Study Guide #1. L. Colonna-Romano/T. Keil. Electricity and Magnetism

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1 PH1120 Electricity and Magnetism L. Colonna-Romano/T. Keil Term B98 Study Guide #1 This is the first in a series of four Study Guides that have been designed to help you get the most out of this course. You will receive the others as the course progresses. The study guides are built around a set of course objectives and include suggested study procedures and problems to help you thoroughly understand those objectives. In addition, the homework assignments are in the study guides. For many students, following the study guides closely has proven to be an effective approach to successfully completing this course. Vectors will be used throughout this course and it may be useful for you to review vectors and operations involving vectors now. In particular, you should be familiar with the contents of Secs. 1-8 through (All references of this type may be found in the course textbook: Hugh D. Young and Roger A. Freedman, University Physics, Addison-Wesley Pub. Co., Ninth Ed., c 1996.) Be certain that you can express a vector in î ĵ ˆk-notation and also by giving a magnitude and direction relative to some well-designated coordinate axes. Unit vectors (Sec. 1-10) are sometimes confusing to students; be certain that you can calculate the components of a unit vector parallel to a specified vector. Objective 1 Coulomb s Law 1) State Coulomb s Law. (This means write it out in symbolic form and make sure you can define each symbol used in the expression. 2) Given a set of point charges (two or more) at rest at specified locations, calculate the resultant force (a vector quantity) on one of the charges caused by the other charge or charges. Suggested Study Procedures for Obj. 1 Read Secs through Study carefully Sec This section contains two important ideas: Coulomb s law and the principle of superposition. The four examples are important; you should be able to do similar problems. (When you study examples, I suggest you do so by first observing the general approach to the problem and then working out all the intermediate algebraic steps with pencil and paper.) Suggested Problems for Obj. 1 1) In each case, determine the unit vector that is parallel to the two-dimensional vector described below: a) from (0, 0) to (0, 3) b) from (0, 0) to ( 4, 0) c) from (0, 0) to (1, 1) d) from (1, 2) to (3, 3) e) from (1, 2) to ( 2, 1) 2) Exercises: 22-6, 22-9, 22-13, ) Problems: 22-57,

2 PH1120B98 Study Guide #1 2 Objective 2 Electric Field and Electric Flux 1) Define the electric field. 2) Calculate the electric field due to a set of point charges at rest at specified locations. 3) Determine the motion of a charged particle passing through an electric field. 4) Calculate the electric flux through a given surface. Suggested Study Procedures for Obj. 2 Study Secs and 22-7 paying particular attention to Examples 22-5 through You should examine Examples through as we will refer to them later in the course. Read Secs through Suggested Problems for Obj. 2 1) Exercises: 22-23, 22-25, 22-28, 22-29, 22-30, 22-32, 22-35, 22-36, ) Problem: Objective 3 Visualizing Electric Fields and Gauss Law 1) Sketch qualitatively the electric field associated with: a single point charge of given polarity; two or more stationary point charges of given relative magnitude and polarities; a point charge or charges in the vicinity if a conducting surface. 2) Use Gauss Law to relate the electric flux through a closed surface to the charge contained within that surface, and to the electric field along the same surface. Suggested Study Procedures for Obj. 3 Study Sec and 23-4 through All the example problems in these sections are important. Electric field lines form a useful way to picture how the electric field behaves in space. The following is a set or rules for sketching electric field lines: 1) Field lines begin and end only on charges. 2) The number of lines beginning at a positive charge or ending at a negative charge is proportional to the magnitude of the charge. 3) The direction of the field line is parallel to the direction of the force experienced by a small positive charge at each point along the field line. 4) The number of field lines passing through an area of one square meter whose surface is perpendicular to the lines (i.e., the density of field lines) is proportional to the magnitude of the electric field. 5) No two field lines can cross.

3 PH1120B98 Study Guide #1 3 6) Under electrostatic conditions, field lines always meet the surface of a conductor perpendicularly; under electrostatic conditions, no field lines penetrate a conductor. Suggested Problems for Obj. 3 1) Sketch the electric-field diagrams for each of the configurations in Fig. 1. a) +q b) -q c) d) +q -2q 3q -q -q (conductor) (conductor) Fig. 1. Configurations for Suggested Problem 1, Objective 3. 2) Exercises: 23-10, 23-16, Homework The homework assignments are an important part of this course and overall will count for 10% of your final grade. Students are free to discuss the homework problems among themselves, however, each student should write up his or her own individual solution for submission. Blatant copying of the work of another student is unlikely to help you understand the material. Please note that because of the limited number of homework problems that you will be submitting for grading, it is important that you also attempt as many of the suggested problems as possible. Although the suggested problems are not to be turned in for grading, they are equally important as the assigned homework in mastering the course objectives. Solutions for assigned and suggested problems are posted. Homework solutions are due at the beginning of your assigned lecture on the due date. Late homework is accepted only in extraordinary circumstances. Homework Assignment #1 due Friday, October 30, 1998 Prob Given the vectors A =3.00 cm î cm ĵ and B = 3.50 cm î 1.00 cm ĵ, calculate a) the magnitudes of A and B, b) the angle B makes with the positive x-axis, c) a unit vector in the same direction as A, and d) a unit vector in the same direction as A + B. Prob a) Two charged bodies exert a force of 40.0 mn on each other. What will the force be if they are moved so that they are only one-eighth as far apart? b) How close must two electrons be if the electric force between them is equal to the weight of one electron at the earth s surface?

4 PH1120B98 Study Guide #1 4 Prob A small charge of C is located at the point x =2.00 m and y = 3.00 m in the x-y plane. A second small charge of Cisatthepoint x =4.00 m and y = 1.00 m. a) Draw a diagram showing the two point charges in the x-y plane. b) Calculate the force that the first charge exerts on the second. Express your answer in î ĵ-notation. Show this force in your diagram. c) Calculate the force that the second charge exerts on the first charge. Homework Assignment #2 due Monday, November 2, 1998 Prob Two point charges are placed on the x-axis as follows: charge q 1 =1.00 µc is located at x = m, and charge q 2 =5.00 µc isatx =0.600 m. What is the magnitude and direction of the total force exerted by these two charges on a charge q 3 =4.00µC located at the origin? Prob Four point charges are placed at the corners of a rectangle as shown in Fig. 2. The magnitude of each charge is q =1.20 µc and the sign of each charge is as shown in the figure. If L =1.200 m and W =0.800 m, what is the electric field at the position of the charge located at the lower left corner of the rectangle? What is the force exerted on the charge at this position? y -q -q q L q W x Fig. 2. Prob Prob An electron is injected into the region of space between two horizontal parallel plates 3.00 cm long with a velocity of m/s directed 10 above the horizontal. The magnitude of the uniform electric field between the plates is 1000 N/C directed upward as shown in Fig. 3. a) Find the maximum distance the electron rises above its initial elevation. b) After what horizontal distance does the electron return to its initial elevation? c) How much time does the electron spend between the plates? d) If the electron is injected midway between the plates, what is the minimum plate separation if the electron is to avoid hitting the plates? e) Sketch the trajectory of the electron.

5 PH1120B98 Study Guide #1 5 y Fig. 3. Prob v x E 3.00 cm Homework Assignment #3 due Wednesday, November 4, 1998 Prob A point charge, q 1 =3.00 nc, is placed at x = 2.00 cm, y = 0 and a second point charge, q 2 = 3.00 nc, is placed at x =3.00 cm, y =2.00 cm. a) Compute the electric field at the point x =1.00 cm, y = 1.00 cm due to the two point charges. b) If a proton were to be placed at x =1.00 cm, y = 1.0 cm, what force would the other two charges exert on it? Prob Three point charges of equal magnitude are evenly spaced along a vertical axis; the outer charges are positive, the central one, negative. a) Sketch the electric field lines due to this configuration of charges. b) Where is the electric field zero? You need not work the algebra out completely but at least write an equation that would allow you to solve for the zero-field locations in terms of L, the distance between consecutive charges. Explain your reasoning; be sure to discuss the symmetry of the problem. Prob A cube is placed in a three-dimensional coordinate system with an edge (L = 4.00 cm) along each of the three positive axes. There exists a uniform electric field everywhere in space given by E = 1.30 N/C î N/C ĵ. Find the electric flux through each of the six faces of the cube and the total electric flux through the entire cube. Homework Assignment #4 due Friday, November 6, 1998 Prob Two small spheres, each with mass 8.5 g, are hung by silk threads of length m from the same point. The spheres are given equal amounts of positive charge and move apart until each thread makes an angle of 18 with the vertical. a) Draw a diagram showing all forces acting on each sphere. b) Find the magnitude of the charge on each sphere andthetensioninthethread. Prob Exercise 23-8 on p. 725 in the text. Prob Problem on p. 728 in the text. Also, if b = 1.00 cm and α = 2.00 nc/m, what is the magnitude of the electric field 1.00 m away from the tube? LCR sg1.tex 22 Oct :13a.m.