MATERIALS - The Simulation for this lab is at https://www.geogebra.org/m/yYyHRNsV - A spreadsheet (Excel or Google sheets) - Electronic Data notebook V. PROCEDURE Open the simulation. The simulation calculates and displays the magnitude and direction of the force on up to 4 charges (q1, q2, q3, q4) that is due to the presence of a nearby charge, identified here as charge Q. The magnitudes of the charges in the simulation can be varied from negative to positive or zero. The units are in microcoulombs (1 mC = 1x10-6 Coulombs). Explore what the simulation can do by changing the magnitudes, signs, and location of the charges, and setting the charge magnitude to some to zero (which effectively eliminates the charge from the simulation) The left menu of the simulation screen shows the (x,y,z) coordinates of the position of the charges. The resulting arrow on the cartesian plot is the vector of the Force that is experienced on each of the charges. Near the bottom of the left menu you will find the magnitude of the (x,y,z) components of those force vectors.

Montgomery College PHYS 262 Coulomb's Law Setup Set the multiple interactions slider to 1. This setting is consistent with the superposition principle - it includes the contributions to the Coulomb force on a particular charge, q, due to all the surrounding charges. (When the multiple interactions slider is set to 0, then each pair of charges is examined individually and the contributions from other neighboring charges are neglected, which may be interesting for some purposes, but is not what happens in reality.) In Part 1, you will examine the magnitude and direction of the Coulomb Force between two charges, Q and q1. Set the magnitude of q2-4 to zero, place Q at the origin, and place q1 at some location along the positive x axis. It does not matter where the three other charges are located. Part I 1. Observe the Coulomb force on each charged object. Quantitative values for the (x,y,z) components of the Coulomb force vectors are provided at the bottom of the left-hand column, and are labeled, "FE." Compare these numerical values with the lengths of the vectors on the screen. Do the forces on each charge have the same magnitude? Why or Why not? 2. Change the separation distance to at least five different values. Record the position and the resulting Coulomb Forces. 3. Using a spreadsheet, construct a graph of Coulomb force (on the vertical axis) vs. separation distance r (on the horizontal axis). Be sure to label the graph and axes and include the units of each axis. Include a text box on your plot that contains the value of the charge on each object. Make a second plot of the Coloumb force vs 1/(square of the separation distance). 4. Determine the mathematical relationship represented by the data using a curve fit (trendline) for both curves. In the first curve (vs r), how does this relationship compare with Coulomb's law? In the second curve, what is the equation of the line, and what does this slope represent? (hint: recall your analysis from the Hooke's Law lab) Part II In Part II, you will keep the positions of the two charges constant and will vary the magnitude of the charge on q1. Let q1 be a positive charge for this sequence and leave the magnitudes of q2-4 set at zero. 1. Observe the Coulomb force on each charged object as you change the magnitude of q1. Are the forces the same magnitude on each charged object? Why or Why not? 2. Change the charge on q1 to at least five different positive values. Record the charge and the resulting Coulomb Force in a table. 4 Montgomery College PHYS 262 Coulomb's Law 3. Using a spreadsheet, Construct a graph of Coulomb force Fe (on the vertical axis) vs. charge (on the horizontal axis). Be sure to label each graph and axis. Include a text box on your plot that contains the separation distance between the charges. 4. Determine the mathematical relationship represented by the data using a curve fit (trendline). How does this relationship compare with Coulomb's law? Part III In Part III, you will add to the data that you collected in part II by examining at least five values of q1 that have negative charges (electrons). Leave the magnitudes of q2-4 set at zero, as before. 5. Change the charge on q1 to at least five different negative values. Record the charge and the resulting Coulomb Force. 6. Add to the spreadsheet that you developed in Part II. Construct a new graph of Coulomb force Fe (y axis) vs. charge (x axis), now including all positive and negative charges. Be sure to label each graph and axis. Include a text box on your plot that contains the separation distance between the charges. 7. Is this plot what you expected from Coulomb's law? Explain why. What general statements can you make about the force between charges? Part IV In Part IV, we will expand the simulation from two charges to three. Now, your screen will have Q, q1, and q2. Make sure q3 and q4 are still set to 0. Q and q1 should remain at the position that you left them in Part III. For mathematical convenience, place q2 on the positive vertical axis. Assign it a value that is the same magnitude as q1 and make both q1 and q2 positive. You should see three force vectors, one on each charge. If you do not see three vectors, then your setup is not correct. 1. In Parts I-III, the force vectors were on a line that connected the pairs of charges. Why are the three force vectors no longer on an imaginary line that you could draw between each of the three pairs of charges? 5 Montgomery College PHYS 262 Coulomb's Law 2. Using Coulombs law, calculate the force that acts on q2 that is caused by Q. Then calculate the force that acts on q2 that is caused by q1. Add these two forces together. Calculate the % difference between your calculated total force on q2 and the value predicted in the simulation. If the result is not very close, say within 5%, then repeat this part. VI. QUESTIONS 1. What happens to the force between two charges when the magnitudes of both charges is doubled? 2. Describe the difference in the forces between positive and negatively charged objects. 3. In each part above, how does the force on charge Q compare to the force on the field charges (that is, q1 and q2)? How would you describe the nature of Coulomb forces? 4. According to the graph produced in Part I, what is the relationship between separation distance and Coulomb force? 5. According to the graph produced in Part II, what appears to be the relationship between charge and Coulomb force? 6. Suppose the magnitude of the Coulomb force between two charged objects is 10N when they are separated by a distance of 10 m. If the same charges were separated by a distance of 5m, what will be the magnitude of the Coulomb force between them? 7. Suppose the magnitude of the Coulomb force between two charged objects is 10N. o If the charge strength of one of the objects is doubled, what happens to the magnitude of the Coulomb force between them? o Suppose the charge on both objects is doubled. What happens to the magnitude of the Coulomb force between the two objects? 8. When two electrons are separated by a distance of 1 centimeter, what is the ratio of the Newtonian Gravitational Force between those electrons and the Coulomb force? Do those two forces act in the same direction, or in opposite directions? If those electrons are located in our classroom, how does the weight of the electron compare to the magnitude of those two forces? VIII. SUBMITTAL REQUIREMENT This is an informal lab. All results should be within your Electronic Data Notebook. Compile your data tables, plots, calculations, and the answers to questions both within the lab and in Part V into a single pdf file and submit to your instructor