Compute sphere flux using enclosed charge and permittivity. Inspect area, field, and radius relationships instantly. Learn formulas, compare cases, and export clear result reports.
| Mode | Input Summary | Radius | Permittivity | Electric Flux |
|---|---|---|---|---|
| Known enclosed charge | Q = 1 μC | 0.20 m | Vacuum | 112940.906684 N·m²/C |
| Known enclosed charge | Q = 2 μC | 0.15 m | εr = 2.5 | 90352.725347 N·m²/C |
| Known surface field | E = 5000 N/C | 0.25 m | Vacuum | 3926.990817 N·m²/C |
| Known surface density | σ = 0.4 μC/m² | 0.30 m | Vacuum | 51093.262473 N·m²/C |
Main relation: Φ = Q / ε
Surface area of a sphere: A = 4πr²
Uniform radial field form: Φ = E × A = E × 4πr²
From surface charge density: Q = σ × 4πr²
Average field at the surface: E = Φ / A = Q / (ε × 4πr²)
Here, Φ is electric flux, Q is enclosed charge, ε is absolute permittivity, r is sphere radius, A is sphere area, E is radial field, and σ is surface charge density.
Electric flux measures how much electric field passes through a closed surface. A sphere is a common choice because symmetry makes many calculations easier. This calculator helps you estimate flux, enclosed charge, surface area, and average field values from practical inputs.
A spherical surface appears often in electrostatics problems. It is useful for point charges, charged shells, and radial fields. When the field is symmetric, Gauss law gives a fast answer. You can test charge based inputs, field based inputs, or surface charge density inputs in one place.
For a closed sphere, net electric flux depends on enclosed charge and medium permittivity. It does not depend on sphere size when enclosed charge stays fixed. Radius still matters when you want surface area, average field strength, or equivalent charge density across the sphere.
Use enclosed charge mode when charge is known. Use field mode when surface field and radius are known. Use surface charge density mode when charge per unit area is known. You can also switch between vacuum permittivity and a custom relative permittivity for materials. It also reduces manual unit conversion errors during repeated calculations.
The main result is electric flux in newton square meters per coulomb. The calculator also shows surface area, enclosed charge, average field magnitude, electric displacement, and equivalent surface density. These extra values help students verify steps and compare how geometry and materials change related quantities.
Seeing the formula beside the result improves understanding. Students can connect symbols with values quickly. This supports homework checking, self study, and exam revision. The worked relationships also show why a larger sphere changes field strength while total flux can remain the same.
Use this tool for classroom examples, engineering reviews, physics practice, and quick concept checks. It is also helpful when comparing vacuum with dielectric media. Because export options are included, you can keep a result sheet, share example values, or print a simple report for later study.
It represents the net electric field passing through the entire closed spherical surface. For closed surfaces, flux links directly to enclosed charge through Gauss law.
Not when enclosed charge and permittivity stay fixed. Radius changes surface area and field strength, but total net flux remains the same for the same enclosed charge.
Permittivity controls how electric fields behave in a medium. Higher permittivity reduces flux for the same enclosed charge in this calculator’s electric flux form.
Use charge mode when the enclosed charge is known directly. It is the fastest option for point charge and closed surface practice problems.
Use field mode when the average radial field at the sphere surface is known. The calculator multiplies that field by total sphere area.
It is useful when charge per unit area is known. The tool first finds total charge on the sphere, then computes electric flux and related values.
Electric flux is shown in newton square meters per coulomb. This is the common electrostatics unit for flux based on electric field.
Yes. The result section includes CSV export and a PDF button. The PDF option opens a printable view for saving the result report.