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# Chapter 24: Gauss's Law

Electric fields decrease with distance from their source as 1/r^{2}. Compare the surface area of a cubic box with sides of length r with a sphere of radius r. Their surface areas are 6r^{2} and 4πr^{2}, respectively. Although the constants differ, each surface area increases by r^{2} as the size of the object increases. The observation that the field strength decreases in the same proportion as the area increases leads to Gauss's law. Nineteenth century physicists were fond of analogies between fields and fluid flow. If fluid flows from a source, then the amount of fluid flowing through any surface that encloses that source must be constant regardless of the shape of that surface. The amount of fluid passing through a surface is sometimes called the flux. Although it would be incorrect to think of electric and gravitational fields as fluids, the mathematical machinery is identical and we will need to calculate a quantity known as the electric flux that is the product of the field strength and surface area.

# Table of Contents

## Illustrations

- Illustration 24.1: Flux and Gaussian Surfaces.
- Illustration 24.2: Near and Far View of a Filament.
- Illustration 24.3: A Cylinder of Charge.

## Explorations

- Exploration 24.1: Flux and Gauss's Law.
- Exploration 24.2: Symmetry and Using Gauss's Law.
- Exploration 24.3: Conducting and Insulating Sphere.
- Exploration 24.4: Application of Gauss's Law.

## Problems

- Problem 24.1: Rank the point charges.
- Problem 24.2: Rank the line charges.
- Problem 24.3: Describe the charge density.
- Problem 24.4: Different size flux detectors to describe a hidden charge density.
- Problem 24.5: Determine flux through spherical shells.
- Problem 24.6: Determine flux through a box.
- Problem 24.7: Describe Gaussian surfaces for a capacitor.
- Problem 24.8: Symmetry and field at distances far away.
- Problem 24.9: Line of charge or sheet of charge?
- Problem 24.10: Charge on coaxial cable using Gauss's law.
- Problem 24.11: Charge on capacitor using Gauss's law.
- Problem 24.12: Spherical charge distribution with Gauss's law.