PHYS 122 Lab 2 Report Draft

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Feb 20, 2024

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Name(s): Kirsten North Date: 09/12/2023 Electric Fields Purpose The objective of this laboratory experiment is to enhance comprehension of the electric field concept and its visualization through the use of field lines. Additionally, we want to develop a connection between the electric field and the simulated electric force generated by a designated source charge magnitude, considering different magnitudes of test charges. Apparatus - Coulomb’s Law lab simulation: https://phet.colorado.edu/sims/html/coulombs-law/latest/coulombs-law_en.html Procedure 1. Recording the source charge: Access the simulation at the atomic scale. Record the value of the positive source charge. This source charge corresponds to the amount of charge at the 0 pm position. This remains constant throughout the experiment and serves as a control. 2. Selecting test charge position: Choose a specific position in the simulation to place the test charge. This position can be any measurable distance away from the source charge. Record the distance between the test charge position and the source charge. 3. Recording force: Record the force acting on the test charge due to the source charge at the chosen position.
Name(s): Kirsten North Date: 09/12/2023 4. Varying test charge amount: Adjust the amount of test charge by using the slider for charge 2 in the simulation. Record the value of the force acting on the test charge each time you change the test charge amount. 5. Data table: Create a data table to record the following information for each test charge amount: a. Test charge magnitude (varying from 0 to +10 e, where e is the elementary charge, 1.602 x 10 -19 C ). b. Force magnitude acting on the test charge. Note the sign of each charge (positive or negative) and whether the force is attractive or repulsive. 6. Drawing a force diagram: Create a single, representative force diagram that visually represents the force acting on the test charge due to the source charge. 7. Data entry into Excel or nPlot: Put the recorded data from the table into an Excel spreadsheet or nPlot. 8. Independent and dependent variables: The independent variable is the test charge magnitude as it is intentionally varied by changing the slider for charge 2 in the simulation. The dependent variable is the force magnitude acting on the test charge. This depends on the test charge magnitude and is recorded as you change the test charge amount. Data q 1 (e) q 2 (e) Distance (m) Force (N) q 2 Magnitude (C) 2 4 2 x 10 -11 4.61 x 10 -6 6.40 x 10 -19 2 5 2 x 10 -11 5.77 x 10 -6 8.01 x 10 -19 2 6 2 x 10 -11 6.92 x 10 -6 9.61 x 10 -19 2 7 2 x 10 -11 8.07 x 10 -6 1.12 x 10 -18 2 8 2 x 10 -11 9.23 x 10 -6 1.28 x 10 -18 2 9 2 x 10 -11 1.04 x 10 -5 1.44 x 10 -18 Based on the data in the table and the sign of each charge, all of these forces are repulsive. Evaluation of Data Force diagram: 2 e 4 e F = 4.61 x 10 -6 The diagram visually shows the scenario with positive charges where the test charge (+4e) experiences a repulsive force when placed near the source charge (+2e).
Name(s): Kirsten North Date: 09/12/2023 - Write the equation of best fit for this line, using the variables you have plotted. ࠵? = ࠵?࠵? + ࠵? Or it could be seen as: ࠵? = ࠵? ∗ |࠵?| + ࠵? A = (6.8937166 ± 0.17486528) × 10 12 B = (2.6249206 ± 1.8825352) × 10 -7 - What are the units of the slope in the equation of the line that you have just written? What is the value of the slope? It’s probably necessary to click on the ‘format trend line label’ and choose scientific notation. The units of the slope A would be N/C. This represents the force per unit magnitude of the test charge. Force Magnitude (N) q2 Magnitude (C) E (N/C) 4.61 x 10 -6 6.40 x 10 -19 7.20 x 10 12 5.77 x 10 -6 8.01 x 10 -19 7.20 x 10 12 6.92 x 10 -6 9.61 x 10 -19 7.20 x 10 12 8.07 x 10 -6 1.12 x 10 -18 7.20 x 10 12 9.23 x 10 -6 1.28 x 10 -18 7.21 x 10 12 1.04 x 10 -5 1.44 x 10 -18 7.22 x 10 12 - Write the expression for Coulomb’s law, this time with q 1 & q 2 replaced by q source and q test . Factor out q test and divide both sides by q test . This quotient F / q test is in general the
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Name(s): Kirsten North Date: 09/12/2023 meaning of the electric field strength. In this case the source of the electric field was the source charge (point source). ࠵? = ࠵? ∗ |࠵?࠵?࠵?࠵?࠵?࠵?࠵? ∗ ࠵?࠵?࠵?࠵?࠵?| ࠵? ! ࠵? = ࠵? ∗ |࠵?࠵?࠵?࠵?࠵?࠵?࠵?| ࠵? ! ∗ |࠵?࠵?࠵?࠵?࠵?| ࠵? = ࠵? ∗ |࠵?࠵?࠵?࠵?࠵?࠵?࠵?| ࠵? ! - Using the values you’ve recorded earlier, calculate the % difference between F / q test and the slope of the line. F / q test = 7.20 x 10 12 Slope of the line = 7.07 x 10 12 Absolute difference: 1.30 x 10 11 Average of those values: 7.135 x 10 12 % Difference: (absolute difference/ average) x100 = 1.82% - What does the slope of the line represent? The slope of the line represents the relationship between the force (F) and the magnitude of the test charge (q test ). The slope quantifies how the force changes as the magnitude of the test charge varies. In other words, it represents the electric field strength (E). - Describe qualitatively the relationship between the amount of test charge and the magnitude of the force. The qualitative relationship observed in this lab is that as you increase the magnitude of the test charge, the magnitude of the force it experiences increases linearly, and this relationship is characterized by a constant electric field strength (E). Conclusion - Write the general physics formula for the relationship that you’ve discovered from the graphical analysis. ࠵? = ࠵? ∗ |࠵?࠵?࠵?࠵?࠵?| - Describe in words, using the proper physics terms, the relationship between the variables investigated above. The relationship between F and |q test | is characterized by the direct proportionality and linearity. This meaning that if you change the magnitude of the test charge, the force it experiences changes in a consistent and proportional way, following a straight-line
Name(s): Kirsten North Date: 09/12/2023 pattern on a graph. As the magnitude of the test charge increases, the force it experiences increases linearly, following the principles of Coulomb’s law. - Must we have a test charge at the chosen location in space in order for an electric field to exist there? What is the requirement for the existence of an electric field? Based on this lab, the presence of a test charge at a chosen location in space is not a requirement for an electric field to exist there. Electric fields exist in space due to the presence of charged objects, such as the source charge in this experiment. - Does the electric field at a fixed position change with the amount of test charge? No, it does not. The electric field strength (E) at a fixed position remains the same as long as the source charge and the distance remain constant. - Describe the meaning of the term electric field in your own words, as it pertains to this experiment. The term electric field refers to an invisible area or region in space around a charged object, known as the source charge. This field exists because the source charge exerts a force on other charged objects in its vicinity. The electric field is a way of describing the effect that the source charge has on its surroundings due to its electrical charge. - Sketch the pattern of the electric field lines from a positive point source, include the pattern in your report. How does this pattern change if the point source is negative? For a positive source charge, the lines radiate outward, indicating repulsion, while for a negative source charge, the lines point inward, indicating attraction.