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PROBLEM #2: ELECTRIC FIELD FROM A DIPOLE You have a summer job with a solar power company. To measure the electric fields produced by solar cells the company plans to use conductive paper. They will arrange the cells on the paper and measure the field at different points on the paper. You are assigned to test the soundness of this process for measuring the fields by using it to determine the electric field created by a simple pattern of charged objects. You create a two-dimensional dipole field by giving two parallel metal rods opposite charges with a battery while their tips are in contact with a sheet of conducting paper. You then measure the electric field in the paper. To see if the paper can be used to correctly map an electric field you first make a detailed qualitative prediction of the electric field produced by an electric dipole at different points in space. Instructions: Before lab, read the required reading from the textbook and the laboratory in its entirety. In your lab notebook, respond to the warm up questions and derive a specific prediction for the outcome of the lab. During lab, compare your warm up responses and prediction in your group. Then, work through the exploration, measurement, analysis, and conclusion sections in sequence, keeping a record of your findings in your lab notebook. It is often useful to use Excel to perform data analysis, rather than doing it by hand. At the end of lab, disseminate any electronic copies of your results to each member of your group. Read: Tipler & Mosca Chapter 21 sections 21-1 – 21-5. It also might be a good idea to review Chapter 1 Section 1-6 & 1-7. EQUIPMENT You have electrostatic paper, two brass rods (to serve as electrodes), banana cables, alligator clips, a battery and a wood block to increase contact pressure between the electrodes and the paper. Measurements will be made using a Digital Multimeter (DMM) set to read volts connected to a pin tip probe. You will also have the Electrostatics 3D program. A white sheet of paper with a grid similar to the grid on the conducting paper is useful for recording the field (do not write on the conductive paper). Overhead view of setup. Read the sections Electrostatic Paper and Accessories and The Digital Multimeter (DMM) in the Equipment appendix. If equipment is missing or broken, submit a problem report by sending an email to [email protected]. Include the room number and brief description of the problem. ELECTRIC FIELD FROM A DIPOLE – 1302Lab1Prob2 WARM UP 1. Draw a picture of the dipole, (one positive charge and one negative charge separated by a distance d). Label the charged point objects “+” and “-”. Clearly define an x-y coordinate system. 2. Choose an arbitrary position on the dipole diagram. At this position, draw two vectors, one each to represent the electric field due each point charge. (Remember that you can understand the electric field by considering the electric force on a positive “test charge” placed at that point.) How should the length and direction of each vector depend on the position relative to each charged object? What law governs this? Measure the distance from each charged object to the point where you are drawing the vectors to ensure the vectors have correct relative lengths. 3. Draw a darker vector representing the TOTAL electric field at that point. Remember, a total, or net, electric field is constructed at a given position using the law of superposition (vectors add according to the tail-to-head vector sum rule). 4. Repeat this process at different, systematically chosen points (i.e., a grid) until you have a reasonable map of the electric field in the space surrounding the dipole. Where is the field the strongest? The weakest? What is the direction of the field at different points along the dipole’s two different axes of symmetry? Sketch the electric field as function of position along the two axes of symmetry (two different graphs). PREDICTION Determine the physics task from the problem statement, and then in one or a few sentences, equations, drawings, and/or graphs, make a clear and concise prediction that solves the task. (Hint: How can you make a qualitative prediction with as much detail as possible?) EXPLORATION Systematically construct an electric field map using the Electrostatics 3D program. For instructions on how to use this program see the Exploration section of the “Electric Field Vectors” lab problem. Save your result to pdf. Next, construct a physical model of a dipole using the battery, rods, and conductive paper. Make sure to read the suggested appendix materials for details on how to use the DMM and the conductive paper setup. Follow the instructions given there to set up the conductive paper. ELECTRIC FIELD FROM A DIPOLE – 1302Lab1Prob2 Once the rods are connected to the battery, set the digital multimeter (DMM) to DC volts and turn it on. Place the tips of the probe on the conductive paper midway between the tips of the two rods. Adjust the units on the DMM until you obtain reasonable readings. Recall the field maps you generated in the warm up questions and with the simulation software. Rotate the probe so that the center of the probe stays in the same spot. Do the values change (pay attention to the sign)? Is there a minimum or maximum value as you rotate the probe? Are there any apparent symmetries as you rotate the probe? If there are large fluctuations in the readings, determine how you will measure consistently. Determine how you will use the probe to determine the electric field direction at other points. Now place the field probe near, but not touching, one of the rods and rotate the probe as you did before. Record your data. Determine the direction of the electric field. Compare the maximum DMM reading at this point to the one you found at the midway point. Compare your measurements to your prediction; does the value displayed on the DMM become larger or smaller when the electric field becomes stronger? Consider how you will use the probe to determine the electric field strength at other points. Test a few more key points on the conductive paper. Where on the conductive paper is the electric field strongest? Weakest? Consider whether your observations match your predictions. Discuss in your group how you will use the probe to determine the field strength and direction at an arbitrary point on the conductive paper and how you will record the results on the white copy of the conductive paper. Discuss how you could construct a systematic map (hint: think grid) of the dipole’s electric field. MEASUREMENT Complete your measurement plan for mapping the electric field on the conductive paper. Select a point on the conductive paper where you wish to determine the electric field and determine its magnitude and direction. Repeat the measurement to gain an estimate of the measurement uncertainty. Record the result on the white copy of the conductive paper. Repeat for as many points as needed to systematically create a field map that can be used to check your prediction. IMPORTANT: Disseminate electronic copies of your results from this and exploration section to each member of your group. Your TA can provide you with scans of your hand-constructed dipole map, or you may scan it on your own time after lab. ELECTRIC FIELD FROM A DIPOLE – 1302Lab1Prob2 ANALYSIS AND CONCLUSION How does your map compare to your prediction? How does it compare to the simulation program? Where is the field strongest? How do you show this in your map? Where is the field weakest? How do you show this in your map? Do your answers somehow depend on the axis of symmetry under consideration? Overall, was your prediction successful? Why or why not?