Solve enclosed charge and direct field flux cases. Convert units, compare methods, and inspect tables. Clear outputs help practice, validation, documentation, and classroom review.
| Case | Input Summary | Method | Flux Result |
|---|---|---|---|
| 1 | Q = 5 µC, εr = 1 | Φ = Q / (ε0 εr) | 5.647e+5 N·m²/C |
| 2 | E = 300 V/m, A = 2 m², θ = 30° | Φ = E A cosθ | 5.196e+2 N·m²/C |
| 3 | Q = 12 nC, enclosed fraction = 0.5 | Partial enclosed charge | 6.776e+2 N·m²/C |
| 4 | E = 1.2 kV/m, A = 0.25 m², θ = 0° | Normal incidence | 3.000e+2 N·m²/C |
Gauss law states that total electric flux through a closed surface equals enclosed charge divided by permittivity.
Closed surface form: Φ = Qenclosed / (ε0 εr)
Here, Φ is electric flux, Q is enclosed charge, ε0 is vacuum permittivity, and εr is relative permittivity of the medium.
For a known field across a flat surface, the direct form is used.
Direct surface form: Φ = E × A × cos(θ)
Here, E is field magnitude, A is surface area, and θ is the angle between the field direction and the outward normal.
If the field is parallel to the surface, the angle with the normal becomes 90°, so the flux becomes zero. If the field is fully normal to the surface, the cosine term becomes one, giving maximum flux.
Choose the calculation mode first. Use the enclosed charge mode for closed Gaussian surfaces. Use the direct mode for known field, area, and angle values.
Enter your numeric values, then select the matching units. Set relative permittivity if the medium is not vacuum. Keep enclosed fraction at one for a fully enclosed charge.
Use surface count when comparing repeated identical surfaces. Use confidence factor if you want a scaled estimate for lab work, sensitivity checks, or simplified modelling.
After submission, the result appears above the form. You can then download the values as CSV or PDF and inspect the graph for flux trends.
Electric flux measures how much electric field passes through a surface. It is a scalar quantity, but its sign still reflects whether field lines leave or enter a chosen surface. Positive flux usually indicates outward field behavior, while negative flux indicates inward behavior relative to the selected normal direction.
Gauss law is one of the core laws of electromagnetism. It connects the electric field on a closed boundary to the net charge inside that boundary. This relation is especially useful for symmetric distributions such as spheres, cylinders, and planes, where direct field integration may be longer or less intuitive.
In practical study problems, the law helps students move between field, charge, area, and angle relationships. In engineering analysis, it supports quick checks of expected behavior inside dielectric regions, capacitor systems, and electrostatic enclosures. It also provides a strong conceptual bridge between local field behavior and total enclosed charge.
This calculator supports both a Gauss-law mode and a direct surface-flux mode. That makes it useful for textbook exercises, lab preparation, answer verification, and comparison between charge-based and field-based reasoning. The export tools help preserve results for assignments, reports, and revision notes.
Electric flux measures how much electric field passes through a chosen surface. It helps summarize field interaction over an area instead of examining every point separately.
Use Gauss law mode when the problem gives enclosed charge or asks about total flux through a closed surface. It is best for symmetric electrostatic situations.
Use the direct mode when you already know field strength, surface area, and angle with the surface normal. It suits open surfaces and flat-surface calculations.
The flux formula uses the dot product between the electric field and the area vector. The area vector is perpendicular to the surface, so the angle is measured from the normal.
For the same enclosed charge, higher relative permittivity increases the denominator in Gauss law form. That reduces the calculated flux value in this simplified model.
Yes. Flux becomes negative when the field points opposite the chosen outward normal direction. In direct mode, this appears when the cosine term is negative.
This version focuses on flux. It does not derive full field expressions from symmetry, but it helps verify the flux side of many electrostatic problems.
Exports help save classroom work, share calculations, compare cases, and document values for reports. They also make revision and result tracking easier.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.