Students investigate the mathematical and conceptual behavior of electric fields using point charges and the PhET simulation, Charges and Fields.
Emily Habbert & Daniel DuBrow
NetLogo software:
Electric Field Mapping Questions adapted from: AMTA, Modeling Workshop Project 2013: E1 Charge&Field - ws 4a v3.3
PhET Simulation, Charges & Fields: https://phet.colorado.edu/en/simulation/charges-and-fields
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We just learned how to calculate the Electric Force, which is an interaction between any two charges. Now we are going to investigate what is known as the Electric Field, which is a representation of the effect charges have on the space surrounding them.
Uncheck the box labeled, “Electric Field.” Check the box that says “Grid.” Place a +1nC charge at an intersection of major gridlines in the middle of your screen.
Drag a yellow dot out of the box at the bottom labeled "Sensors" onto the grid. Drop the sensor on the page. Then click and hold the mouse button down to drag the sensor around the charge.
What do you notice about the direction of the arrow at all times?
As you click and hold with your mouse, the yellow sensor will move around the screen. What do you notice about the magnitude of the vector (the length of the arrow) as you move farther away from the charge?
What do you think the arrow on the yellow sensor represents?
Now release the mouse button to leave that sensor stationary on the screen. Place three more yellow sensors anywhere on the screen so that they create 3 more vectors of identical length.
What do the four points have in common?
Now, let's figure out a mathematical model that describes an electric field made by one point charge.
Uncheck the box labeled, “Electric Field.” Check the box that says “Grid.” Again, place a +1nC near the top center of the simulation at the intersection of 2 major gridlines.
Place a sensor 10 (small) gridmarks to the right of the point charge. Now, place a second sensor 20 gridmarks below the point charge. Compare the length of the two vectors.
What can you conclude about the relationship between electric field strength and distance? Predict and record a mathematical model that describes the relationship between electric field strength and distance (it's okay if it's not correct yet!).
If you place a sensor 30 gridmarks to the left of the point charge, how will it compare in size to the first vector? Test your prediction and explain your results. Do you still agree with the mathematical model you predicted above? If not, correct it in the previous answer box.
Place another +1nC charge on top of your original +1nC charge so that you have a +2nC charge in the center of the screen.
What happens to the strength of the electric field at the location of each sensor that you had previously placed? What can you conclude about the relationship between electric field strength and the magnitude (strength) of the point charge?
Predict what will happen to the length of the electric field vectors if you place a third +1nC charge at the center. Was your prediction correct? Explain. Write a mathematical model describing the relationship between electric field and charge.
Again uncheck the box labeled, “Electric Field.” Check the box that says “Grid.” Place a +1nC and a –1nC charge on the screen 20 grid marks apart. (Such a configuration of charges is called a dipole). Use the yellow E-field Sensors to probe the electric field around the two charges.
In what place or places is the field the strongest?
In what place or places is the field the weakest?
Check the box titled, “Electric Field.” What appears? What do these arrows represent?
In general, we draw electric field lines as shown below, by connecting what would be a set of arrows into a smooth curve.
When examining this type of field drawing, how is the field strength conveyed? What about the field direction? Explain.
Place two +1nC charges 20 grid marks apart. Use an E-field sensor to probe the electric field around the two charges.
You will find the field is weak far from the positive charges. Where else is the field very weak (even zero) in strength?
If you placed a small positive test charge halfway between the two +1nC charges, how would it move?
Describe as best you can the general direction of the field in the box below. Now, check the box on the simulation labeled "Electric Field." Were you correct?
The field lines around a single charge are always straight. Why do the lines curve for a grouping of 2 (or more) charges? Suggest a possible "rule" about the behavior of electric field lines in this case.
Create two charged “plates,” one positive and one negative by putting 10-20 negative charges in a line and then 10-20 positive charges in a line below the negative charges.
Sketch what you think the field lines would look like in the area between the plates, as well as around the outside of the plates.
Check the box, “Electric Field,” and consider your prediction from question 5.1. Was your prediction correct?
If you placed a positive test charge in between the plates, where would it move? Why?
This simulation shows electric field lines for a fixed dipole charge distribution. Click "setup," and then click the screen to place a positive charge somewhere in the field. Now click "go" to see how the positive charge moves in response to the field. Do this a few times, placing the charge in different locations.
Did you test several initial locations for a positive charge?
Does the positive test charge move along field lines? Why or why not?
What type of motion (constant velocity vs. accelerated) is the charge experiencing? How is the field contributing to the charge's motion? How can your prior knowledge about forces and motion explain what you see?
(Use this question as an opportunity to tie all the pieces together and really show me what you know!)
In the previous page, you brainstormed a few rules for how to draw electric field lines. Here are the rules physicists usually use to draw field lines:
What questions do you have about these rules so far?
Below is an image from the PhET simulation with two positive charges. Using the rules listed above, sketch what you think the field lines would look like for this charge distribution.
Search for an image of the field surrounding two positive charges. How does your drawing compare to the image you found?
The PhET simulation does not use electric field lines to depict the field surrounding a charge. How does the PhET simulation show field strength and direction? When might the PhET "field arrow" model or the electric field line model be best to depict the electric field?
The diagram below shows a solid metal conductor with electrons located on the surface, as we saw in Lesson 1 on charge interactions.
Using the rules we discussed, draw what you think the electric field lines look like outside the conductor due to the charges on the surface.
In a few sentences, explain your reasoning for why you drew your sketch the way you did in question 6.5.
The diagram below shows a solid metal conductor with electrons located on the surface, as we saw in Lesson 1 on charge interactions.
Using the rules we discussed, draw what you think the electric field lines look like inside the conductor due to the charges on the surface.
In a few sentences, explain your reasoning for why you drew your sketch the way you did in question 6.7.
How did your field diagram for outside the sphere (Q6.5) compare to inside the sphere (6.7)? Does this difference make sense based on what you know about charge behavior from earlier in the unit?
