Gauss’s Law (Electric Flux)
ΦE = Qenc / ε0
Quick answer
This calculator solves ΦE = Qenclosed / ε₀ for Electric Flux. With Enclosed Charge 10 µC, the result is 1129 kV·m. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Gauss’s law states that the total electric flux through any closed surface equals the charge enclosed divided by the permittivity of free space. It is one of Maxwell’s equations and lets the field of symmetric charge distributions be found without integration. The flux depends only on the enclosed charge, not on how it is arranged inside the surface.
Variables
- ΦE — Electric flux through the closed surface (V·m)
- Qenc — Net charge enclosed (C)
- ε₀ — Permittivity of free space 8.854×10⁻¹² F/m
Practical Notes
Gauss’s law gives the field of a charged sphere, line, or plane instantly by choosing a symmetric Gaussian surface. It is the electrostatic basis for shielding: no net enclosed charge means zero net flux.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| phiE | Electric Flux | V·m | V·m, kV·m |
| Q | Enclosed Charge | µC | pC, nC, µC, mC, C |
Step by step
- 1. What you know: Enclosed Charge 10 µC
- 2. The relation: ΦE = Qenclosed / ε₀
- 3. Substitute: Q = 10 µC
- 4. Result: Electric Flux = 1129 kV·m
Worked examples
Minimum range
Given: Enclosed Charge 100 nC
Result: Electric Flux = 11.29 kV·m
Low range
Given: Enclosed Charge 1 µC
Result: Electric Flux = 112.9 kV·m
Typical
Given: Enclosed Charge 10 µC
Result: Electric Flux = 1129 kV·m
High range
Given: Enclosed Charge 100 µC
Result: Electric Flux = 11290 kV·m
Maximum range
Given: Enclosed Charge 1 mC
Result: Electric Flux = 112900 kV·m
Solving for each variable
Solve for Electric Flux
Enclosed Charge 100 nC → 11.29 kV·m
Solve for Enclosed Charge
Electric Flux 0.1 V·m → 0.8854 pC
How Electric Flux changes with Enclosed Charge
| Enclosed Charge (input) | Electric Flux (result) |
|---|---|
| 1 µC | 112.9 kV·m |
| 2.5 µC | 282.4 kV·m |
| 5 µC | 564.7 kV·m |
| 7.5 µC | 847.1 kV·m |
| 10 µC | 1129 kV·m |
| 15 µC | 1694 kV·m |
| 20 µC | 2259 kV·m |
| 40 µC | 4518 kV·m |
| 70 µC | 7906 kV·m |
| 100 µC | 11290 kV·m |
The same result in other units
| Unit | Value |
|---|---|
| V·m | 1129000 |
| kV·m | 1129 |
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<p><a href="https://vbatpower.com/formulas/gauss-law-flux/">Gauss’s Law (Electric Flux)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Gauss’s Law (Electric Flux)?
Use ΦE = Qenclosed / ε₀. With Enclosed Charge 10 µC, Electric Flux works out to 1129 kV·m.
What is the formula for Gauss’s Law (Electric Flux)?
The formula is ΦE = Qenclosed / ε₀. Gauss’s law states that the total electric flux through any closed surface equals the charge enclosed divided by the permittivity of free space.
How do you find Enclosed Charge when you know the other values?
Rearrange for Enclosed Charge: with Electric Flux 0.1 V·m, Enclosed Charge is 0.8854 pC.
What units does Gauss’s Law (Electric Flux) use?
Electric Flux is shown in V·m, kV·m. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Fields & Electromagnetism formulas →Need more features?
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