Name Section Physics 208 Spring 2008 Lab 3 (E-1): Electrostatics OBJECTIVE: To understand the electroscope as an example of forces between charges, and to use it as a measuring device to explore charge motion in conductors. APPARATUS: 1. Electroscope, three conducting spheres on insulated stands, black (ebonite) rod, fur, acrylic rod, silk cloth. INTRODUCTION: We said that charge is free to move around on conductors but it is only the electrons that can move. You will use the electroscope as a measuring device to determine where charge has moved, and how much of it has moved. The electroscope, pictured at left, consists of a conducting case and two aluminum leaves hanging from a conducting rod with a ball on top. The rod does not make electrical contact with the case where is passes through so electrons (or charge) cannot flow between the rod and the case. The leaves are extremely thin aluminum foils. Black banana-plug cable connected to wall ground. WARNING: The electroscope is very sensitive, so unknown charges anywhere in the vicinity can influence your results. WARNING! WARNING! Make sure charged rods, rubbing fur, other spheres, your hands, etc, are far away when you don t want them to influence your system. If you are not sure they are far enough away, wiggle them around and see if the electroscope is affected. Inadvertently touching a wire or conducting object can discharge it. Having your hand or other conducting object near any part of the system can influence the results. Water vapor in the air can drain charge from materials (particularly on humid days). The insulating stands of the conducting spheres can drain charge from the sphere when they get dirty. Your TA can clean them with alcohol for you. A person may be carrying an electrostatic charge (particularly in the winter), mostly depending on what clothes they are wearing (synthetics are worst, cotton is best). If one of your lab partners is not successful in discharging a sphere or electroscope by touching it, let someone else in your group try.
1) In this section you use an electroscope to make measurements of a test object. The base of the electroscope should be connected to the black banana-plug cable that comes from the wall ground. Take the longest banana-plug cable from the wall. Tape one end to the top of the electroscope so that it makes electrical contact, and plug the other end into one of the conducting spheres on insulating supports. Make sure the cable is suspended so it does not touch the lab table (charge will drain to the lab table if it touches), and keep your hands and charged objects away from the cable. A conducting cable now connects the electroscope and conducting sphere. No touch! Connect base of electroscope to ground a. Charge the black rod with the fur, and touch it to the conducting sphere (you may need to scrape it against the sphere) and remove the rod far away from the sphere and electroscope. Explain what the electroscope leaves do, and describe the charge distribution. On the last page of this packet are drawings where you can sketch out charge distributions if it helps. b. Charge the black rod again, and transfer some more charge to the sphere. Remove the rod far away from the sphere and electroscope. What happened to the leaves? c. Use the information from parts a and b to describe what physical quantity the deflection of the electroscope leaves measures here. In the next section, you construct a model of the electroscope that can make a more quantitative prediction. 2
Model Building I: the electroscope deflection You are using the electroscope to measure the charge. In this section you develop a model of the electroscope. In particular, how is the deflection of the leaves related to the charge on the leaves? You will use the same techniques you used in the Physics 207 blood pressure lab. You have a problem that is too difficult to solve exactly, but it should be clear that the leaves are moving apart because there are charges on them that are repelling each other. Your goal is to make a model that preserves this principle, but lets you calculate a relation between the deflection angle of the leaves and the charge on the leaves. You have a choice between a quantitative or qualitative model. Guidelines for Model Building A model is usually developed in order to understand an observation, or to make a prediction about the system that is being modeled. A model represents a particular phenomenon in terms of simpler, easy-to-understand terms (often employing pictures). The simplification involved in modeling is often guided by the questions you are trying to answer. If you think a particular detail of the system you are modeling will not play a big role in what you want the model to accomplish, you can leave it out. But this means that there are some things that your model will not explain, or will get wrong. These are the limitations of your model. Model-building does not have rules to use that always work when building a model. Building good models relies on creative thinking and insight. Build a qualitative or quantitative model of the electroscope. You can choose which one. A quantitative model will likely use equations to represent physical principles, along with some supporting words explaining how the equations are used. A qualitative model will use mostly physical principles and logic. Your model should address one or both of the following questions: Quantitative: How many Coulombs of charge is on the leaves when their deflection is 30? Qualitative: How does the deflection angle vary with charge on the leaves? Sketch a graph of the charge Q (arbitrary units) vs the leaf deflection (degrees) to answer this. 3
Your model should have a) a diagram, b) an identification of the relevant physical principles, c) a discussion of the model s assumptions and limitations caused by the assumptions. d) an explanation of the diagram and how it is used to answer the questions above Write your model on the next page so that someone not in your group can understand what is going on. After you have developed your group s model, copy it to the large sheet of paper at your table and put it on the wall for others to see. Go and look at the other groups models on the wall. Your TA will lead a discussion of the different models. Here are some questions you could ask yourself in developing a model. Why do the leaves repel each other? Why do the leaves hang at a certain angle? What are the forces involved in the problem? Is there any way I can figure out those forces? If not, can I model the system more simply so that I can figure out the forces? What is happening at extreme deflection angles? For instance compare directions of the forces when the leaves are hanging straight down (0 ) to when they are straight out (90 )? Does the distribution of charge on the leaves make any difference? Is there any way I can know the charge distribution on the leaves? If not, can I model the system more simply so that I do know the charge distribution? Does it make any difference how heavy the leaves are? For a particular charge on the leaves, would they deflect at the same angle if they were twice as heavy? If I need to, how can I estimate the mass of the leaves? density of aluminum = 2.7 g/cm 3 common thicknesses: 20# sheet of paper ~ 100 µm 13# Single-ply toilet paper ~65 µm Thin hair ~ 50 µm Cheap 1 mil garbage bag = 0.001 =25 µm 4
Diagram of model: Relevant physical principles Simplifications/assumptions made, and resulting limitations of model: Explain how the drawing answers question 5
2) Now you use the conducting sphere and electroscope as you did in Part 4 to figure out why touching your hand to charged conductors discharges them. First you need to make sure you can discharge the sphere. Charge it up to deflect the electroscope leaves, then touch your hand to the sphere. The electroscope leaves should fall to 0 deflection. If you can t do this, touch a large piece of metal, such as the lab table frame, or the grounded electroscope base, with one hand and discharge the sphere with the other. Or find someone in your group who is neutral enough to discharge the sphere. Don t go on until you can reliably discharge the sphere. a. Charge up the conducting sphere with the black rod until the electroscope leaves deflect about 45. Move the black rod far away. If you re not able to charge the system to ~ a 45 angle, or if the leaves slowly come back together, ask your TA some of the insulators may be dirty and charge is leaking off. Bring your hand close to the conducting sphere without touching it. Describe the deflection of the leaves, and explain how the charge distribution in various parts of the system has changed. You may need to have one person watch the electroscope while the other positions a hand. b. Discharge the 2 nd sphere with your hand. Slide it along the table slowly right up next to the 1 st sphere, without touching them. What has happened to the electroscope leaves? If you can t tell, quickly move the 2 nd sphere away from the first while watching the electroscope leaves. Compare the behavior with that of your hand in part a. c. Again bring the 2 nd (neutral) conducting sphere up to the 1 st sphere but this time touch them together. What happens to the electroscope leaves? Remove the 2 nd sphere and describe any changes. Explain how the charge distribution differs before and after touching the spheres. 6
d. Now take the 3 rd sphere and connect it to the 2 nd with the shortest banana-plug cable you can find. Make sure the cable connecting them is far from the table and far from your body. Touch your hand to one of the connected spheres to neutralize it. Slide one of the connected spheres toward the 1 st sphere, making sure your hand stays away from the banana-plug cable. Watch the electroscope as you touch the 1 st sphere with the connected spheres. Explain what happened to the charge distribution. e. If there are extra spheres not being used, you can connect more and more spheres together and repeat d above (making sure to charge the 1 st sphere to 45 on the electroscope). But you probably see the trend. Describe the trend below. f. Again charge the 1 st conducting sphere to 45. Now touch the 1 st conducting sphere with your hand. What happens to the electroscope leaves? Remove your hand and describe any changes. Explain how the charge distribution differs before and after you touched the sphere. g. Explain why touching a charged object with your hand discharges it. 7
3) Model Building II: can the electroscope determine the charge on an object? You have been using the electroscope to measure the charge on an object. Does that really work? Is the electroscope deflection (and hence the charge on the leaves) determined only by the charge on the object to which it is connected? Based on your measurements in part 2), each person at your table should on their own write a few sentences on a note card that qualitatively address the question How is the charge on the electroscope related to the charge on an object to which it is connected? Try to make the connection between the physics and your explanation as explicit as possible. Write it so that someone other than you can read it! Each person in your group should exchange his/her note card for one in the box on the TA table (no peeking!) Your lab group should now look through the three note cards you have selected. Using one or more of these ideas, or some of your own if you are not impressed with the ones on the note cards, build a qualitative model that describes how the electroscope deflection is related to the charge on an object to which it is connected. In a qualitative model, you might end up using an equation, but the model will probably be best expressed in words. Write your model on the next page. Here are some questions you could ask yourself in developing your model. What do my experiments of the previous section say about the question? What causes charge to flow to the electroscope leaves when I connect it to a charged object? What causes the charge to stop flowing to the electroscope leaves after I connect it to a charged object? Is the charge on the electroscope leaves equal to, less than, or greater than the charge on the object to which it is connected? 8
Drawing of model: Relevant physical principles Simplifications/assumptions made, and resulting limitations of model: Explain how drawing answers question 9
4) In this section you figure out how a nearby charge can distort the charge density on a conducting object. You do this using a technique called charging by induction. Set up as below, and discharge all spheres and electroscope by touching with your hand. Touching 3 2 1 Bring rod close here, but do not touch a. Charge the black rod with the fur. Bring the rod close to sphere 1 on the side opposite its contact point with sphere 2, but do not touch. If you hear a spark jump (small crack) you have transferred some charge, and you need to discharge the spheres and start over. Without moving the black rod, pull sphere 2 away from sphere 1. Put the black rod far enough away that it doesn t influence sphere 1. Move spheres 2 and 3 far enough away that they don t influence sphere 1 (be careful not to touch the cable connecting spheres 2 and 3. Describe what happened, and describe the final charge distribution on your system. b. Move spheres 2 and 3 back towards sphere 1, and touch spheres 1 and 2. Careful again not to touch anything inappropriate. Move spheres 2 and 3 away from 1. What happened to the electroscope leaves? Describe the charge distribution now. 10
c. Neutralize all spheres. Repeat the procedure of part a. After you finish, charge the black rod again and slowly bring it toward sphere 1. Describe what happens to the electroscope leaves, starting from when the rod is very far away. Explain how this is consistent or inconsistent with the charge distribution you determined in part a. If inconsistent, revise your charge distribution. d. Repeat the procedure of part a, but use your hand instead of spheres 2 and 3. Is the effect bigger or smaller? Explain why. e. What is the moral to the story told in this section? 11
Use these pictures to sketch out charge distributions if you find it helpful. 3 2 1 3 2 1 1 1 12