All charged objects produce a thing we call their electric field. It is not observable in the conventional sense and might be thought of as a clever way to keep track of how charged objects interact. The field from one electron can influence another electron and the result is they feel a repelling force.

Large electric fields are in the atmosphere during storms.

https://www.youtube.com/watch?v=SglzRDD1oNI

## Pre-lecture Study Resources

Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class.

### BoxSand Videos

## Required Videos

non-uniform E-field - conceptual point q(7min)

uniform E-field - infinite plate(6min)

E-field from point charge - algorithm calculation with rHat(11min)

## Suggested Supplemental Videos

### Learning Objectives

## Summary

Summary

## Atomistic Goals

Students will be able to...

### BoxSand Introduction

## Electric Fields | Point Charges

*Point Charge*

The electric field for a point charges points away from positive charges and towards negative charges. It's magnitude has an inverse square dependency on the distance from the charge. If you double your distance from the charge the field decreases by a factor of 4. All of this information is contained in the expression below.

Electric Field for a Point Charge

$\overrightarrow{E}_q(\overrightarrow{r}_p) = \frac{kq}{|\Delta \overrightarrow{r}|^2}\Delta \hat{r}$

The above equation reads that the electric field from charge $q$, at point $p$, is equal to a constant ($k=8.99 x 10^9 N m^2/C^2$) times the charge, divided by the square of the absolute value of the change in position from $q$ to $p$, multipled by the delta $r$ hat direction. The $\Delta \hat{r}$ is a unit vector, meaning it has magnitude of 1 and only provides a direction.

$\Delta \overrightarrow{r} = <\Delta{x}, \Delta{y}, \Delta{z}>$

$\Delta \hat{r} = < \frac{\Delta x}{|\Delta \overrightarrow{r}|}, \frac{\Delta y}{|\Delta \overrightarrow{r}|}, \frac{\Delta z}{|\Delta \overrightarrow{r}|}>$

## Key Equations and Infographics

Now, take a look at the pre-lecture reading and videos below.

### OpenStax Reading

## Additional Study Resources

### YouTube Videos

Pre-Med Academy has a lot of videos about the Electric Field and Force, too many to list here. We really recommend checking out the content repository for this section and check out the rest of their videos Here are just a few on *The Electric Field*, *Electric Field of a Point Charge*, and *Electric Field of an Infinite Wire*.

Youtube: Pre-Med Academy - Electric Field

Youtube: Pre-Med Academy - Electric Field of a Point Charge

Doc Schuster has a few good videos on the Electric field.

Youtube: Doc Schuster - The Electric Field

Youtube: Doc Schuster - How to Draw and Interpret Field Lines

Youtube: Doc Schuster - Conductors in Electrostatic Equilibrium, Rules for Electric Fields

### Other Resources

This link will take you to the repository of other content related resources .

### Simulations

This flashphysics applet lets you create charge distributions from point charges and plot the corresponding electric field. Try placing test charges in the region of space to watch possible trajectories!

This * PhET* interactive is a test of skill! place charges to guide a charged hockey puck around obstacles and into the goal

This Puzzle by * Duffy* will help you connect the charge and the field.

The Puzzle by * Duffy* is a bit more challenging.

Use this 3D applet by * Falstad* to visualize the field for various charge distributions.

For additional simulations on this subject, visit the simulations repository.

### Demos

### History

Oh no, we haven't been able to write up a history overview for this topic. If you'd like to contribute, contact the director of BoxSand, KC Walsh (walshke@oregonstate.edu).

### Physics Fun

### Other Resources

Use the supplemental resources below to support your post-lecture study.

Boston University's Page on electric Field is a neat reference with a couple of example problems

PPLATO is a complete resource with a lot of information, and several practice questions per subject. This webpage covers electric charge, the electric field, and electric potential, we've already covered charge, so focus on the electric field, we'll get to electric potential in the next section.

The Physics Classroom's section on electric fields.

Isaac Physics' section on the electric field is a good short resource on the electric field. On this page there are two drop down sections on electric potential, we'll get to those in the next section, so have a look at the *Electric Field,* *Visualizing and adding electric fields* and *Electric Fields in Conductors* sections

### Other Resources

This link will take you to the repository of other content related resources .

## Problem Solving Guide

Use the Tips and Tricks below to support your post-lecture study.

### Assumptions

### Checklist

### Misconceptions & Mistakes

### Pro Tips

### Multiple Representations

Multiple Representations is the concept that a physical phenomena can be expressed in different ways.

### Physical

### Mathematical

### Graphical

### Descriptive

### Experimental

## Practice

Use the practice problem sets below to strengthen your knowledge of this topic.

### Fundamental examples

(1) What is the magnitude of the Electric field at a location $r = 2 \hspace{0.2 cm} nm$ from a point charge with charge $q=10 \hspace{0.2 cm}nC$ that is located at the origin?

(2) Three point charges $q_1 = q_2 = q_3 = 5 \hspace{0.2 cm}nC$ are placed equidistant from each other on the x-axis: $q_1$ is located at $x= -2 \hspace{0.2 cm}nm$, $q_2$ is located at the origin, and $q_3$ is located at $x = 2 \hspace{0.2 cm} nm$. A point charge $q_4 = 1\hspace{0.2 cm} nC$ is placed on the y-axis, 2 namometers up from the origin. (a) What is the magnitude of the electric force that $q_4$ feels? (b) What is the direction of the electric force on $q_4$? (c) What is the direction of the electric force if $q_4 = -1 \hspace{0.2 cm}nC$ instead?

(3) A point charge $q_1 = -20 \hspace{0.2 cm}nC$ is located at a position $r_1 = <-3,0> \hspace{0.2 cm}nm$. (a) What is the magnitude of the electric field at point $r_a = <0, 3> \hspace{0.2 cm}nm$. (b) By what factor does the magnitude of the electric field at point $r_a$ decrease if another point charge with magnitude $q_2 = 20 \hspace{0.2 cm}nC$ is placed at the origin? (c) Calculate the magnitude and direction of the force that a point charge with magnitude $q_3 = -1 \hspace{0.2 cm}nC$ would feel if it were placed at position $r_a$ for both cases (a) and (b). [Optional (d) What is the electric force on $q_3$ if charge $q_1$ is removed?]

(4) (More time-consuming - practice with computing the electric field from multiple source charges in an arbitrary configuration) Three point charges $q_1 = 5 \hspace{0.2 cm}nC$, $q_2 = 10 \hspace{0.2 cm}nC$, and $q_3 = -2 \hspace{0.2 cm}nC$ are placed as follows: $q_1$ is located at $r_1 = <- 3,0> \hspace{0.2 cm}nm$, $q_2$ is located at $r_2 = <0,0> \hspace{0.2 cm}nm$, and $q_3$ is located at $r_3 = <1, 2> \hspace{0.2 cm}nm$. (a) What is the magnitude and direction of the electric field at point $r_p = <8, 8> \hspace{0.2 cm}nm?

Solutions found HERE

Short foundation building questions, often used as clicker questions, can be found in the clicker questions repository for this subject.

### Practice Problems

BoxSand practice problems - Answers

BoxSand's multiple select problems

BoxSand's quantitative problems

Recommended example practice problems

- *OpenStax, has practice problems at the end of every section
- Electric Field: Concept of a Field Revisited, Website Link
- Electric Field Lines, Website Link
- Conductors and Electric Fields, Website Link

- PhysicsClassroom, 27 problems on charge and the electric field, Website Link
- University of Greenbay: Guided problem on the electric force, Website Link

For additional practice problems and worked examples, visit the link below. If you've found example problems that you've used please help us out and submit them to the student contributed content section.