# Gauss's law

The total electric flux through a closed surface equals the enclosed charge divided by epsilon zero.

Physics (university) · Part 07: Electric fields and potential · Card 5 of 10 · Last updated 2026-10-19

## Analogy

Counting how many arrows leave a balloon to learn how much charge is inside.

## Example

**Flux of 1 nC**

flux = Q / epsilon0
= 1e-9 / 8.85e-12
= 113 N m^2/C

## In practice

A 1 nC charge inside any closed surface gives a flux of about 113 N m squared per C.

## Practice

### Flashcards

- **What does Gauss's law connect?** Electric flux through a closed surface and the charge inside.

### Interview questions

**Use Gauss's law to find the field outside a charged conducting sphere of charge Q and radius R.**

- Choose a spherical surface
- Field is the same size everywhere on it
- E x 4 pi r^2 = Q / epsilon0 gives E = kQ/r^2

## Questions people ask

### When is Gauss's law useful?

It is easiest when charges are spread in a symmetric shape, such as a sphere, a long line or a flat sheet. Then you can choose a surface where the field is constant and perpendicular, which turns flux into field times area. For messy shapes, you need other methods.

### What is electric flux?

Flux measures how much field passes through a surface, calculated as E times area times cosine of the angle between the field and the surface's normal. Its unit is N m squared per C. A field running parallel to the surface gives zero flux, while a field straight through gives maximum.

## Related concepts

- [Electric field](https://studyvisually.com/learn/science/physics-university/physics-university-part-7/physics-university-part-7-concept-3)
- [Electric charge](https://studyvisually.com/learn/science/physics-university/physics-university-part-7/physics-university-part-7-concept-1)
- [Coulomb's law](https://studyvisually.com/learn/science/physics-university/physics-university-part-7/physics-university-part-7-concept-2)
- [Field lines](https://studyvisually.com/learn/science/physics-university/physics-university-part-7/physics-university-part-7-concept-4)

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