Part a - Simulation 1:One Point (Positive) Charge

Find Your Potential!

Teacher Notes

Part A - Simulation 1:One Point (Positive) Charge

Google “PhET”, go to the University of Colorado website that is the first choice, and run the Physics simulation called “Charges and Fields”

Note: Use the Google directions if sending this home with students. If doing it in lab or classroom you may want to download the PhET simulation and place it on the desktop of the computer to avoid internet/network interruptions during the lab.

2.In the control box, at the bottom right of the screen, click on grid and show numbers. Note that 10 units is equal to one meter (see scale on the bottom left window).

3.Drag one positive charge onto the grid. Center the charge in the intersection of two grid lines. This will be the point of origin (0, 0). Place the Voltage meter at (-1, 0). Record the values for the x & y coordinates in meters as well as the magnitude of the Potential (not the degrees) at that point in columns x, y, and V. For the next steps, repeat for 20 data points. Choose points 5 points in each quadrant randomly ranging from -1 to 1 on both the x and y axis.

Sample Data

Part A: Single Positive Charge

x (m) / y (m) / Potential (V)
-1 / 0 / 9
-.3 / .1 / 29.2
-.2 / .7 / 12.5
-.7 / .9 / 7.8
-1.1 / .4 / 7.6
-.8 / .2 / 11
-.5 / -.5 / 12.6
-.2 / -.2 / 29.5
-.4 / -.3 / 18.1
-.8 / -.8 / 7.9
-.2 / -1.2 / 6.8
0 / -.4 / 22.2
.5 / -.2 / 16.4
.2 / -.4 / 19.5
.3 / -.7 / 11.8
1.2 / -1 / 5.7
0 / 8 / 11.4
.7 / .7 / 9
1.2 / .7 / 6.4
.4 / 1.2 / 7.2
.2 / .6 / 14.2

4.Use Excel to chart your data, graph it and find the line of best fit or “trendline” as Excel calls it.

Open a new Excel file.

Put “x (m)” at the top of column A, “y (m)” at the top of column B, “r (m)” at the top of column C, and “Potential (V)” at the top of column D.
Type your data into the appropriate columns.
The “r (m)” column is the radial distance of the potential and is calculated . Excel will calculate this value for each point. Type this equation into Excel, click on row 2 of Column r (m), type “=SQRT(“, click on row 2 of Column x(m), type “^2+”, click on row 2 of Column y(m), type “)^.5. It should look like “=(A2^2+B2^2)^.5”. Press enter.
Assuming that you put the column headings in row 1, click on row 2 of Column r(m). Press Ctrl-C (Apple Command-C) or right-click, “Copy” to copy the equation. Click on the row below and drag to the last row of data (it should highlight Row 2 to Row 21) and press Ctrl-V (Apple Command-V) or right-click, “Paste”.
Select the r(m) and Potential (V) columns by clicking on “C” & “D” at the top of the columns. The columns will be highlighted.
To insert a graph (Excel calls it a “chart”), click on the “Insert” tab, then “Charts” >”Scatter” icon, then choose the first graph that shows the axes and data points scattered on it. A graph titled “Potential (V)” should appear. (Note: Different versions of Excel may require other directions. If this series of instructions does not match what is on your system, use the “Help” feature for Excel to add a chart.)
Teachers – if you are doing this with all of your students in a classroom or computer lab where all of the computers have the exact same version of Excel, it may be worth while for you to work through it and give more specific instructions here. If students are taking it home, it is recommended that you leave the general directions and encourage them to use the “Help” feature as stated.
Format the chart to have labels and units on each axis using “Chart Tools”. Double click the graph title and change it to “Potential (V) vs r(m)”. Change the Axis Titles to Potential (V) on the Vertical axis and r (m) to the Horizontal Axis. Again, specifics directions may vary with versions of Excel. Consult the help feature if needed.
Make a note that this data represents the potential of a single positive charge. Click on Column D Row 1 “Potential (V)” and change it to “Potential (V) of a Single Positive Charge”. Press Enter.
Students should label this spreadsheet and graph to identify it as data for a Single Positive Charge. This can be done as above or students could add a second line to the title of the graph.
Add a line of best fit or “trendline” and find its equation for your data. Use the “Power" equation to model your data. Be sure to check the box so that the equation appears on your graph. Consult the “Help” feature if needed.
Move the equation box so that it is displayed clearly. Resize the font if needed (at least 14 font is recommended). Edit the equation box so that it shows the equation with the meaningful variables “V” and “r” instead of the generic “y” and “x” respectively.

Below is some sample data and an example of how the spreadsheet could appear.

Analysis – Single Positive Point Charge

Compare the equation for Electric Potential with your “trendline” equation. What relationship can be seen?

The simplified equation for the Electric Potential near a point charge is
The equation of the “trendline” from the “power” regression is
Students should get a power of d to be very close to -1. If we round that value to -1 the equation becomes

The constant A then corresponds to the product of kq

Use the values from the “trendline” equation to calculate the experimental value of the charge.

We are assuming the value of k = 9E9 Nm2/C2 is previous knowledge.
In our sample data, the value of A is 8.9, so …

8.9 = (9E9)(q)

q = 8.9/9E9 = 9E-10C or 0.9E-9 C

Theoretically the value of the charges in the simulation are 1 nC. Find your percent error.

List some possible reasons for this error.

Error possibilities include
accurate placement of charges
accurate placement of the meter

How did taking data in all four quandrants affect your data? What was good about it? What was bad?

The purpose of this question is to get students to acknowledge that the potential is equal to distance from the charge regardless of which direction they move away from the charge.

Part B -Simulation 2 : Opposite Point Charges

Open the “Charges and Fields” PHet simulation (or “Clear All”), Click on grid.Place a positive charge as you have done in the Part A.
Drag a negative charge and place it 1 meter to the right of the positive charge.
Along the x-axis, take 5 points of data on the left side of the positive charge, 7 points between the charges, and 5 points on the right of the negative charge within the range of x=-1 m to x=2 m. Record the values in the table of the answer sheet.
Use Excel to plot the Potential (V) vs r(m) as you have done in Part A. Note: for “r” you can simply use the x – position.

Students should have something similar to what is shown below.

Analysis- Opposite Point Charges

Describe in words the trends in your data in each of the regions of this charge system.

Outside the system near the positive:

As you move from a distant point toward the positive charge, the value of readings increases

Between the charges:

Moving along the line from the positive to the negative charge, readings decrease (smaller positive values) until you cross the midpoint at which they turn negative, then continue to decrease (larger negative values) as you approach the negative charge.

Outside the system near the negative charge:

Moving away from the negative charge causes the readings to increase (become smaller negative values).

Is this data what you expected? Were there any surprises? Give specific examples.

Based on your data, what is the electric potential at the location of the charge? Cite evidence of your claim.

Students did not take data at the charges. If they did the simulation would give them a very large value and because placement of the meter would never be exactly on top of the center of the charge, you would not get the answer which is that the potential is undefined at that point.

Using the Electric Potential formula, what would you expect the value to be at r = 0. Does this match your data?

The idea of the limit as r  zero, making the value approach an asymptote may need to be developed with students to enable them to answer this question.
If r=0, then kq/r is undefined because you can’t divide by zero
My data shows that the Potential approaches an asymptote from both sides at the location of the charge.

Part C - Simulation 3 : Two Like Charges

Open the “Charges and Fields” PHet simulation (or “Clear All”), Click on grid. Place a positive charge as you have done in the Part A.
Repeat Part B using two positive charges.
Plot the Potential (V) vs r (m). Note: for “r” you can simply use the x – position.

Students should have something similar to what is shown below.

Analysis – 2 Like Charges

Describe in words the trends in your data in each of the regions of this charge system.

Outside the system:

As you move from a distant point toward the positive charge, the value of readings increases

Between the charges:

Moving along the line from one charge to the other, readings decrease until you cross the midpoint at which begin to increase again approaching the other charge.

Is this data what you expected? Were there any surprises? Give specific examples.

Based on your data, what is the electric potential at the location of the charge? Cite evidence of your claim.

Again, the potential is undefined at the location of the charge.
The data seems to approach an asymptote at the charge location.