# PHYS 2212 Module 2.3

## Applying Gauss’s Law

2.3 Applying Gauss’s Law

### Learning Objectives

By the end of this section, you will be able to:

• Explain what spherical, cylindrical, and planar symmetry are
• Recognize whether or not a given system possesses one of these symmetries
• Apply Gauss’s law to determine the electric field of a system with one of these symmetries

### Applying Gauss’s Law

This video provides examples of how we can apply Gauss’s Law to situations with symmetric charge distributions. It’s a longer than usual video (15 minutes) – just wanted to let you know.

### Strategy for Applying Gauss’s Law

1. Identify the spatial symmetry of the charge distribution. This is an important first step that allows us to choose the appropriate Gaussian surface. As examples, an isolated point charge has spherical symmetry, and an infinite line of charge has cylindrical symmetry.
2. Choose a Gaussian surface with the same symmetry as the charge distribution and identify its consequences. With this choice,  is easily determined over the Gaussian surface.
3. Evaluate the integral  over the Gaussian surface, that is, calculate the flux through the surface. The symmetry of the Gaussian surface allows us to factor  outside the integral.
4. Determine the amount of charge enclosed by the Gaussian surface. This is an evaluation of the right-hand side of the equation representing Gauss’s law. It is often necessary to perform an integration to obtain the net enclosed charge.
5. Evaluate the electric field of the charge distribution. The field may now be found using the results of steps 3 and 4.

Practice!

Discuss!

Reflect on this question and take notes on how you would answer it. Then we will share these thoughts together in a class discussion.

Given an infinite sheet of charge as shown in the figure. You need to use Gauss’s Law to calculate the electric field near the sheet of charge.

Which of the given Gaussian surfaces (A – D) are best suited for this purpose? Note: you may choose more than one answer.

Practice!