Lesson 2. Electrical Interactions and the Electric Force

Daniel DuBrow, Emily Habbert, Shruti Researcher
Physics
2 pd
High School
v3

Overview

Students vary charge and distance to qualitatively and quantitatively determine Coulomb's Law.

Standards

Next Generation Science Standards
  • Physical Science
    • [HS-PS2] Motion and Stability: Forces and Interactions
    • [HS-PS2-4] Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.
    • [HS-PS3-5] Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction.
  • NGSS Practice
    • Using Models
    • Arguing from Evidence
    • Conducting Investigations
    • Analyzing Data
    • Constructing Explanations, Designing Solutions
  • NGSS Crosscutting Concept
    • Systems
Computational Thinking in STEM
  • Data Practices
    • Analyzing Data
    • Collecting Data
    • Creating Data
    • Manipulating Data
    • Visualizing Data
  • Modeling and Simulation Practices
    • Assessing Computational Models
    • Designing Computational Models
    • Using Computational Models to Understand a Concept
    • Constructing Computational Models
  • Computational Problem Solving Practices
    • Computer Programming
    • Preparing Problems for Computational Solutions

Credits

  • Electric Field Mapping Questions adapted from AMTA, Modeling Workshop Project 2013: E1 Charge&Field

Acknowledgement

For the model itself:

  • Sengupta, P. and Wilensky, U. (2005). NetLogo Electrostatics model. http://ccl.northwestern.edu/netlogo/models/Electrostatics. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
  • Updates & modifications by Gabby Anton & Conner Bain (Northwestern) and Daniel DuBrow (Evanston Township High School)

NetLogo software:

Activities

  • 1. Introduction to Electrical Interactions
  • 2. Determining a mathematical model for the Electrical Interaction
  • 3. Combining our Three Equations together into One!
  • 4. Behind the Scenes - How does the Simulation Work?

Student Directions and Resources


  • Use Coulomb’s Law to represent the relationship between electric force, charge and distance of separation.
  • Determine the electrostatic force acting on the bodies with given information about the quantity of charge on two bodies and the separation distance.
  • Recognize the similarities and differences between Coulomb’s Law and the Law of Universal Gravitation. 

1. Introduction to Electrical Interactions


Now we are going to try to figure out a mathematical model for the electrical interaction between two charges.

Please take a few minutes to "play" with the simulation. Think about which variables you can control, and what you can measure.

To use the simulation, first, adjust any slider bars you wish. Then click "setup" and "compute". To try different values, click "go" again so it is de-selected. Then move the sliders to new values and hit "setup" and "compute" again.  

 


Question 1.1

Take a few moments to explore this simulation. What do you think this simulation is showing?



Question 1.2

In this simulation, what variables can you identify as independent variables? (those you can change)



Question 1.3

What variables can you identify as dependent variables?



Question 1.4

What do the arrows on the two charges represent? What happens to these arrows as you change the location of q1? What happens to them as you change the amount or sign of the charges?

(Remember to press "setup" after making any changes)

2. Determining a mathematical model for the Electrical Interaction


Now that we have explored the simulation a little, let's take some time to construct a mathematical model to represent this electrical interaction between two charges.

We decided that our independent variables would be the amount of excess charge each particle has, and the separation between the charges.  The strength of the electrical interaction between charges is the value of the force.

We are going to use an automated graphing program (CODAP) to collect our data.  You will then be able to apply different fits to the data to obtain a linear relationship between all of the variables.  

In order to collect a data point, 1) Change the slider bars to the values you want.  2) Click on "Setup".  3) Click on "Compute".  4) Click on "Collect data point".  This will enter your data into the CODAP data table with all of the appropriate values. 

If you don't see a data table, click on "Tables" and then click on "Experiment Results".  If you don't see a graph, simply click on "Graph" then drag it to where you want.

IF you need to linearize data at some point:

  1. Decide what you have to do to the data to linearize.  Usually we think about doing stuff to the independent variables on the x-axis.
  2. In your data table, look for a little + sign that says "Add a new attribute to this table" when you hover your mouse over it.
  3. Click that + sign and then type in a name for this calculated variable. For example, if you decided to take the square root of charge_1, you might want to call this variable "charge_1^0.5" so you know what that column represents.
  4. Now after you hit enter, left-click on the new variable, then click on "edit formula". 
  5. Click on "insert value" then from the list select charge_1 (click on it).  It will now be in the formula box, and then just type " ^0.5 " which will take the square root of charge_1.  There is also an arithmetic function that does this but typing ^0.5 is easier.
  6. Click "Apply" and you will have a new data column.  Drag this column to the appropriate axis on your graph, and you should now have linearized data!
  7. Now you can click on the graph, then click on the ruler tool, then on the "least-squares line".  This will draw a best fit line through your (linear) data.  You can then write this in correct linearized form.  Remember to use variables, not x & y, and determine what the units must be for slope and intercept.  Write your mathematical model in the answer box.

Question 2.1

Conduct and run an experiment to determine the relationship between the charge of the first particle, charge_1, and the force.  Collect data points using the "Collect data point" button when the simulation is running. Change your independent variable at least 8-10 times to collect different values of the dependent force. Then, drag these variables from where they appear in the table to the correct axes on the graph, and CODAP will create a graph for you.  

Note: It is not necessary to collect multiple trials of each data point.

What type of relationship do you observe between force and charge_1?



Question 2.2

Upload your graph that depicts the relationship between force and charge_1 by clicking on the camera icon to the right of the graph.

Upload files that are less than 5MB in size.
File Delete
Upload files to the space allocated by your teacher.


Question 2.3

Let's now find a mathematical relationship between charge_1 and force.  

Is this data linear? If so, we can click on the graph, then click on the ruler tool, then on the "least-squares line". This will draw a best fit line through your (linear) data. You can then write a mathematical model that describes the line. Remember to use the actual variables, not x & y, and to determine what the units must be for slope and intercept.  Write your mathematical model in the answer box.

If your original data was not linear, follow the procedure listed below the simulation to linearize your data with CODAP.



Question 2.4

Conduct and run an experiment to determine the relationship between the charge of the second particle, charge_2, and the force.  Collect data points using the "Collect data point" button when the simulation is running.  Change your independent variable at least 8-10 times to collect different values of the dependent force.  Then, drag these variables from where they appear in the table to the correct axes on the graph, and CODAP will create a graph for you.  

Note: It is not necessary to collect multiple trials of each data point.

What type of relationship do you observe between force and charge_2?



Question 2.5

Upload your graph from the previous question by clicking on the camera icon to the right of the graph.

Upload files that are less than 5MB in size.
File Delete
Upload files to the space allocated by your teacher.


Question 2.6

Now use your simulation and CODAP to write a mathematical model that describes the relationship between charge_2 and force.  Use the same process as you did in question 2.3 above to linearize your data if necessary.  Write your mathematical model in the space below.



Question 2.7

Conduct and run an experiment to determine the relationship between the separation of the two charges and the force. Collect data points using the "Collect data point" button when the simulation is running. Change your independent variable at least 8-10 times to collect different values of the dependent force. Then, drag these variables from where they appear in the table to the correct axes on the graph, and CODAP will create a graph for you.  

Note: It is not necessary to collect multiple trials of each data point.

What type of relationship do you observe between force and separation?



Question 2.8

Upload your graph from the previous question by clicking on the camera icon to the right of the graph.

Upload files that are less than 5MB in size.
File Delete
Upload files to the space allocated by your teacher.


Question 2.9

Now use your simulation and CODAP to determine write a mathematical model that describes the relationship between force and separation. Use the same process as you did in 2.3 above to linearize your data if necessary. Write your mathematical model in the space below.



Question 2.10

While you are waiting for other groups to finish this part of the lab, compare your mathematical models from questions 2.3, 2.6, & 2.9 with at least one other group.  Record any similarities or differences you notice.

3. Combining our Three Equations together into One!


Now we will look at what we found for how each of the three independent variables (charge_1, charge_2, and separation) relate to the overall force. We will try to make sense of it all.

Remember that when we linearize, the value (and units!) of the slope and intercept are important. We can use our 5% rule to see that for the most part, we shouldn't have a y-intercept for any of the equations.


Question 3.1

Let's look at the three relationships we determined on the last page:

  1. Force is directly proportional to both charge_1.
  2. Force is directly proportional to charge_2.
  3. Force is inversely proportional to the square of separation.

Knowing this, let's write one proportion that says how force relates to all three of these variables. 

Hint - we did something similar with Gravity not too long ago!



Question 3.2

Our proportion with all the variables isn't an equation because on one side we have force which is in Newtons but on the other, we have charge_1 * charge_2 (in Coulombs2) and separation2 (in meters2). Those units aren't equal to each other!

This inconsistency means we need a constant of proportionality, which we will call k. Rewrite your proportion as an equality using k.

Hint - when we studied gravity we did something similar. We called that constant G and wrote it in front of all of our variables, like 

F = G*(our proportionality). See if you can do the same thing with the electric force but use k instead. Write your complete equation in the answer box below!



Question 3.3

Now we are ready to find that constant of proportionality, k. Use the simulation to record one trial. Plug in the values of the force, both charges, and separation, and see if you can solve for k. We are looking for the value of k and also its units. Record your answer in the box below question 3.4.

  Got it!


Question 3.4

What value did you determine for the constant, "k" in the equation? Be sure to report a value AND appropriate units!

4. Behind the Scenes - How does the Simulation Work?


Now that we have figured out the mathematical model for the electrical interaction (which we call Coulomb's Law of electric force), we can look at the computer code that makes the simulation work. Scroll further down this page and click on "NetLogo Code" and click the arrow to open up that section. We will use this code to answer a few questions.


Question 4.1

In the last section, we found a value for the proportionality constant k. This number has to be programmed into the code somewhere.  See if you can find what line of code the value for k shows up. 

What line (#) of code defines k?

Hint: if you skipped the directions above, click on the dropdown button labeled NetLogo Code...



Question 4.2

Along with k, the program needs to know the value of the charges and their separation.  Let's look at a few NetLogo interface buttons to see how to set values using the slider bar.  At the top of the NetLogo window, you'll see a little lock sign next to the phrase "Mode: Interactive". Click on this lock and it should change to "Mode: Authoring". Now right click on the button that controls charge_1, and click "edit". The value of "charge_1" is a "global variable" because it works throughout the whole program. Try changing it to another name such as your name, and click "OK". 

What happened? Why do you think this happened? Could you change the code in such a way that this name would work?



Question 4.3

The most important thing our program does is actually calculates the value of the electric force interaction. Look through the code to see if you can find where this takes place, and then copy/paste the line(s) of code that calculates the electric force.  

Hint: NetLogo uses the command "set" to store a value. For example, if I wrote set answer 3 + 4, the variable "answer" would hold the value "7".



Question 4.4

Brainstorm with your partner(s) about how you could add to the program to allow you to look at the effect of two charges acting on a third. For now let's keep it simple and pretend like all three charges are colinear (in a straight line). List any ideas you come up with for what you would need to change or add to make this happen.

Note: You don't have to be a NetLogo whiz to answer this question. Just try to think about what the program does now, and brainstorm what you would have to do to let the program work with three charges instead of two.