Unit 2: Electrostatics

Transcription

1 Unit 2: Electrostatics You probably associate electrostatics with physics class, but you probably also have lots of experience with static electricity at home. Of course, it s the same stuff! 1 I. What interacts? 1 In the plastic bin on your table, you will see several materials, including Styrofoam picnic plates, several types of cloths, an assortment of rods (glass and plastic; solid and hollow; 3 total), and clear tape. WHEN YOU ARE DONE WITH THESE MATERIALS, PLEASE PUT THEM BACK IN THE BIN FOR THE NEXT LAB GROUP. THANK YOU! :) A. Take the different types of rods and rub them with the different types of cloths. Are there any signs of static electricity that you observe with the rods? (Sparks? Crackles? Interactions?) B. Take a piece of paper and tear it up into little bits (maybe 5mm on a side). Take the rods that have been rubbed with cloths and bring them close to the little pieces of paper. How do the rods interact with the little bits of paper when they re not touching them? Things that attract little bits of paper are said to be electrically charged. The attraction is one kind of electrical interaction. C. Now find a way to charge the Styrofoam plates with the materials you have. Use the bits of paper to make sure it is charged. D. Get a piece of tape (4-6 inches long) and fold over a little bit of one end. Stick the tape to a smooth plastic binder or table surface and then pull it off. Is it charged? How can you tell? 1 Section I adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 University of Maryland Physics Education Research Group, 2010 Unit 2 Worksheet- 1

2 E. Make electrically charged objects and then find good ways to make them uncharged. Try some or all of the following techniques or invent your own. Different techniques may be more effective (or appropriate) with different objects. (Please don t render the objects unchargeable for other students.) Touch it in one place with your hand Touch it all over with your hand Wipe it off with your hand Wipe it off with a cloth Set it aside for a while Shake it vigorously Blow on it Breathe on it Put it in your pocket Run it over the tip of your nose Roll it on the floor Touch it to something else that s charged (other) Before you go on, prove to an instructor that you can charge, then uncharge, each of the following objects: (1) a Styrofoam plate and (2) a piece of tape. II. How do things get charged? 2 You have probably already started to wonder how it is that objects become charged, or uncharged. To explore how something happens, it s often useful to think about when it doesn t happen, or when you think it might not. A. Have you ever noticed an electric charge when you rub your hands together? How about if you rub someone else s hands? Try it if you re not sure, using your test for charge from part I. Why do you think this is the case? B. Make a prediction for what would happen if you were to rub two uncharged Styrofoam plates together. If they had no net charge to begin with, would either one have a net charge as a result of rubbing? What do you think is going on? Make sure your two Styrofoam plates are uncharged, then try rubbing them together and see if they get charged. Does the explanation you tried in part B fit with what you observe? C. Think about the piece of tape that you charged by peeling it off the desk. What s your theory about how that got charged? 2 Section II adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 University of Maryland Physics Education Research Group, 2010 Unit 2 Worksheet- 2

3 D. Think about some of the ways you found to uncharge your charged objects. What do you think is going on there? Explain your ideas to an instructor before you proceed. III. Types of charge 3 We ll continue investigating how things get charged by making some new charged objects. i. Charge a piece of tape like you did in part I (stick a piece 4-6 inches long onto a smooth surface and pull it off don t forget the folded handle ). Hang it up somewhere where it will not be disturbed. This will be your test tape. ii. Stick another piece of tape (also with a handle) to the same smooth surface. Write the letter B (for bottom ) on the tape. iii. Stick another piece of tape (again with a handle) directly on top of the first tape. Write the letter T (for top ) on that tape. iv. Pull the tapes off the desk together, so that they are still stuck to one another all along their length. Uncharge the pair of tapes using whatever method you have found most effective and appropriate for tapes. v. Hold the folded handles of the two tapes in your opposite hands and pull the two tapes apart. A. Which tape is charged: the T tape, the B tape, neither, or both? Give evidence. What s your explanation for how that happened? B. What kind of interaction, if any, do the T and B tapes have with each other? What kind of interaction does each have with the test tape? How does the interaction change with distance between the objects? 3 Section III adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 University of Maryland Physics Education Research Group, 2010 Unit 2 Worksheet- 3

4 C. You probably already know the rule that like charges repel and opposite charges attract. But you could figure that out even if someone didn t tell you. 1. Show that the test tape is either a T tape or a B tape. Make more T, B, and test tapes if you need to. 2. See what happens if you take a T and B tape and stick them back together. What is the charge on the resulting object? Explain how that supports calling the charge on T and B positive and negative. Do you have any evidence to tell you which is positive (T or B)? 3. Suppose we have two objects, labeled 1 and 2. Object 1 attracts object 2. From this observation alone, what can you say about the charge on object 1? on object 2? Explain your ideas to an instructor before you proceed. IV. Representing Charge 4 In our model of electricity, everything is loaded with positive and negative charges (protons and electrons), but in nearly identical numbers. If you wanted to represent all the charges around in a drawing, you could draw lots of pairs of + and symbols everywhere, but that would get tedious. So it s customary to draw + and symbols only to show that there s more of one or the other. (You could draw a couple of pairs to remind yourself what s going on, though.) Also according to our model, the amount of charge can be distributed in different ways in an object: Different parts of an object may be charged differently. So we use + and symbols to show where on the object there s an excess of which kind of charge. A. A bottom (B) piece of tape and a top (T) piece of tape are separated halfway. Use + and symbols on the diagram to indicate the parts of the tapes that are charged and the type of the charge (Can you tell which tape is + or? If not, just pick one!). B. Based on the above, is charge conserved or can it be destroyed? Do the B and T tape pieces contain similar or dissimilar charges? 4 Section IV adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 University of Maryland Physics Education Research Group, 2010 Unit 2 Worksheet- 4

5 C. If you earn $500 and $150 is deducted in taxes, the amount of money that you take home ($350) is called your net income. The word net is used similarly to describe the relative amounts of charge on an object. (We also sometimes use the word total or excess. ) If there is more positive charge than negative charge then the object is said to have a net positive charge. If an object has the same amount of both types of charge, then it is common to say that the object has a net zero charge. (We also sometimes say it has no charge, but that could be misleading!) 1. In part A, was the sign of the net charge on the pair of tapes taken together positive, negative, or zero? Explain how you know. Check that the drawing you made in part A is consistent with your answer. V. Connecting to Typical Problems 5 You just took real- life interacting charged objects of all shaped and sizes and represented them as objects with a net charge, either positive, +, or negative, -. This is how you will often see problems presented to you in class, ones where two or more charged objects interact, and your goal will be to understand how these objects are affecting one another. Like all forces, this electrical force is a vector quantity, possessing both a magnitude and direction, and it is described by Coulomb s Law. Coulomb s law states that the electric force between two point charges acts along the line connecting the two points. The magnitude of the force on either of the charges is proportional to the product of the charges and is inversely proportional to the square of the distance between the charges. r Q F!"!# = k Q q r! q Above right, Q and q are the two interacting charges, and r is the distance between them. k is Coulomb s constant, and has a value of about 9 x 10 9 Nm 2 /C 2. A. Consider the below charges to be two positive point charges +q and +Q (with Q > q ) held a distance s apart. 1. At each charge, indicate the direction of the electric force exerted on each charge by the other. +Q s +q 5 Section V adapted from Laws, P.W. The Physics Suite: Module 4, Electricity and Magnetism. Wiley, 2004 and McDermott, L. C. et al. Tutorials in Introductory Physics. Prentice Hall, Unit 2 Worksheet- 5

6 2. Is the force on the +q charge by the +Q charge greater than, less than, or equal to the force on the +Q charge by the +q charge? Explain. Is it attractive or repulsive? Why? B. Now consider the above charges to be one positive and one negative point charge, - q and +Q (with Q > q ) held a distance s apart. 1. At each charge, indicate the direction of the electric force exerted on each charge by the other. +Q s - q 2. Is the force on the - q charge by the +Q charge greater than, less than, or equal to the force on the +Q charge by the - q charge? Explain. Is it attractive or repulsive? Why? VI. More Problems 1. Consider two point- like objects, each possessing a net charge. Suppose they lie along the x- axis. A net charge of 2.0 x 10-9 C is located at x = 3.0 cm and a net charge of x 10-9 C is located at 5.0 cm. What is the magnitude of the force on the negatively charged object? What is its direction? 6 KNOW: WANT: STRATEGY: 6 Problem adapted from Law, P.W. The Physics Suite: Module 4, Electricity and Magnetism. Wiley, Unit 2 Worksheet- 6

7 2. Two small objects each with a net charge of Q (where Q is a positive number) exert a force of magnitude F on each other (Top image). We replace one of the objects with another whose net charge is 4Q (Bottom image). 7 (i) The original magnitude of the force on the Q charge was F; what is the magnitude of the force on the Q now, in terms of F (the original force)? Explain your reasoning. (ii). What is the magnitude of the force on the 4Q charge, in terms of F? Explain your reasoning. (iii) Next, we move the Q and 4Q charges to be 3 times as far apart as they were. Now what is the magnitude of the force on the 4Q, in terms of F? Explain your reasoning. (iv) In the original state (2 charges Q) if the symbol Q were taken to have a negative value, how would the forces change compared to the original state? Explain your reasoning. 7 Problem adapted from Redish, E.F. The Physics Suite: Activity Base Physics. University of Maryland Unit 2 Worksheet- 7

8 3. 8 (a) Two small non- conducting spheres have a total charge of µc ( 1 microcouloms [µc] = 1 x 10-6 C). When placed at a distance of 1.0 m apart, the force each exerts on the other is 16.2 N and it is repulsive. What is the charge on each? KNOW: WANT: STRATEGY: (b) Two small non- conducting spheres have a total charge of µc. When placed at a distance of 1.0 m apart, the force each exerts on the other is 19.8 N and it is attractive. What is the charge on each in this case? KNOW: WANT: STRATEGY: 8 Problem adapted from PHY 214 Studio Physics Workbook: Engineering Physics II; Department of Physics, Kansas State University, Unit 2 Worksheet- 8

9 4. You and a friend are doing the laundry when you unload the dryer and the discussion comes around to static electricity. Your friend wants to get some idea of the amount of charge that causes static cling. You immediately take two empty soda cans, which each have a mass of 120 grams, from the recycling bin. You tie the cans to the two ends of a string (one to each end) and hang the center of the string over a nail sticking out of the wall. Each can now hangs straight down 30 cm from the nail. You take your flannel shirt from the dryer and touch it to the cans, which are touching each other. The cans move apart until they hang stationary at an angle of 10 from the vertical. Assuming that there are equal amounts of charge on each can, you now calculate the amount of charge transferred from your shirt. 9 KNOW: WANT: STRATEGY: 9 From the Minnesota Context Rich Problem Archive Unit 2 Worksheet- 9