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Gauss's Law Flux Calculator — result sheet
Calculate electric flux, enclosed charge, and the ideal spherical-surface electric field using Gauss's law.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Phi = Q/(epsilon0 epsilonr); for a spherical Gaussian surface, E = Phi/(4 pi r²). In reverse, Q = Phi epsilon0 epsilonr.
Gauss's law connects the net electric flux through a closed surface with the net charge enclosed by that surface. The spherical-field output is an additional symmetry result, not a claim that every charge arrangement has a uniform field on the chosen sphere.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Calculation direction — 2 choices
- Enclosed charge — µC; minimum -1000000; maximum 1000000
- Electric flux — N·m²/C; minimum -1000000000000; maximum 1000000000000
- Relative permittivity — minimum 1.0E-6; maximum 1000000
- Spherical Gaussian radius — m; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Calculation direction | charge-to-flux |
| Enclosed charge | 2 |
| Electric flux | 225882.7 |
| Relative permittivity | 1 |
| Spherical Gaussian radius | 0.1 |
Flux ≈ 225,881.8 N·m²/C; ideal spherical field ≈ 1.798 MN/C.
Assumptions and limits
- Charge and flux use SI-compatible units, and the relative permittivity is positive.
- The field output assumes a spherically symmetric enclosed charge distribution or an ideal point charge at the sphere centre.
- External charges can affect the local electric field but do not change the net enclosed charge term in Gauss's law.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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