Module 2-1 Equipotential I (1)

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Feb 20, 2024

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Physics 9L/19L Module 2.1: Electric Potential & Electric Field Module 2.1: Electric Potential & Electric Field Version 1.0 (2/9/2020) Abstract: You will determine the electric field by measuring electric potential for various charge distributions. Learning Goals: After completing this lab, you should be able to: 1) Use a digital multimeter (DMM) to detect electric potential. 2) Use a power supply to apply a potential difference to lab apparatus. 3) Visualize electric fields and electric potential using field lines and contour lines. 4) Estimate the magnitude of the electric field from the previously detected equipotential lines. PART 1: INTRODUCTION In this lab, you will explore the relationship between electric potential and electric field. For a point charge, the electric potential is V = kQ r Electric potential has units of Volts. Note that the electric potential is not the same thing as potential energy. C. v5 Given the electric potential, you can find the electric field (in 1 dimension) by E x = − dV dx − ∆V ∆ x The following figures from the PhET simulation: Charges & Fields illustrates the relationship between field and potential. Figure 1. +2 nC to the left and -1 nC to the right. Electric field direction is indicated by the arrows. Electric field strength is indicated by the arrows’ transparency. Notice in Figure 1 that the electric field lines start at positive charge and go towards negative charge. 1

Physics 9L/19L Module 2.1: Electric Potential & Electric Field Figure 2. +2 nC to the left and -1 nC to the right. The electric potential values are indicated by color. In Figure 2, notice how the positive 2 nC charge dominates − 1 nC charge. White indicates where the potential is zero Volts. Figure 3. +2 nC to the left and -1 nC to the right. The electric potential values are indicated by color. Equipotential lines are shown. Figure 3 includes the equipotential lines. The voltage is the same along an equipotential line. An equipotential line is also called a contour line. Figure 4. +2 nC to the left and -1 nC to the right. The electric potential values are indicated by color. Equipotential lines and electric field arrows are shown. Notice that the electric field lines are ori- ented perpendicular to the equipotential lines. The electric field is strongest where the equipotential lines are closest together. 2

Physics 9L/19L Module 2.1: Electric Potential & Electric Field The electric field arrows effectively point from high potential towards low potential. Overview  You will locate and draw the equipotential lines for different charge distributions.  You will use these lines to sketch the electric field lines and calculate the its magnitude at various locations. PART 2: EQUIPMENT SETUP 1. The power supply and multimeter should be off at the beginning of the lab. 2. You will be mapping equipotential contour lines for the three different charge configurations shown below. 3. Attach a sheet of graph paper (from TA) to the top of the CENCO Overbeck Electric Field Mapping apparatus. By pressing down on the board, you can secure the paper under the rubber mounts near the corners of the board. Do not reposition the paper once you’ve started mapping equipotentials. 4. Position the plastic template for the configuration at your station over the blank paper using the alignment pegs at the top of the apparatus board. Trace the appropriate outline, and then place the template to the side. 5. WITH THE POWER SUPPLY OFF: a. Connect a black lead from the negative (–) output from the power supply to the electric binding post on the left-hand side of the apparatus, and b. Connect a red lead from the positive (+) output from the power supply to the 3 Figure 6. Experimental Setup

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Physics 9L/19L Module 2.1: Electric Potential & Electric Field electric binding post on the right-hand side of the apparatus. c. Connect the red lead from the Voltage plug on the multimeter to the long U-shaped probe. d. Connect the black lead from the common (COM) plug on the multimeter to the binding post on the left-hand side of the apparatus by stacking the black/COM multimeter lead on top of the black power supply lead connected at the same binding post (see Figure 6). 6. Position the U-probe with one arm passing under the apparatus to make an electrical contact between the resistance board and the multimeter and the other arm passing on top; the silver thumbscrew and the hole for a pen or pencil to pass through to mark the paper should be on top. Note: do not squeeze the U-probe to squish the apparatus while moving the probe on the board; this damages the resistance board underneath. Always move the probe using the silver thumbscrew on top. PART 3: PREDICTIONS 1. Based on the figures from the PhET simulation and using the whiteboards provided, sketch your prediction of the equipotential contour lines for each charge configuration. Take a picture of each prediction and paste them below. Then, explain your thinking: why did you draw the equipotential contour lines in this way? [paste your 3 prediction contour plots here] We think the contour lines will be two large spheres. The top and bottom have different volt values from each other. The is an area in the middle that has a value zero so we believe there will be space between each line. 2. Now, play around with the U-probe for a few minutes. Pay attention to the values you see on the DMM. What rule will you and your partner use to decide whether or not a particular point is on a specific contour? Note: you are free to modify your rule as you collect data but do not change your answer here . There are no “correct” answers at this point. We just want to make a record of your current thinking before you start collecting data. [write your rule(s) for determining if a value is on the contour here] If there is a cluster of the same points that is considered the contour line. 3. How many data points do you think you’ll need to determine the general shape of a contour? How many contours do you think you’ll need to reveal the general shape of the equipotential surrounding the objects? Do you anticipate any places where you’ll need more data points compared to other regions? 4

Physics 9L/19L Module 2.1: Electric Potential & Electric Field [write your plan for taking data points here] PART 4: PROCEDURE 1. Turn the power supply on and dial up the voltage to approximately 7-10 Volts, using a minimum amount of current. The power supply maintains that potential difference between the two electrical binding posts, which are connected to the various conducting areas on the apparatus board. 2. Turn on the multimeter to the VDC setting. 3. Measuring and marking equipotential contour lines. a. Using the probe and the multimeter, measure the potential at a few different locations within each of the charged regions you traced with the template. Label each charged region with the measured potential and note the voltage applied with the power supply. b. Marking the equipotential contour lines : Move the probe (using the silver knob) until you find a position where the multimeter reading is 1V and mark that position on the paper (there is a hole on the top of the U-probe for this purpose). Find 4 – 5 other positions, separated by 1 – 2 centimeters, where the multimeter reading is also 1V. Connect these dots by a smooth, dashed line and write down the measured value (1V in this case) near the end of the line. You have mapped your first equipotential for this charge configuration. c. Repeat step (b) for every 0.5-1V until the applied voltage is reached, making sure to label each equipotential contour line with its represented value. To better see the pattern of the equipotential contour lines, add more lines where needed. Each set of electrodes should have at least 7 lines of equipotential. d. Turn off the power supply and the multimeter after taking your measurements. 4. Once you’re finished with one charge configuration, move to another one that is available. 5. Follow steps 1 through 3 for the other two charge configurations. TA Progress Check-in At this point in the lab, write your table number on the board to indicate you are ready to check in with your TA. PART 5: DATA AND CALCULATIONS 1. Drawing the E-field lines: Using solid lines, draw electric field lines for each charge configuration, including arrows on the field lines to show the direction of the electric field. Explain here how you know how to draw the fields. 5

Physics 9L/19L Module 2.1: Electric Potential & Electric Field [Take a picture of each of your equipotential plots and paste your pictures here] [Write you explanation for how you knew how to draw the field lines here] 2. Calculating the E-field magnitudes: a. Mark locations A – L on your configurations, as shown below, on the electric field lines you sketched in question (1), making sure the marks are between two equipotential lines. b. Using your data and a ruler, estimate the magnitude of the electric field at each. Hint: E x = − ∂V ∂x . Units of V m are especially convenient for the electric field in this case. c. Show your work and fill in the values in the table below. Although both partners will have the same images in their lab notebook, each person should measure ∆ x , calculate ∆V , and | ⃗ E | for each point (A – L) themselves. [Enter your values in this table] Configuration Location ∆V ∆ x | ⃗ E | Paired circular charges A B C Parallel plate capacitor D E F G H Plate and circular charge I J K L 6

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Physics 9L/19L Module 2.1: Electric Potential & Electric Field PART 6: ANALYSIS 1. How did your prediction of the equipotential contour lines of the plate and circular charge compare to your measurement? Explain any differences. [discussion about similarities and differences between prediction and measurement here] 2. In question 2 of the Predictions section—before you collected any data—you came up with a rule to decide whether or not a point should be included on a specific contour. Did you need to modify your rule at all? If so, what parts of your original thinking needed to be modified and why? [discussion of how/why the rule needed or didn’t need to be modified here] 3. In question 3 of the Predictions section—before you collected any data—you made a plan for the number of data points you would need to capture the shape of the equipotential. a. Reflecting back, did you end up changing that plan? If so, how? If not, would you change your plan if you were to map out the equipotential lines for another charge distribution? b. Describe the characteristic(s) of equipotential lines that required the dots located with the U-probe to be spaced more closely together. 4. To calculate the electric field, you needed to find the difference between the DMM readings at two points divided by the distance between the two points. | ⃗ E | = | − ∆V ∆ x | = | DM M 1 − DM M 2 ∆x | Which of these measurements do you think contributed the most to any uncertainty in your answers? Why? [discussion of which value contributed the most to the error/uncertainty here] 5. According to theory, the electric field for the parallel plate configuration should be a uniform field. Is this consistent with your experimental result? Clearly state the evidence for your answer and discuss any differences. [discussion comparing theory to reality here] 6. What feature(s) of the equipotential map indicates where the electric field is the strongest? Why? Is the electric field strongest where you expect it to be? 7

Physics 9L/19L Module 2.1: Electric Potential & Electric Field [response here] 7. What do you consider the most helpful guide when attempting to determine the shape of the electric fields for the different charge configurations? [response here] PART 6: FINISHING UP Clean up your area. Return all materials to their appropriate places, and make sure the power supplies and the multimeters are turned off. Final TA Sign-Off Before leaving the lab, log out of the lab computer (if you were using it). Reset your lab station to be ready for the next lab session. Indicate to your TA that you are ready for the final sign-off. 8