In this lesson, you will explore Coulomb's Law and connections between Kinematics and Electrostatics Motion. You will use computational models built in a modeling environment called NetLogo to explore how charged particles interact. 

Recall that opposite charges attract and like charges repel. These interactions result in an electric force between the two particles. 

The force between two charges depends on two variables:  how strong the charge is, and the distance between the two charges.

The model is built in a modeling environment called NetLogo. NetLogo models are agent-based, meaning that it is composed of individual components which are coded to interact. In the model below, the agents are coded to behave like charged particles. The element of time is experienced in NetLogo through a unit called ticks. With each tick, all agents of the model take commands and perform them (or do nothing if told so), and then the tick counter progresses forward by one. Then any monitors or graphs expressing data from the model are updated. 

The elements of the model can be changed using sliders that let you control specific elements, but it can also be modified using code. Scroll down to look at the code tab if you are curious what NetLogo code looks like. The command center is used to write specific code to interact with the model. 

Explore the model below to see how the amount of charge and the distance between two charges affects Coulombs' force. 

To interact with the model:

1) Adjust sliders on the left side of the model to desired levels. In this lesson, you will mostly be concerned with the TEST-CHARGE slider.

2) Press SETUP. You will see the black space change to a color. If the TEST-CHARGE slider is at a positive value, you will see a blue positive charge appear in the model. If the TEST-CHARGE slider is at a negative value, you will see a red negative charge appear in the model.

3) Press GO. Click the mouse anywhere in the green space. You will see a blue particle appear. Hold down and drag the mouse to move this blue charge in the model. You can also lift up the mouse which will stop the model from ticking forward (you can then press down again to interact with the model).

Using the Electrostatics NetLogo model, plot distance vs. Coulomb's Force. 

To create a plot:

1) In the model, use the TEST-CHARGE slider to choose an electrostatic charge value. Then, click SETUP, then GO as you did before. 

2) Click anywhere in the green box to place the blue charge. Click on the charge and drag it around to adjust the distance between the blue and the other (smaller, red or blue) charge.

3) As you run the model, your data is collected in a data table on the right. Drag the column titled Coulomb's Force to the y-axis of the graph below the data table. Drag the column titled Distance to the x-axis of the graph. 

4) Repeat with different electrostatic charge values. 

Using the Electrostatics model, plot distance vs. potential energy. 

To create a plot:

1) In the model, use the CHARGE slider to choose an electrostatic charge value. Then, click SETUP, then GO.

2) Click anywhere in the green box to place the grey charge. Click on the charge and drag it around to adjust the distance between the grey and blue charge. 

3) Your data has been collected in a data table on the right. Drag the column titled Potential Energy to the y-axis of the graph below the data table. Drag the column titled Distance to the x-axis of the graph. 

4) Repeat with different electrostatic charge values. 

Now that you have used a NetLogo model to explore how the distance between particles effects potential energy and Coulomb's force, answer the questions below. You can use the model below to aid in your explanations. 

In this lesson, you will continue your investigation of the motion of electrons due to electric forces. You will explore the notion of electric field lines, which are visualizations of electric field.

Every charged object emits an electric field that extends outward into the space that surrounds it. We call this charged object the source charge. To explore the source charge's electric force, we can bring a smaller test charge close to it and see how the test charge is effected. 

The Electrostatics Model that you've used doesn't model or show you the electric force field, but instead shows how two charges are effected by each other's electric force fields. For example, in the electrostatics model if you move a positive source charge closer to a positive test-charge, the test-charge will be repelled and move away from the source charge. You can think of the positive source charge as having a force field around it that determines how other charged particles that come close to it will behave. 

Make some guesses now: How can you visually represent the force field around the source charge in the Electrostatics Model? Run the model again and observe how the particles move in order to come up with one or more possible ways to visually represent the force field.

The model below shows one possible representation of electric lines of force. Electric fields are typically represented as lines that point in the direction that a positive test charge would accelerate if placed upon the line. 

So, if you use test-protons (that have a positive charge) the lines are directed away from positively charged source charges and toward negatively charged source charges, and if you use test-electrons (that have a negative charge) the lines are directed toward positively charged source charges and away from negatively charged source charges. 

To create electric field lines and use the model:

1) Click SETUP then GO

2) Click ADD POSITIVE + SOURCE CHARGE. Drag the positive source charge anywhere in the black box. 

3) In the CREATE drop-down menu choose test-protons.

4) Click anywhere in the black box to test protons in the space you've created. Make sure to test many protons. Observe how the test proton charges behave in the space and how the electric field lines are drawn. 

5) Repeat with different numbers and positions of positive and negative source charges. You can do this by hitting the ADD POSITIVE + SOURCE CHARGE button and the ADD NEGATIVE - SOURCE CHARGE multiple times. Also, be sure to also test your space with test electrons, by selecting test-electrons in the CREATE drop-down menu.

The image below shows an electric field with an orange negative source charge on the left and a blue positive source charge on the right, the two source charges are equal in magnitude. This is called a dipolar electric field. Now imagine that you are placing test-protons at positions along the three lines shown in the image: A (left), B (middle) & C (right).

Now create a scenario like the one shown in the image below, using the Electric Field model. First, create a dipolar field with a positive source charge and a negative source charge, and then run your model by placing test-protons along the three lines shown in the image: A (left), B (middle) & C (right). Place test-charges at various positions along the three lines. 

To create a dipolar field by using the model:

1) Click SETUP then GO

2) Click ADD POSITIVE + SOURCE CHARGE. Drag the positive source to the right side of the black box, as it is in the picture. 

2) Click ADD NEGATIVE - SOURCE CHARGE. Drag the negative source to the left side of the black box, as it is in the picture. 

3) In the CREATE drop-down menu choose test-protons.

4) Click in the black box on numerous positions along the three lines shown in the picture to test protons in the space you've created. Make sure to test many protons along these lines. Observe how the test proton charges behave in the space (based on where they started) and how the electric field lines are drawn. 

In this lesson you will explore how electric current flows in a wire and explore how current depends on applied voltage and wire width. Additionally, you will start to explore ways to measure current and compare data with your classmates. 

In this activity, you will use a model to identify how electric current depends on applied voltage.

This model shows a microscopic look at how electric current flows through a wire connected to a battery. It shows how electric current depends on the number of free electrons and how fast these red electrons are traveling towards the positive end of a battery. This speed depends on (1) the applied voltage difference and (2) the obstacles that the electrons encounter in their way, which are represented in this model by blue atoms.

In this model, time is represented in terms of ticks, which can be adjusted using the slider at the top to slow down or speed up the model. 

To use the model:

1) Click SETUP then GO. You will start to see electrons flow through the wire, see data readings on the monitors, and a plot form on the graph. 

2) You can change the voltage at any time, even while the model is running. However, to have accurate comparable readings it might be best to hit SET-UP and GO to reset the model after you've changed the parameters to where you'd like them. 

Now using your explorations with the model, and the screenshot below, make a prediction about how wire width will impact current. 

Consider how electrons might flow differently through a wire that is half as wide. 

Use the model to test your hypothesis about how wire width will impact current.

To use the model:

1) Click SETUP then GO. You will start to see electrons flow through the wire, see data readings on the monitors, and a plot form on the graph. 

2) If you'd like to change the wire's width, select 2 or 1 from the drop-down menu WIRE-WIDTH. 

Now that you've compared your data list with your classmates' data lists or trials with the same conditions, consider the data you collected on your own and the data collected by the rest of the class. 

Now you will look at what happens to the average current after a long period of time. You will see that an average current counter has been added to the model in the lower right corner. 

1) Set the VOLTAGE slider to 1 and the WIRE-WIDTH drop down menu to 1. 

2) Click SETUP then GO. 

3) When your model has gone for at least 600 ticks, hit GO again to stop your model. Take note of the AVERAGE CURRENT

In this lesson you will explore how electric current flows in a wire and explore how current depends on applied voltage, wire length, and wire material. Additionally, you will continue to explore ways to measure current and find ways to aggregate your own data. 

Yesterday, you used this model to explore how wire width affected current and how current can be measured. Now, based on your prior explorations with the model, make a prediction about how wire length will impact current. Use the screenshot below as a reference and answer the question below. 

Use the model below to test your prediction about how wire length affects current.

When you were examining wire width, you compared data with other classmates to come up with a more accurate measurement representing current. Now you can use the modeling tool below to run multiple trials and aggregate your own data.

With your classmates, you found averages by conducting multiple trials and averaging the data collected across trials. Now, you'll be introduced to a tool that allows you to calculate a running average that will average all the measurements for current within one trial. To find that the average current within an individual trial, you can average all the individual current now measurements that you take.

In the workspace below is the model, now with an empty table and empty graph. As you run your model, the table will automatically update data from the model at each tick. Each time you press setup, you will begin a new “run” or trial of data collection. You can graph these data by pulling the variable headers from the table into an axis of the graph. You can also calculate specific information about the data by updating the table with formulas. 

There are instructions on using the data table and graphing tools are embedded in the model's instruction window. You can move this window by dragging it's blue headers and also resize it by dragging any side of it. If you close the instructions, click the GUIDE button that looks like a book in the upper right-hand corner and select "Show Guide". 

Using prior explorations with the model, make a prediction about how wire type will impact current. The model contains three types of wire, each with a different resistance. Resistance is an electrical quantity that measures how the material reduces electric current flow through it. The materials in the model are lead, tin, and aluminum. Use the chart of resistance and the screenshots below to identify what metal matches each model state.

The Ohm meter is a measure of resistivity, with higher values reflecting greater resistance. 

Metal 1 

Metal 2 

Metal 3

Use the model below to test your prediction about how wire metal affects current. When you were examining wire width, you compared data with other classmates to come up with a more accurate measurement representing current measurements taken from multiple trials. Now, just like you did to learn about wire length, you can use the modeling tool below to run multiple trials and aggregate your own data in a similar way.

There are instructions on using the data table and graphing tools are embedded in the model's instruction window. You can move this window by dragging it's blue headers and also resize it by dragging any side of it. If you close the instructions, click the GUIDE button that looks like a book in the upper right-hand corner and select "Show Guide". 

Here, you will further develop their understanding of different ways to measure current. Further, you'll explore how this data is managed and visualized in the NetLogo model you've been using. 

When you drive a car, you typically don't drive the same speed the whole time. The car's speedometer changes as you drive and tells you the instantaneous speed at that moment in time. 

The current through a wire functions in a similar way: current changes at different points in time because the flow of electrons through the wire is changing. This means that the number of charges passing through one part of the wire is changing. Imagine pausing time and then measuring the current in the wire at one point--that is the instantaneous current.

This NetLogo model does not measure the exact instantaneous current. So, to estimate instantaneous current, the model takes a very small amount of time which simulates one instant. This small amount of time is called the sampling rate and can be adjusted in the model using the "sampling-rate" slider. Remember that NetLogo time units are called ticks. 

Use the model below to change the sampling-rate slider and then answer the questions below. Try using both very small and very large values of sampling-rate and observe the graph.

Try putting sampling-rate on the x-axis of your graph, and then currentNow on the Y axis. 

1) Use the SAMPLING-RATE slider to start the sampling rate at a very low value of 1. 

2) Hit SET UP and GO to run the model. 

3) Hit GO to stop the model between trials.

4) Move the SAMPLING-RATE slider to a new value. 

5) Hit SET UP and GO to run the next trial. 

6) Repeat these steps until you have a graph that allows you to make a conclusion. You may also be able to make conclusions by looking at the data in the table. 

Now you will learn how to graph average current in the model, just as instantaneous current is. The code below shows how instantaneous current was plotted in the model.

set-current-plot-pen provides a label for the graph and tells the model to start plotting something

plotxy ticks tells the model what to plot every tick (or time point)

current-now-list is a list that contains values representing how many charges are passing through this section of the wire at every tick for the past n ticks where n is the sampling rate in the slider

sum  adds up all the values in a list 

length finds the length of a list. For current-now-list, this will always be the sampling rate

Now, open the code tab of the model. To do this:

1) Scroll down in the model on the left and you will see three tabs "Command Center", "NetLogo Code", and "Model Info".

2) Click "NetLogo Code" to open the code tab. 

You can find the plotting code from above if you scroll down in the code tab to lines 378 and 379. Look in the code tab and find current-now-list. This shows how the current now (stored in current-now-list) is plotted in the graph within the model. 

If you want to see how current-now-list look at lines 204 and 205 which contain code that states if the length of the list is greater than the sampling-rate (that is set by you with the slider), the first item of the list is removed. So, if you set your sampling rate to 50, then my-charge-list shows how many charges pass through this sections of the wire for the most recent 50 ticks. You can see in lines 201 and 202 how the code adds the current at each tick to lists.  

With the model below, there is another list introduced called average-current-list which also shows how many charges are passing through this section of the wire at every tick like current-now-list, but average-current-list does not remove items when the length of the list surpasses the sampling rate. This means all values remain in the list and none are ever removed. 

Explore the model and look at the code tab to examine this.