reducing field strength in proportion to εr.
3) Inverse-square behavior with distance
Field magnitude scales as 1/r². Doubling distance decreases |E| by a factor of four. For example, with q = 2 µC in air, |E| is about 1.80×10⁶ N/C at 0.10 m, and about 4.49×10⁴ N/C at 0.50 m.
4) Sign and direction of the field
A positive charge produces a field pointing radially outward; a negative charge points inward. Distance mode reports a signed radial value so you can track direction, while coordinate mode reports signed components. This is useful for quick checks in electrostatics problems and field superposition workflows.
5) Coordinate mode for engineering geometry
In 3D, the calculator forms ⃗r = (x−xq, y−yq, z−zq) and computes ⃗E = k q ⃗r / r³. This gives you the component-wise field at a specific point, enabling comparisons against sensor placement, insulation clearances, and directional constraints along an axis.
6) Modeling materials using relative permittivity
Relative permittivity εr approximates how a medium reduces electrostatic field intensity. A value near 1 matches vacuum/air, while higher values can model many dielectrics. As a quick rule, if εr increases from 1 to 4, the field drops to one quarter.
7) Unit handling and numeric stability
Inputs accept common charge units (C, mC, µC, nC, pC) and length units (m, cm, mm, km, in, ft). Internally, everything converts to SI units before calculation. Extremely small distances can yield very large fields; avoid using r near zero unless you are intentionally exploring a limiting case.
8) Exporting results for reports
Use the CSV export for spreadsheets and batch comparisons, and the PDF export for lab notes and client documentation. The exports include normalized inputs, computed constants, and the final field values. This reduces transcription errors and keeps your calculation trail consistent across teams.
FAQs
1) Why do N/C and V/m represent the same field unit?
N/C and V/m are equivalent because electric field can be defined as force per charge or potential gradient. In SI, both reduce to the same base units.
2) What does relative permittivity change in the result?
It divides the field by εr. If you set εr = 5, the field becomes one-fifth of the vacuum value for the same charge and geometry.
3) Can I use negative charge values?
Yes. A negative q reverses the direction of the field. In coordinate mode, the component signs flip; in distance mode, the signed radial value becomes negative.
4) What happens if the field point equals the charge location?
The point-charge model predicts an unbounded field at r = 0. The calculator blocks this case and asks you to choose a field point different from the charge location.
5) Which mode should I use for homework problems?
Use distance mode for standard radial problems where only |E| is needed. Use coordinate mode when a problem asks for components, direction, or geometry in 2D/3D.
6) How accurate are the constants used?
The calculator uses a high-precision value of ε0 and computes k from it. Results are appropriate for most educational and engineering estimates.
7) Can this calculator handle multiple charges?
This page focuses on a single point charge. For multiple charges, compute each field vector at the same point and add the components to apply superposition.