Name TA guide Physics 208 Spring 2008 Lab 3 (E-1): Electrostatics Section 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 conducting metal foils. WARNING: The electroscope is very sensitive, so unknown charges anywhere in the vicinity can influence your results. Make sure charged rods are far away when you don t want them to influence your system. Inadvertently touching a wire or conducting object can discharge them. 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.
1) In this section you use an electroscope to make measurements of a test object. 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! 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. Charge has been transferred to the sphere/electroscope system. The charge spreads throughout the conducting system (sphere/cable/electroscope), and some of it ends up on the leaves, which repel each other. The sign of the charge is the same everywhere. 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? The leaves move further apart more charge is on them. 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. There is also more charge on the conducting sphere. This means that the electroscope measures the charge on the conducting sphere. But the electroscope does perturb the system, since the charge distributes itself throughout the sphere/cable/electroscope system. 2
Model Building I: the electroscope deflection You are using the electroscope to measure the charge on various objects. In this section you develop a model of the electroscope, using the same techniques you used in the Physics 207 blood pressure lab. Here are some reminders from that lab: 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 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. 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 physical principles and logic in a mostly essay analysis. Your model should address: Quantitative: What is the relation between the charge on the leaves and the deflection? Qualitative: Is electroscope equally sensitive at large and small deflections? 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. 3
You will need to put a time limit on this, probably 30 minutes. This is because you want the entire lab to participate in a discussion after the models are posted. If some groups are trying to race through and get done early, go and talk to them about the limitation section of their model. This can be quite challenging, and they can work on this while the other groups finish up. Here is the scenario: Students have a problem that is too difficult to solve exactly, but it is clear that the leaves are moving apart because there are charges on them that are repelling each other. The goal is to make a model that preserves this principle, but can be solved. For instance, suppose that all the charge is concentrated at points at the ends of the leaves. This is a problem in the current HW assignment. Most groups may make this approximation, but then they ll need to know how heavy the balls should be. You should write these things on the board, maybe after someone realizes it is needed: 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 On the next page is an example of a particular quantitative model. Remember that there are many models than can explain the behavior of the electrosope. A qualitative model could use the same diagram, but talk about the physical interactions in words instead of equations. For instance, when the balls are far apart very little of the tension in the string cancels the couloumb repulsion, so it doesn t take much charge to push the balls apart. For large separations, the string tension is mostly antiparallel to the coulomb force, so that much of it is canceled by the tension and more charge than expected is required. So electroscope should be more sensitive at small angles. This is not the best explanation, but something along these lines! 4
Diagram of model: Relevant physical principles: Coulomb repulsion between balls. Force of gravity on balls. Force from tension in string. θ L T F C Q/2 mg 2Lsin" Q/2 Simplifications/assumptions made, and resulting limitations of model: Main assumption is that all the charge is concentrated at the end of the leaves, and that all the mass is concentrated at the ends. This is clearly not correct, but makes the problem do-able. What limitations might this lead to? It means that the relation between charge and deflection angle is not completely correct. In the real electroscope leaves, the charge distribution is more uniform along the leaves, and not concentrated at the ends. What difference does this make? It probably underestimates the deflection since some parts of the leaves are quite close together, and there will be some charge at those points when it is more uniformly distributed. But the fact that the force depends on the square of the charge probably evens things out a bit. So maybe not such a bad approximation. Explain how drawing answers question: F c " T sin# = 0 mg " T cos# = 0 $ T = mg /cos# F c = mgtan# k e ( Q/2) 2 ( 2L sin" ) $ mg' 2 = mgtan" # Q = 4L& ) % ( k e 1/ 2 ( tan" ) 1/ 2 sin" Using the small-angle approximation gives Q = 4L mg 1/ 2 " % $ ' ( 3 / 2 with θ in radians. # k e & L~3cm Estimate m: take all mass and concentrate it at the ends. Guess that foil is ~20µm thick, 3 cm long, 1 cm wide. 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. a. Continue to charge up the conducting sphere with the black rod until the electroscope leaves each deflect about 45. Take the black rod far away. If you re not sure if it is far enough away, move it around and see if the electroscope reading changes. If you re not able to charge to 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. The deflection of the leaves decreases. The charge on the sphere induces a dipole in your hand, which then attracts charges of the same sign as on the sphere to your hand. This pulls them away from the electroscope, making the leaves closer together. In this case the electroscope is not doing a good job of measuring the charge on the sphere. b. Touch the 2 nd conducting sphere with your hand to make sure it is discharged. You want to see what happens when this neutral object is brought close to the conducting sphere. 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. Again, one person should watch the electroscope while another positions the sphere. The electroscope leaves again get closer together, for the same reason. The effect is very small because the conducting sphere is much smaller than your body. 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. The electroscope leaves get a little closer together. But this is a different effect, as you can see because it remains when sphere 2 is removed. Here, the charge moved to distribute itself over a larger volume, so the charge density everywhere is less. In particular, the leaves don t repel as much. The electroscope makes a good measurement of the charge density after you remove the 2 nd sphere. 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 finger 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. The same thing happens as in c, but the effect is much larger, because the conducting area is now much larger. 6
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. The trend is that as the area of the conducting object gets larger, the effect becomes more pronounced, both in induction and conduction. 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. If you touch your hand to sphere 1, the electroscope leaves immediately deflate. This is because you are a very large conducting object. You are a good ground. g. Explain why touching a charged object with your hand neutralizes it. See answer to above. 7
Model Building II: using the electroscope to measure charge on an object. 3) 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 electroscope deflection 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. Write your model on the next page. Remember that your model should contain: 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 describe how the electroscope deflection is related to the charge on the object it is measuring The mechanics here are a little bit different. It is designed to give everyone an equal opportunity to contribute, albeit somewhat anonymously. Each student makes an individual card, and the group uses three cards from another table (drawn from the box) to get ideas for their model. They do not post their model on the wall. Make sure there are some index cards on each table (more than 3, in case someone wants to start over). When they finish their cards, they should take one out of the box, and put theirs in. This means that the first lab section has to be done a little differently. You can either put in some cards you made up, or just ask them to wait a little. For the later lab sections, take the previous sections cards out of the cabinet and put them in the box to start. Put your sections cards in the cabinet after the lab. The modeling here is conceptually more difficult than the previous. It should be clear from their experiments that the measurement of the electroscope depends on the geometry of what is connected. Technically it is the capacitance of what is connected that determines how much charge must be rearranged to make everything an equipotential. But we won t get to electric potential until after exam 1. So they will need to be creative in their ideas. They might see from their measurements that the physical size is one of the controlling factors. On the next page is an attempt at a model where physical size plays a role. 8
Drawing of model: Relevant physical principles + + + + + Force: Coulomb interaction pushes charges apart. Equilibrium: charges stop moving when there are no net forces + + + Simplifications/assumptions made, and resulting limitations of model: Not so clear here what the assumptions are. Basically that charge density is determined by the overall size of the system. This is assuming that charge spreads uniformly. Limitations: we know there are situations where charge does not spread uniformly. For instance, charge will concentrate at a sharp point, so that a spark will jump from a sharp point before it jumps from a smooth object. That is ignored here. How does this affect the result? Maybe electroscope reading also depends on shape of object connected and not just physical size. Explain how drawing answers question Drawing sort of shows charge pushing away from each other and spreading to electroscope. If the object is small, then more charge will be transferred to the electroscope. A larger object transfers a small amount of charge to the electroscope. So the electroscope is not just measuring the charge on the object. 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. This is charging by induction, with the two connected conducting spheres playing the role of ground. The charged rod pulls charge of the opposite sign toward the part of the sphere closest to it. Part of this charge comes from the electroscope, and part of it from the touching spheres. When the sphere 2 is disconnected from sphere 1 before removing the rod, the charge pulled from those spheres is still on sphere 1. When the rod is pulled away, the charge is distributed over sphere 1 and the electroscope, same sign everywhere. 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. When sphere 2 again touches sphere 1, the charge flows back and the system reaches overall neutrality. Electroscope leaves are not deflected. This emphasizes that the charge was pulled from somewhere. But if you happen to touch the cable or the spheres when you move spheres 2 and 3, they will discharge and you will not get these results! 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. After part a, sphere 1 (and the electroscope leaves) has a charge opposite to that of the ebonite rod. As the rod approaches sphere 1, the leaves first get closer together, then farther apart again. This is because the ebonite rod is attracting charges opposite to its own sign toward it on the sphere. These charges are the same sign as those on the electroscope leaves. They are pulled away from the electroscope leaves, first causing the charge density on the leaves to decrease. It reaches zero, then becomes of the opposite sign and the leaves move apart again. 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. The effect is bigger because your body is bigger (more capacitance) than the spheres. More charge can be pulled from it e. What is the moral to the story told in part 6? The moral of the story is that charged objects near a conductor can distort the charge density. It does this because charge of the opposite sign is attracted to it, or charge of the same sign is repelled from it. Could also say that local electric fields will distort the charge density. 11
Use these pictures to sketch out charge distributions if you find it helpful. 3 2 1 3 2 1 1 1 12