Lab 2: Electric Fields & Forces

1. Introduction As we learned from our previous lab, a useful model for electric charge includes “rules of charge” that describe the behavior of charged objects. As it turns out, some of this

behavior is a result of a fundamental force of nature called the electromagnetic force (you may recall working with gravity, another fundamental force, in 5AL). But what quantifies the size and the direction (repulsive or attractive) of this force? How do charges become “aware” of each other, and what communicates this force?

In this lab, you will relate the size of the electric force to the size and type of charge as well as their separation by applying Coulomb’s Law. You will also perform some experiments to learn more about the nature of electric fields, as well as how static charges can interact by altering the space surrounding them. These forces help explain the structure of atoms, polarization of the heart muscle, and how and why the charge moves through the circuits you constructed in Lab 1. For relevant references to this lab, refer to Chapters 20.3-20.7 in the Knight textbook. 2. Experiment Activity 1 - Exploring Coulomb’s Law In this activity, you will investigate the relationships between the electric force and size and configuration of stationary (i.e., static) charges. To begin, navigate to the following simulation, and choose the ‘Macro Scale’ option. You should see a screen similar to Figure 1 below. Uncheck the ‘Force Values’ option for now. Investigate the features of the simulation. You can move the circles representing the charges along the top of the length scale in centimeters cm (1 cm = 10-2 m). Discuss and agree within your group how to identify the precise location of the charges along the scale given the circles are ~1 cm in diameter themselves. You can also use the sliders below Charge 1 (q1) and Charge 2 (q2) to vary the magnitude (i.e., size) and sign (positive > 0; negative < 0) of the charge values in microcoulombs µC (1 µC = 10-6 C).

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Now create a configuration of charges with q1 = -6 µC, q2 = +6 µC at a separation r = 3 cm. Should the forces be attractive or repulsive? Does this agree with your prior learning with static electricity in Lab 1? For deliverable 1, include a screenshot of your simulation with the above settings, including a brief description of how to predict for this particular set of charges whether the forces are attractive or repulsive. Check your answer by enabling the force vectors checkbox. By further experimentation with the simulation and its settings, verify the sets of conditions that determine whether there will be attractive or repulsive forces between two charges. For deliverable 2, describe two of your verification experiments and observations (1-2 sentences each), including screenshots of the simulation.

Figure 1: Coulomb’s Law simulation screen Next, let’s connect Newton’s Laws to electric forces. Through your various experiments above, can you find evidence that Newton’s 3rd Law (see Chapter 4.8) applies to electrostatic forces? Share your ideas with your group members. How does the value of the electric force vary with the values of the charges? For deliverable 3, include screenshots and accompanying explanations that justify your conclusions about the dependence on q1 and q2. How does the value of the electric force vary with the distance r between the charges? For deliverable 4, include

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screenshots and accompanying explanations that justify your conclusions about the dependence on charge separation r. Activity 2 - Apply Coulomb’s Law Now you will apply your qualitative understanding of the electric force to calculate the value of Coulomb’s constant (also sometimes called the electric constant) k using Coulomb’s Law in equation 1 below:

.F = k r2|q ||q |1 2 (1)

Our static charges q1 and q2 are separated by a distance r. If we use SI units for the charge in Coulombs (C), the separation in meters (m), and the force F in Newtons (N), then your calculated value of k will also have SI units of N m2 C-2. Determine your value of k by rearranging equation 1 to solve for k and using measurements from your simulation for values of F, q1, q2, and r. For deliverable 5, show your work for determining k from your two sets of measurements, and include screenshots of your simulation. Verify your result for k with research and include a citation. Using your value of k, calculate the electric force for a -4 μC charge that is 3 cm away from a +5 μC charge. For deliverable 6, show your work and your answer for the force in N. Discuss with your group how to verify your answer using the simulation. Activity 3 - Coulomb’s Gauntlet Using your intuition of how the electric force works gained in activities 1 and 2, you get to complete a challenge! Navigate to the following applet to start the Coulomb Gauntlet, which should look like Figure 1. The magenta circle with a ‘t’ inside is your test charge. The first row of controls is (from left-right) to play, pause, frame-advance, and restart the challenge. Your goal will be to get the test charge into the ‘Finish’ box without colliding with a wall. There are also controls for adding positive and negative charges, as well as for clearing all charges and starting over.

Figure 1: Coulomb’s Gauntlet startup

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Figure 2: example run of Coulomb’s Gauntlet Try adding a single positive or a single negative charge to your simulation, click and drag your added charge somewhere nearby the test charge and press the play button . What do you observe? As the test charge moves in response to any force, it will trace its path (see Figure 2). You can also move your added charge as often as you like and watch the test charge respond to your changes. If you want to repeat the experiment with the opposite sign of added charge, select the ‘clear all charges’ button to reset the simulation. You can also experiment with adding your charge and moving it to different starting positions relative to the test charge and see how the test charge responds differently to the Coulomb Force. How can you use this simulation to verify the sign of the test charge? What happens if you add another charge and try again? For deliverable 7, take a screenshot of your gauntlet with your added charge(s) and explain how the outcome of the simulation verifies the sign of your test charge. Now the fun part - by adding and moving any combination of charges you wish, try to maneuver the test charge into the finish box without hitting a wall. If your test charge hits a wall, the game will stop and indicate a collision. If your test charge goes off the screen, select the reset button to try again. You can also start/stop the game and move your added charges around. For deliverable 8, include a screenshot of the outcome of one of your successful runs and a brief (1-2 sentence) explanation of your technique. What is it about the Coulomb Force that made running the gauntlet a challenge? Share your explanation with your group members. Activity 4 - Electric Field of Static Charges In this set of experiments, you will use a simplified model to determine the relevant variables that set the size and the direction of the electric field, which communicates the electric force we’ve been experimenting with so far. We are also interested in how to predict the electric field at a particular location given an arrangement of electrostatic charges. This activity will first introduce you to the shape and the direction of electric field lines around a point charge before considering the field of multiple charges. Navigate to the following charges and fields simulation. You will see various options for displaying electric field, voltage, values (lengths), and a grid. Uncheck the ‘Electric Field’ option and check the ‘Grid’ option for this first part. From the icons along the bottom, drag a single positive (red) point charge (+1 nC; 1 nC = 10-9 C) to the intersection of two major (thicker) grid lines. Your initial workspace should look similar

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to Figure 3. Now check ‘Electric Field’ to display the array of arrows that are fixed to the background grid to display the electric field. Your point charge should now look like one of the regions shown in Figure 4. The grid is configured so that a charge placed off of the major gridlines will look more like the right side of Figure 4 (although odd, it is still correct). How does the result compare to the images of the electric field of a point charge in your textbook? At this point, discuss with and come to agreement with your group members whether or not the simulation is also indicating the strength of the electric field at various points at varying distance from the charge.

Figure 3: initial simulation workspace for a point charge How are the arrows different from field lines? For deliverable 9, include a screenshot of your simulation window with the field of your positive point charge displayed. The icon at the lower right clears the workspace if you need to start again. Figure 4: two possible displays of electric field near the point charge

Now create a +2 nC charge by selecting the +1 nC charge from the icon menu and placing it directly on top of your first +1 nC charge. Did you notice any change in your electric field arrows? As a group, evaluate your understanding of how the electric field is represented in the paragraph above.

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Repeat the above experiment by clearing the workspace and creating a -1 nC (or -2 nC or -3 nC) charge. For deliverable 10, include a screenshot of the simulation that shows your choice of negative point charge with the field line arrows displayed. Describe any difference(s) between this result and what you obtained for deliverable 9. For this last section, we will investigate how the presence of another charge modifies the electric field. Clear your workspace and uncheck the electric field arrows, then create a configuration with a single +1 nC and a single -1 nC charge, similar to Figure 5. Based on your results from this activity so far, predict what the electric field will look like at four (4) different points. Verify your prediction by enabling the field arrows again.

Figure 5: example charge configuration Figure 6: example field sensor on grid Does your result match your prediction? Now create your own configuration of at least two charges of your choice. Display the electric field arrows and observe how the field changes as you move the charges around on the grid. Based on what you have learned about the electric fields of point charges and using vector addition, can you predict where the field of your charge configuration should be strongest? Weakest? Test your predictions by dragging one os the yellow electric field sensors onto your grid, which gives the size of field in Volts/meter (V/m), the relative orientation in degrees from the horizontal, and a vector whose direction and length correspond to the net electric field at that location (see Figure 6). You can also add more than one sensor at different locations on the same workspace. For deliverable 11, include a screenshot of your chosen charge configuration that includes your sensors positioned at points to test your predictions of where the strongest and where the weakest field points are located.

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3. Deliverables For full credit please include the following in your lab report. Follow the template provided on the Weebly Lab 2 page and include one deliverable per Google Slide in the order that they are presented for your set of activities below. Always label your images.

1. A screenshot of your Coulomb’s Law simulation with q1 = -6 µC, q2 = +6 µC

separated by r = 3 cm. 2. Describe two experiments and observations (1-2 sentences each), including

simulation screenshots to determine if the electric force is attractive or repulsive. 3. Screenshots and explanations of how the value of the electric force varies with

the values of the charges. 4. Repeat the above for the dependence on charge separation r. 5. Your result for k from two sets of measurements, including screenshots. Verify

your result and include a citation. 6. Use k to calculate the electric force for -4 μC and +5 μC charges at r = 3 cm.

Show your work and report your force in Newtons (N). 7. A screenshot of your gauntlet with your added charge(s) and explain how to use

the simulation to verify the sign of the test charge. 8. A screenshot of the outcome of a successful run and a 1-2 sentence explanation

of your technique. 9. A screenshot of your electric field simulation window showing the field of your

positive point charge. 10.Repeat the above for your chosen value of the negative charge. Describe the

difference(s) with deliverable 9. 11.A screenshot of your chosen charge configuration showing your sensors at the

points you used to test your predicted locations of strongest and weakest field.

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