Introduction This material corresponds with Hecht, Chapters 15 and 16. In this lab you will focus on the concepts of electric fields, electric potential, and parallel-plate capacitors. It is a good idea to read all the steps in each part before you start. Pre-Lab Homework These Pre-Lab Homework problems are to be done before you get to lab. They are predictions your hypotheses of what might happen. You will perform each of the experiments and discover if your predictions were correct. Write down what you honestly think will happen, so that at the end of the experiment you can compare your ideas with what you observed. Your TA s will be able to better help you in lab if they can see what ideas you have about what is going on from your Pre-Lab. You will not be graded down for wrong predictions, but you will lose points for missing predictions. 1. For each of the four configurations listed in the step 1 of the Experimental Set-Up, predict what the electric fields and equipotentials will look like. Label one electrode positive (+) and the other negative ( ), and draw the electric field lines and at least two equipotentials for each of the four configurations. 2. In what sense do the two conductive straight-line electrodes, confined as they are to the plane of the black paper, mimic a parallel-plate capacitor (a three-dimensional structure)? 3. Imagine bringing together a whole bunch of positive (+) point charges and lining them up face-toface with a line of negative charges. Describe with pictures and words how the electric fields due to the point charges add up like vectors to create the net electric field between the plates. 4. Figure (a) shows the electric potentials on a grid. Draw the 50-V, 75-V, and 100-V contours in Fig. (a). If the gridlines in (a) are 1 cm apart, estimate the magnitude and direction of the electric field at points A, B, C, and D. (The electric field is not the same as the electric potential, but they are related.) 5. Figure (b) shows an equipotential contour map. In this figure, where is the electric field strongest? Where is it weakest? Suppose you were pushing a proton from the 0-V contour to the 8-V contour. Which route would you take? Does the energy required depend on the path? If an electron is placed in the electric field and is free to move, where would it end up? 2001 UCSD-PERG Page 1
Experimental Set-Up In this lab you will work in groups of two students. The following set-up instructions apply for each group of two. Materials: One photocopied Teledeltos paper per person One power supply Two electrodes One electrometer Set Up: Fig. 1: Electrode configurations. 1. Your group will have one of the following four shapes (Fig. 1) written in silver conductive ink on black Teledeltos paper: Two dots (point charges: one positive, one negative) Two lines (charged parallel plates: one positive, one negative) A line and an open circle (a charged plate near a hollow sphere: one has a positive charge, the other has a negative charge) Two concentric open circles (two concentric hollow spheres: one positive, one negative) Each configuration contains two elements that may be lines and/or dots. Regardless of their shape and size, each element will carry charge and will be called an electrode. 2. Each person must trace or copy their group s design onto the photocopy of the Teledeltos paper. Similar gridlines appear on both the Teledeltos paper and the photocopy. Procedure: Experiment A: Measuring Electric Fields 1. If it is not already set up, use plastic push-pins to attach the black paper (with the electrodes drawn in silver) to the corkboard. 2. Tape the flat metal ends of the red and black wires to the silver shapes (electrodes) on your black paper as shown in Fig. 2. Be sure to tape each wire to a different electrode and make sure the tape is pressed down firmly. Do not remove the tape. BLACK WIRE PROBE RED WIRE TAPE ELECTRODES Fig. 2: Teledeltos paper with red and black wires taped to the electrodes. 2001 UCSD-PERG Page 2
Experiment A (cont d): 3. Connect a wire from the (-) terminal on ELECTROMETER the power supply to the ground (GND) terminal on the electrometer. Both ends of this wire must be rounded banana plugs. 4. Plug the rounded end of the red wire into the positive (+) terminal on the power supply, and the black wire into the negative (-) terminal. Note that the black wire can be plugged into the wire that is already in the negative (-) terminal. This is shown in Fig. 3. 5. Connect the red probe to the INPUT terminal on the electrometer. 6. Turn on the power supply and set both the power supply and the electrometer POWER SUPPLY to their 30-V scales. Fig. 3: Power Supply and Electrometer wired for Expt. A. 7. Turn on and zero the electrometer by turning the zero adjust knob until the reading is zero. The red probe of the electrometer is now ready to measure the potential at the desired location on the paper. 8. The electrometer will measure the potential difference between the point probed on the paper and the negative silver electrode. To measure this potential difference at a given point, gently press the red probe against the black Teledeltos paper without puncturing the paper. The value of electric potential at a given point can be read from the electrometer. 9. Find three equipotential contours using the following method: (a) Choose an arbitrary voltage (say, 7 V). (b) Using your probe, find a point at that voltage (7 V) on the Teledeltos paper. (c) Mark the location and voltage of that point on the white photocopied page. Use the grid marks on the black paper to help transfer your readings onto the photocopy. (d) Repeat steps (b) and (c) until there are a sufficient number of points at that voltage to connect-the-dots and form an equipotential curve. Be sure to investigate all over the surface of the paper to find points with equal voltages. (e) Repeat this entire procedure for two new arbitrary voltages to find two more equipotential contours. Questions: ELECTROMETER A1. Describe what your equipotentials look like compared to your electrodes. 2001 UCSD-PERG Page 3
Procedure: Experiment B: Mapping Electric Field Lines 1. Turn off the electrometer and power supply. Disconnect the short wire that connects the ground (GND) on the electrometer to the negative (-) output terminal on the power supply. Reconnect the black wire that is taped to the electrode to the negative terminal of the power supply, if necessary. 2. Plug the black probe into the ground (GND) terminal of the electrometer. (The red probe should remain connected to the electrometer, as before.) 3. Switch the electrometer to the 10-V scale for increased sensitivity, as shown in Fig. 4. (The power supply should still be on the 30-V scale). Fig 4: Power Supply and Electrometer set up for Expt. B. 4. Tape the two probes together as shown below in Fig. 5. Now, touch both probes to the black paper. The electrometer reads the potential difference (or voltage) between the probes. Since the probe separation is about 1 cm, the electrometer indicates the potential difference directly in V/cm. 5. For a given spot chosen on the paper, rotate the probe about that spot, keeping contact with the paper, until the maximum voltage reading on the electrometer occurs. 6. The electrometer reads the change in voltage from the red probe to the black probe. Record the direction of maximum voltage with an arrow and the magnitude of V on your white paper. Be sure the direction is correct. This data gives both the direction and magnitude of the electric field at the point chosen. Choose your spots to be between equipotentials. 7. Find electric field lines in various regions of your paper, marking the magnitude and direction on your white photocopied page. Fig. 5: Two probes taped together. 2001 UCSD-PERG Page 4
Questions: Experiment B (cont d): B1. Electric field lines should be perpendicular to lines of equipotential. Based on the electric field mapping that you completed, is this the case? B2. At least one group should have mapped electrodes that included an open circle. What is the magnitude of the electric field inside the circle? In what sense does this agree with Gauss Law? B3. Look at the maps that have the same configurations as the ones you made predictions for in the Pre-Lab Homework. (You may need to look at the data from other lab groups and in your lab notebook to sketch the electric fields and equipotentials for those configurations that your group did not work on.) Comparing your predictions with the actual data, how close were your predictions? Describe how the equipotentials and electric field lines in the actual data are similar or different from your predictions. 2001 UCSD-PERG Page 5