---
title: "Electric Flux and Gauss's Law"
description: "Flux counts how much field passes through a surface, and Gauss's law says the flux out of any closed surface is set only by the charge inside. The shape of the surface is free, which is what makes the"
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source: https://lightmysky.com/learn/science/electric-flux-and-gausss-law-mt_Z5dZQvik6o.md
retrieved: 2026-09-12
---

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# Electric Flux and Gauss's Law

Flux counts how much field passes through a surface, and Gauss's law says the flux out of any closed surface is set only by the charge inside. The shape of the surface is free, which is what makes the law useful.

Subject: Science · Area: Electricity & Magnetism · Ages 18 to 19
Page: https://lightmysky.com/learn/science/electric-flux-and-gausss-law-mt_Z5dZQvik6o

## Ready when they can

- Calculates the flux through a flat surface for a uniform field at any angle
- States Gauss's law and explains why charge outside the surface contributes nothing
- Chooses a closed surface whose symmetry matches a given charge distribution

## Lesson: Counting field lines through a surface

Flux counts how much electric field passes through a surface. For a flat patch in a uniform field, multiply field strength by area by the cosine of the angle. Square on to the flow catches the most, while edge on catches nothing.

Curved surfaces are handled by chopping them into tiny flat pieces and adding up. For a closed surface, keep the sign straight: field leaving counts positive and field entering counts negative. What enters at one spot and leaves at another cancels out.

**Example.** Wrap a sphere around a point charge and add up the flow. The area grows with distance squared while the field fades the same way, so size drops out. The total flux equals the inside charge divided by the vacuum permittivity.

**Tip.** Only enclosed charge sets the total flux out of a closed surface. Outside charges still bend the field lines, but every line of theirs that enters also leaves, adding zero. That freedom to choose any shape is what makes the law useful.

**Recap.** Flux measures field flow through a surface, and closed surface flux equals inside charge over permittivity.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [The Electric Field of a Continuous Charge Distribution](https://lightmysky.com/learn/science/the-electric-field-of-a-continuous-charge-distribution-mt_IIcVqWapC1)

## Opens up

- [Applying Gauss's Law to Symmetric Charge Distributions](https://lightmysky.com/learn/science/applying-gausss-law-to-symmetric-charge-distributions-mt_1LZboKPJ4D)