Unit 3: Electric Fields

Transcription

1 Unit 3: Electric Fields I. nalogy to electric field: Wind 1 The point of this tutorial is to introduce electric fields. ut instead of doing so immediately, we ll start with an analogy to wind.. n industrial- strength fan creates the wind pattern indicated in this diagram. Someone holds a small kite at point. Then the person holds a larger kite at that same point. In both cases, the kite directly faces the fan and therefore catches the wind. 1. In what sense is the wind stronger on the large kite than it is on the small kite? 2. In what sense is the wind equally strong at both kites? 3. student says, The wind itself is equally strong at point no matter which kite you hold there or even if you don t hold a kite there. The large kite feels more force than the small kite because it has more area and therefore catches more wind, not because the wind itself is stronger. Does this student agree with the answers you just gave? If not, do you think the student makes good points? In what ways do you disagree? 1 Section I adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 University of Maryland Physics Education Research Group, 2010 Unit 3 Worksheet- 1

2 s a convenient catchphrase, let s define the wind field as the strength and direction of the wind itself at a given point (whether or not an object is held there). So, according to the student, the wind field at point stays the same whichever kite you put there; but that same wind field produces a different wind force on kites of different sizes. Now you ll figure out a way to define the wind field more precisely. 4. The smaller kite has cross- sectional area 0.50 m 2. When held at point, it feels a wind force of 3.0 N. The larger kite has exactly twice the cross- sectional area (1.0 m 2 ) of the smaller kite. What wind force would you expect the larger kite to feel at point? Explain. 5. Now a kite of cross- sectional area 2.0 m 2 is held at point. What wind force do you expect it to feel? Why? 6. Here s the punch line. Each of the three kites from question (4) and (5) feels a different wind force at point. ut they should each feel the same wind field because the wind itself is the same at point no matter which kite you hold there. Is there some number having to do with wind force and cross- sectional area that s the same for all three kites and could therefore work as a definition of wind field? This is hard; try it for a while, and if you get stuck, move on to the next question. 7. Here are two proposed definitions of wind field: (i) wind field = wind force cross- sectional area, or (ii) wind field = wind force cross- sectional area. Which of those definitions, if either, better captures the intuitive sense of what wind field is supposed to mean? 8. Let s think more about the better definition of wind field from question (7). What are the units of that number? Unit 3 Worksheet- 2

3 9. Explain what that definition of wind field means in terms your roommate could understand (assuming your roommate isn t a physics person). Consult an instructor before you proceed.. Does the wind force depend on the fan, the kite, or both? What about the wind field? riefly explain. II. pplying field ideas to electric stuff 2 We just saw that the wind field is the strength and direction of the wind, independent of whether the wind acts on anything. In general, a field is the strength and direction of something, independent of whether that something acts on an object. Let s apply these ideas to electric fields. glass rod is given a positive charge by rubbing it with silk. elow is a side and top view of the rod, with a few test points labeled.. Sketch vectors at each of the points marked with a to represent the electric force exerted on a positive test charge if it were at that location. Rod Rod Side View Top View How does the magnitude of the force exerted on the test charge at point compare to the magnitude of the force on the test charge at point? 2 Section II adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 University of Maryland Physics Education Research Group, & McDermott, L. C. et al. Tutorials in Introductory Physics. Prentice Hall, & Dr. eth Thacker PHYS 1404 Unit 03 Lab: Electric Field Unit 3 Worksheet- 3

4 . Suppose the value of the charge, q test, on the test charge were halved. Would the electric force exerted on the test charge at each location change? If so, how? If not, explain why not. Would the ratio F/q!"#! change at each location? If so, how? If not, explain why not. C. The quantity F/q!"#! evaluated at any point is called the electric field E at that point. How does the magnitude of the electric field at point compare to the magnitude of the electric field at point? Explain. D. Sketch vectors at each of the points marked with a to represent the electric field E at that location. Would the magnitude or the direction of the electric field at point change if: Rod the charge on the rod were increased? Explain. Top View the magnitude of the test charge were increased? Explain. the sign of the test charge were changed? Explain Unit 3 Worksheet- 4

5 You have been representing the electric field due to a configuration of electric charges by an arrow that indicates magnitude and direction of the field at a particular point. This is the conventional or vector representation of an electric field. n alternative representation of the vector field involves defining electric field lines. E. t right is a series of diagrams with electric field lines drawn for +1C, +2C, and - 1C charges. a. From looking at the diagrams how do you tell where the field is strongest? Explain. How do you tell where the field is weakest? How do you tell the direction of the field? Explain. b. ased on the diagrams for electric field lines, draw a diagram at right with electric field lines for +3C charge. c. Draw an electric field line diagram for 1.5C charge. d. Is there an electric field at points in space where there are no electric field lines drawn? Explain Consult an instructor before you proceed. III. From concepts to problem solving 3 To correctly apply the formula for the electric field, you need to relate it to the underlying concepts when thinking through a problem. This problem gives you practice doing so when you have lots of information to deal with. If you find yourself getting confused, think back to the wind. 3 Section IV adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 University of Maryland Physics Education Research Group, 2010 Unit 3 Worksheet- 5

6 In this diagram, beads 1 and 2 carry charges 1.0 nc (nanocoulombs) and 2.0 nc, respectively. P is just a point in space, not a charge. The electric force exerted on bead 2 by bead 1 is 12 N. The overall electric force that would be felt by a 2.5 nc charge at point P is 20 N; but a 2.5 nc particle is not present for now. 1 2 P. First let s think about the effect of bead 2 on bead Find the electric force exerted by bead 2 on bead 1. Yes, you have enough information; use a basic law of physics from last semester. 2. Find the electric field due to bead 2 at the location occupied by bead Is your part. 2. answer greater than, less than, or equal to the electric field due to bead 1 at the location occupied by bead 2? Explain.. Given that beads 1 and 2 feel different fields, it s reasonable to expect that they also feel different forces. ut they don t! To reconcile this apparent conflict, explain in intuitive terms how beads 1 and 2 can end up experiencing the same force even though they feel different fields. Hint: Think of a bigger and littler fan facing and blowing on each other. IV. More problems. 1. The electric field vector E! at point, at a distance of 2.5 cm from the charge q, is shown in the figure. (a) Draw accurately, in both direction and magnitude, the electric field vector at point, which is at a distance of 5 cm from the charge q. (b) How would the magnitude and the direction of the electric field vectors at and change if the charge q is replaced by a charge 2q and (c) by a charge q? 4 +q 4 Problem adapted from PHY 214 Studio Physics Workbook: Engineering Physics II; Department of Physics, Kansas State University, Unit 3 Worksheet- 6

7 2. The following graph shows two point particles with charges of q = +2.0 x 10 9 C and q = 2.0 x 10 9 C that are separated by a distance of 8.0 cm. They are fixed so that they cannot move. 5 (i) Calculate the value of the electric field at point 1 due to charge. Start by drawing the electric field vector, due to charge, at point 1. q #1 q (ii) Calculate the value of the electric field at point 1 due to charge. Start by drawing the electric field vector, due to charge, at point 1. (iii) Use the principle of superposition to calculate the total electric field at point 1. WORK SPCE: 5 Question from Dr. eth Thacker PHYS 1404 Unit 03 Exercises: Electric Field, adapted from Priscilla W. Laws, Workshop Physics ctivity Guide, John Wiley & Sons, Inc., New York, Unit 3 Worksheet- 7