Electrostatic force lab

Lab 1 – Coulomb’s Law Investigating the force between charged objects Purpose: to investigate the quantitative aspects of the electric force between two objects, including the dependences on both distance and charge. Also, to place the electric force into context with our force problem-solving process from first-semester physics. Introduction Coulomb’s Law: “The magnitude of the electric force that a particle exerts on another is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.” Mathematically, the magnitude of this electrostatic force FE acting on two charged particles (q1, q2) is expressed as: 𝑞 𝑞 FE = k 𝑟1 2 2 Where r is the separation distance between the charged objects and k is a constant of proportionality, called the Coulomb constant, k = 8.99 × 109 Nm2/C2. Part 1 – Determining the value of Coulomb’s constant k Experiment 1-A: How the force depends on distance 1- Click on the following link and select the “Macro Scale” version of simulation. Set your own values for Charge 1 (q1) and Charge 2 (q2), and write their values in the first row of Table 1 below. These values will remain the same for all trials in Table 1. https://phet.colorado.edu/sims/html/coulombs-law/latest/coulombs-law_en.html 2- Change the distance between the two charges to match each of the values given in Table 1. The ruler is marked in centimeters, and each charge can be placed to the nearest centimeter. 3- For each distance value, record the force value given by the simulation. 4- Fill in the rest of Table 1 by calculating the values of r2 and 1/r2 in the specified units. Table 1 q1 (𝜇C) q2 (𝜇C) -4 8 r (cm) 10 9 8 Use the same charge values above in all trials that follow. 7 6 5 4 3 2 r2 (m2) 1/r2 (1/m2) FE (N) 0.01 100 28.760 0.0081 123.457 35.506 0.0064 156.25 44.938 0.0049 204.08 58.694 0.0036 277.778 79.889 0.0025 400 115.041 0.0016 625 179.751 0.0009 1111.111 319.557 Analysis for Experiment 1-A: 5- Use Excel software and the data from Table 1 to make a graph of FE versus r. (With r on the horizontal axis.) What do you notice about the shape of the graph? Fe VS r 1200 1000 Fe (N) 800 600 400 200 0 10 9 8 7 -200 6 5 4 3 r (cm) As the distance decreases the force increases 6- Use Excel to make a graph of FE (in Newtons) versus 1/r2 (in 1/m2). Add a trendline to the graph and use its slope to find Coulomb’s constant k. Fe VS 1/r2 1200 1000 Fe (N) 800 600 400 200 0 10 -200 9 8 7 6 1/r2 (1/m2) 3 5 4 3 7- Calculate the percent error in k (where kknown = 8.99 × 109 Nm2/C2). Also, is the percent error value what you would expect in this case? Why or why not? Note: Include screenshots of all created graphs with your lab report. Experiment 1-B: How the force depends on charge 8- Reset the “Macro Scale” simulation, and set the value of charge q2 and the distance r, as shown in Table 2. These values will remain the same for all trials in Table 2. https://phet.colorado.edu/sims/html/coulombs-law/latest/coulombs-law_en.html 9- Change the charge of object 1 to match each of the values given in Table 2. In each instance, record the value of the electric force given by the simulation. Table 2 q1 (C) q2 (C) r (cm) 10 5 6 9 8 7 6 Use the same values above for q2 and r in all trials that follow. 5 4 4 FE (N) 3 5 Analysis for Experiment 1-B: 10- Use Excel software and the data from Table 2 to make a graph of FE (in Newtons) versus q1 (in Coulombs). What do you notice about the shape of the graph? 11- Add a trendline to the graph and use its slope1 to find Coulomb’s constant k. (See the footnote below for a hint about graphing accurately in Excel.) 12- Calculate the percent error in k (where kknown = 8.99 × 109 Nm2/C2). Also, is the percent error value what you would expect in this case? Why or why not? Note: Include screenshots of all created graphs with your lab report. 1 By default, the slope of this graph will probably be displayed in scientific notation but with far too few digits. To correct this, right-click on the displayed equation, select “Format Trendline Label…”, change the Category to Scientific, and increase the number of digits to at least 3. 6 Wrapping-up Part 1: 13- Are the two values you calculated for k similar to each other? Should they be? 14- If one of the charge values is increased, what kind of change would we expect to see in the value of the force? Possible answers are directly proportional, inversely proportional, proportional to the square, etc. 15- If the separation between charges is increased, what kind of change would we expect to see in the value of the force? Possible answers are directly proportional, inversely proportional, proportional to the square, etc. 7 Part 2 – Determining the charge Q on a repelling balloon Consider the following experiment, which has already been performed. You do not need to set up the experiment yourself. Measurements for you to analyze will be given below. A. Blow up 2 balloons, tie them closed, and charge them by rubbing with fur. Try to get an even charge by rubbing all over each balloon, not just one part. The rubber of the balloon is an insulator so charge tends to stay in one place. B. Now tie the balloons to a pair of strings hanging down from the ceiling. They will most likely discharge during this process so once they’re hung, charge them again. The balloons should separate from each other and make a 10- or 20-degree angle between the strings. C. Measure the vertical height h, and/or the diagonal distance L along the string, from the ceiling to the center of one of the balloons. D. We need to determine the angle between the strings, but use of a protractor at the ceiling is usually too difficult. Instead, measure the distance r between the centers of the balloons, to the nearest centimeter or two. Trigonometry can then be used to find the half-angle 𝜃 (shown in the diagram below) based on the values of r and h (or r and L).