Instructors Manual including Answer Key with Solutions for E & M TIPERs: Electricity and Magnetism Tasks (Inspired by Physics Education Research) Curtis J. Hieggelke Joliet Junior College [email protected]David P. Maloney Indiana University-Purdue University Fort Wayne [email protected]Stephen E. Kanim New Mexico State University [email protected]Thomas L. O'Kuma Lee College [email protected]Supported in part by Grants # 9952735 and #0125831 from the Division of Undergraduate Education (DUE) under the Course, Curriculum, and Laboratory Improvement (CCLI) Program of the National Science Foundation (NSF) November 1, 2005 Full file at http://testbank360.eu/solution-manual-em-tipers-1st-edition-hieggelke
Transcript
Instructors Manual including Answer Key with Solutions
Supported in part by Grants # 9952735 and #0125831 from the Division of Undergraduate Education (DUE) under the Course, Curriculum, and Laboratory Improvement (CCLI) Program of the National
Science Foundation (NSF)
November 1, 2005
Full file at http://testbank360.eu/solution-manual-em-tipers-1st-edition-hieggelke
E & M TIPER Sets Overview TIPERs tasks are instructional materials based on formats that are inspired by the insights provided by education research into students’ reasoning. Good research tasks and questions often make good instructional materials. These TIPERs are designed to target important concepts and reasoning skills in order to promote and establish a strong functional understanding of physics. This understanding provides a base upon which physics students can solve problems with better understanding. These tasks can be used as tools for learning and informative assessment. They are designed to provide small incremental changes to teaching styles that teachers should find less stressful and more acceptable to utilize. Students enter courses with beliefs about the way the world behaves. Some of these beliefs may be only partially consistent with the physically correct perception. The goal of these tasks is to help students change their ideas when necessary. In many cases, it is very difficult to modify the students’ thinking. There is some evidence that instructional approaches which emphasize putting the students into confrontations with phenomena and their peers while debating predictions, testing ideas, and explanations leads to more productive learning. One aspect of this approach is the importance of asking questions in different ways and asking very similar questions that are interrelated. TIPERs provide tasks that encourage using and support active learning and they require little learning on the part of students to handle the task formats effectively. TIPER formats in this book include: Ranking Tasks (RT); Working Backwards Tasks (WBT); What, if anything, is Wrong Tasks (WWT); Troubleshooting Tasks (TT); Bar Chart Tasks (BCT); Conflicting Contentions Tasks (CCT); Linked Multiple Choice Tasks (LMCT); Changing Representations Tasks (CRT); Predict and Explain Tasks (PET); Qualitative Reasoning Tasks (QRT); and Comparison Tasks (CT). In a particular TIPER set, not all formats are used but there usually are three or four different formats depending on the focus of the set. The sets are much broader in electricity and much more focused in magnetism. There are two major categories of tasks in this book: electricity (but not circuits) and magnetism. Within each category, tasks are listed by task format. This was done in order to prevent students from readily recognizing tasks dealing with the same question or issue. Each title task has a part that describes briefly the setup and a second part that indicates the target aspect of the task such as force or field. Tasks with identical task setups often are part of the same set. Each task has a short ID such as eT7-TT1 or mT2-QRT1 to allow for quick searches for a task. In the other part of this instructor’s guide, a solution including answer and a short explanation to each task is provided with a special color indicating a solution. The solution pages match the student edition. Several common conventions are employed in these tasks. All electric currents are conventional currents unless otherwise specified. A circle with a dot in the center is used to represent a vector pointing out of the page and a circle with an x in the center is used to represent a vector pointing into the page. Uniform fields, electric or magnetic, will be constant both in space and in time. There are no other forces or fields such as gravitation in these situations unless explicitly identified. In this manual, there is an alternative table of contents in which the tasks are listed by the topics typically found in most textbooks to help educators select tasks for their students. This alternative table also includes a task level where F represents a Foundational Task level suitable for all students, I represents an Intermediate Task, and A represents an Advanced Task level that may use calculus or other aspects such as flux. One way of using the TIPERs is to have students work on TIPERs individually, then have them compare their work with other students and finally have a class discussion on the issues. Students are encouraged to discuss what they did and the rationale for their responses. It is the expectation that they will eventually come to a correct consensus viewpoint in their group or class. Another way of using them is to place students in small groups where each person can work on a different task from the same set and eventually the issues with each task can be discussed and resolved in the group. There are several other ways to use them such as homework; each instructor needs to find a technique which is comfortable. TIPERs are intended to be very flexible. Instructors can use individual tasks or any combination of tasks that they think would be useful. While the tasks within a set are correlated, they do not need to be used together. The basic unit is the
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individual task. TIPERs can be used to introduce new material, to review previous material or ideas, to introduce lab work, as test items, as homework, as group work in class, or as class discussion items. The various formats provide alternative ways of focusing students on important or confusing ideas and concepts. We know that students’ understanding will be more robust if they deal with multiple representations or tasks on important issues.
TIPER Formats
Ranking Tasks (RT) A Ranking Task is an exercise that presents students with a set of variations, ranging from four to eight, on a basic physical situation. The variations differ in the values (numeric or symbolic) for the variables involved but also frequently include variables that are not important to the task. The students’ task is to rank the variations on the basis of a specified physical quantity. Students must also explain the reasoning for their ranking scheme and rate their confidence in their ranking. These tasks require students to engage in a comparison-reasoning process that they seldom do.
For the Ranking Task format, there may be two, three or more of the variations that have equivalent values for the target quantity. In these cases, answers need to explicitly show that they are tied either by putting tied answers in the same answer blank or placing a circle surrounding the ones that are tied. Examples of these are found at the end of this document. In addition, one of the options often available is the ranking for (whatever quantity is designated) cannot be determined. With ranking tasks, it may not be possible to figure out specific values for a quantity, but you may still be able to compare the situations to decide which is largest and so on and thus rank the situations.
Working Backwards Tasks (WBT) Working Backwards Tasks, also referred to as “Physics Jeopardy” tasks (Van Heuvelen and Maloney, 1999), essentially reverse the order of the problem steps. For example, the given information could be an equation with specific values for all, or all but one, of the variables. The students then have to construct a physical situation for which the given equation would apply. Such working backwards tasks require students to take numerical values, including units, and translate them into physical variables. Working backwards problems also require students to reason about these situations in an unusual way and often allow for more than one solution.
What, if anything, is Wrong Tasks (WWT) What, if anything, is Wrong Tasks (Peters, 1982) require students to analyze a statement, or diagrammed situation, to determine if it is correct or not. If everything is correct the student is asked to explain what is going on and why it works as described. If something is incorrect the student has to identify the error and explain how to correct it. These are open-ended exercises so they provide insights into students’ ideas since they will often have interesting reasons for accepting incorrect situations and for rejecting legitimate situations; and often students’ responses provide ideas for generating new items.
Troubleshooting Tasks (TT) Troubleshooting Tasks are variations on the What, if anything, is Wrong Tasks. In these items, the students are explicitly told that there is an error in the given situation. Their job is to determine what the error is and explain how to correct it. These tasks can often produce interesting insights into students’ thinking because they will at times identify some correct aspect of the situation as erroneous. Once again, this outcome helps develop new items.
Bar Chart Tasks (BCT) Bar Chart Tasks have histograms for one or more quantities. Frequently histograms are given for before and after some physical process with one bar left off. Students are asked to complete the bar chart by supplying the value for the missing quantity. Requiring the students to translate between representations they are using and this one is usually quite productive in developing a better understanding. These items can be especially useful since most students seem to adapt to and understand bar chart representations relatively easily.
Conflicting Contentions Tasks (CCT) Conflicting Contentions Tasks present students with two or three statements that disagree or conflict in some way. The students have to decide which contention they agree with and explain why. These tasks are very useful for contrasting alternate conceptions with physically accepted statements. This process is facilitated in these tasks because they can be phrased as “which statement do you agree with and why” rather than asking which statement is correct or true. These tasks compliment the WWTs.
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Linked Multiple Choice Tasks (LMCT) Linked Multiple Choice Tasks have one set of answer possibilities that apply to a collection of questions about a related set of cases. In these tasks, different variations of the situation are described and the students choose from a limited set of possible outcomes. These items allow for the comparison of how students think about various aspects and/or variations of a situation. These tasks have the nice feature that one gets both the student’s answer to a particular question and their pattern of responses for the variations presented.
Predict and Explain Tasks (PET) Predict and Explain Tasks describe a physical situation that is set up at a point where some event is about to occur. Students have to predict what will happen in the situation and explain why they think that will occur. These tasks must have situations with which the students are familiar, or have sufficient background information, to enable the students to understand the situation. By doing this, it will make students feel comfortable enough to attempt to complete the task.
Changing Representations Tasks (CRT) These tasks require students to translate from one representation (e.g., an electric field diagram) to another (e.g., an equipotential curves or surfaces diagram). Students often learn how to cope with one representation without really learning the role and value of representations and their relationship to problem solving. Getting students to go back and forth between/among different representations forces them to develop a more robust understanding of each representation. Among the representations that will be employed at times are mathematical relationships, so this task can serve at times as a bridge between conceptual understanding and traditional problem solving.
Qualitative Reasoning Tasks (QRT) These tasks can take a variety of forms, but what they have in common is that the analysis is qualitative. Frequently students are presented with an initial and final situation and asked how some quantity, or aspect, will change. Qualitative comparisons (e.g., the quantity increases, decreases, or stays the same) are often the appropriate answer. Qualitative reasoning tasks can frequently contain elements found in some of the other task formats (e.g., different qualitative representations and a prediction or explanation).
Comparison Tasks (CT) These tasks require making a decision on whether a quantity in one situation is greater than, less than, or equal to that quantity in a second situation along with the reasoning for the decision. These situations may be complicated or difficult but they can be answered without detailed equations and computations. They are useful in eliciting student ideas about underlying concepts. A sequence of related comparison tasks can help in connecting or bridging related concepts and provide for information for assessing and/or guiding future instruction.
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Category eT1: Charge and Charge Density. Tasks in this category ask about the values and/or signs of electric charges or about the values and signs of charge densities for continuous distributions.
Category eT2: Working Backwards Tasks This category contains all of the working backwards tasks since they normally have the identification/construction of a physical situation as their target, rather than some physical quantity.
Category eT3: Force This category contains the tasks where the Coulomb force between charges, charge distributions, and/or objects is the quantity that is asked about.
Category eT4: Kinematic Quantities This category contains the tasks that have acceleration, speed, velocity or some other aspect of the motion of charged objects as their target quantities.
Category eT5: Electric Field This category is for tasks that ask about various aspects, such as magnitudes and directions, of individual or net electric fields.
Category eT6: Work & Electric Potential Energy This category contains items that ask about the work done to move charges or charged objects to locations near other charges or charge configurations.
Category eT7: Multiple Electrostatic Quantities Tasks in this category ask about more than one electrostatic quantity. An example would be a task that asks about both the electric field and the electric potential at a point.
Category eT8: Electric Potential Tasks in this category ask about the electric potential at points near charges, charge distributions or charged objects.
Category eT9: Electric Flux These tasks have electric flux as the target quantity so they normally relate to situations where Gauss’ Law is involved.
Category eT10: Miscellaneous This is the catch-all category where quantities such as capacitance, torque, or any other non-electrostatic quantity is the target that the task asks about.
Category mT1: Electric Charge near a Bar Magnet or a Current Loop This set has electric charges sitting at rest near the poles of permanent magnets or moving along the axial line of a circular coil that is carrying a current. The issue being explored is that of treating magnetic poles as if they have electric charges.
Students often incorrectly think that magnetic poles are charged. They usually take north poles as positively charged, and that they can attract or repel static electric charges. Note that in experiments to test this or demonstrate this effect, electrostatic charges will attract magnetic and non-magnetic materials. Because the electrostatic force cannot be turned off, some of the situations in this set are problematic since they are experimentally unrealizable.
Category mT2: Charges Moving in a Uniform Magnetic Field This set deals with charges moving in magnetic fields. There is some variation among the items in the actual physical arrangements, but all of the items in the set ask about the force on and/or motion of electric charges moving in magnetic fields.
Category mT3: Charges near a Straight Current-Carrying Wire This set deals with electric charges moving near straight current-carrying wires. The questions in the items in the set ask about the force on or acceleration of the particle.
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Category mT4: Straight Current-Carrying Wire in a Uniform Magnetic Field This set deals with only one question. This set deals with the force on a current-carrying wire segment when placed in a magnetic field.
Category mT5: Magnetic Forces This set probes an important aspect of the magnetic interactions between varieties of pairs of objects. Students are asked about the relative magnitudes of the forces the two objects exert on each other.
Category mT6: Magnetic Field near Straight Current-Carrying Wire This set focuses on the magnetic field associated with a long straight current carrying wire. Items ask about magnitude and/or direction of the field at specified points.
Category mT7: Magnetic Field near a Current-Carrying Circular Loop This set focuses on the magnetic field at the center of a circular current-carrying coil of wire. Again the questions in the items ask about magnitude and/or direction of the field.
Category mT8: Magnetic Field near Three Parallel Current-Carrying Wires This set deals with the vector superposition of magnetic fields due to three parallel long straight current-carrying wires.
Category mT9: Force on Parallel Current-Carrying Wires This set deals with the force on a current-carrying wire near two other parallel current-carrying wires.
Category mT10: Energy of a Moving Charge in a Uniform Magnetic Field This set focuses on the issue that a constant and uniform magnetic field does no work on a moving charge since the force and velocity are always perpendicular to each other.
Category mT11: Flux or Flux Change in Loops in Uniform Magnetic Fields This set deals with moving rectangular wire loops that travel into, through, and/or out of a region that contains a uniform magnetic field. The issue targeted is the total flux or the change in flux passing through the loops in the different situations.
Category mT12: Voltage Induced in Loops in Uniform Magnet Fields The induced emf in a rectangular wire loop that is being moved into, through and/or out of a uniform magnetic field is the focus of this set.
Category mT13: Induced Current or Current Changing in Wires near Coils with Bulbs This set is a variation on the theme of mT12 set since the physical situation is the same (a rectangular wire loop being moved into, through and/or out of a uniform magnetic field) but this time the question is about the current in the loop instead of the induced emf. This set also has light bulbs in circular wire coils that are situated next to long straight current-carrying wires. The currents in the wires are changing and the students are to predict, or explain, the comparative brightness of the bulbs. In addition, this set has a physical situation where a circular loop of wire is outside and concentric with a solenoid. The questions in the items focus on the current in the wire loop for changes in the current in the solenoid.
Category mT14: Magnetic Field or Induced Magnetic Field near a Loop in Uniform Magnetic Field This set deals with rectangular wire loops that travel into, through, and/or out of a region that contains a uniform magnetic field. The issue targeted is the total magnetic field at the center point or the induced magnetic field at the center point of the loops in different situations.
Category mT15: Wire Coils and Moving Magnets This set deals with a permanent magnet moving toward, or away, from a circular coil of wire that is suspended from a string. The issue explored is how the induced magnetic field interacts with the changing field from the moving magnet.
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Task Set Task Task Title Page Level1 ID ID2 Setup —Target Quantity #
Charge Density F eT1 RT1 Charged Insulating Blocks—Charge Density 1 F eT1 RT2 Breaking a Charged Insulating Block—Charge Density 2 F eT1 RT3 Charged Insulating Blocks—Charge 3 F eT1 QRT1 Breaking a Charged Insulating Block—Charge and Charge Density 62 F eT1 QRT2 Charged Insulating Blocks—Original Block 63 F eT1 QRT3 Charged Insulating Blocks—Charge and Charge Density 64 F eT1 QRT4 Charged Insulating Rod—Charge and Charge Density 65 F eT1 CCT1 Breaking a Charged Insulating Block—Charge Density 91 F eT1 BCT1 Charged Insulating Blocks—Charge and Charge Density 111 F eT1 WWT1 Breaking a Charged Insulating Block—Charge Density 118 F eT1 WWT2 Breaking a Charged Insulating Block—Charge Density 118 I eT1 PET1 Two Insulating Rods—Charge Density 136
Charges in Insulators and Conductors F eT1 RT7 Charged Rod and Electroscope—Excess Charge 7 I eT1 QRT5 Three Conducting Spheres—Charge 66 I eT1 CCT2 Charged Insulators Connected with a Switch—Charge 91 F eT10 CCT2 Charged Rod and Electroscope—Deflection 105 F eT1 WWT3 Insulator and a Grounded Conductor—Induced Charge 119 F eT1 WWT4 Balloon Sticking on a Wall—Charge Distribution 120 F eT1 WWT5 Neutral Metal Sphere with a Charged Rod—Charge Distribution 120 F eT1 PET2 Electroscope—Charge 137
Forces Exerted by/on Point Charges I eT3 RT2 Charges Arranged in a Triangle—Force 9 F eT3 RT3 Charges in a Plane—Force 10 F eT3 RT4 Two Charges—Force 11 F eT3 RT5 Two and Three Charges in a Line—Force 12 I eT3 RT8 Three-Dimensional Locations near a Point Charge—Electric Force 15 I eT3 QRT1 Two Unequal Charges—Force 67 I eT3 QRT2 Three Charges in a Line—Force 68 I eT3 QRT3 Three Charges in a Line—Force 69 I eT3 QRT4 Three Charges in a Line—Force 70 I eT3 QRT7 Force Direction on Charges in an Equilateral Triangle—Force 73 I eT3 QRT8 Force Direction on Charges in a Right Triangle—Force 73 I eT3 QRT9 Force Direction on Charges in a Square—Force 74 F eT3 QRT10 Two Charges—Force on Each 75 I eT3 LMCT1 Charges Arranged in a Triangle—Force 80 A eT3 LMCT2 System of Charges—Electric Force on a Charge 81 F eT3 CCT2 Two Charges—Force 93 I eT3 CCT6 Conducting Cube Between Point Charges—Force 95 F eT3 BCT1 Three Charges in a Line—Force 112 F eT3 WWT1 Charges Arranged in a Triangle—Force 122 F eT3 WWT2 Two Charges—Force 123 F eT3 WWT3 Two Charged Objects—Force 123 F eT3 TT1 Charges Arranged in a Triangle—Force 130 F eT3 TT2 Two Charged Objects—Force 130 I eT3 PET2 Conducting Cube Between Point Charges—Force 138
1 F-Foundational Task, I-Intermediate Task, and A-Advanced Task 2 Ranking Tasks (RT); Working Backwards Tasks (WBT); What, if anything, is Wrong Tasks (WWT); Troubleshooting Tasks (TT); Bar Chart Tasks (BCT); Conflicting Contentions Tasks (CCT); Linked Multiple Choice Tasks (LMCT); Changing Representations Tasks (CRT); Predict and Explain Tasks (PET); and Qualitative Reasoning Tasks (QRT).
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F eT2 WBT2 Charge Arrangement—Physical Situation 141 F eT2 WBT10 Forces on Three Charges Along a Line—Charge Location 146 F eT2 WBT11 Forces on Three Charges in Two Dimensions—Charge Locations 147
Forces Exerted by/on Objects and Point Charges A eT3 RT6 Charged Rods and Point Charges—Force 13 I eT3 RT7 Charged Curved Rod—Force 14 F eT3 RT9 Sphere and a Point Charge—Force 16 I eT3 CT1 Straight Charged Rod and Two Point Charges—Force 57 I eT3 QRT5 Straight Charged Rod and Two Point Charges—Force 71 I eT3 LMCT3 Straight Charged Rod and Two Point Charges—Force 82 I eT3 LMCT4 Sphere and a Point Charge—Force 83 F eT3 CCT3 Sphere and a Point Charge—Force 93 I eT3 CCT4 Curved Charged Rod and Two Point Charges—Force 94 F eT3 CCT5 Pairs of Charged Conductors—Force 94 I eT3 WWT4 Straight Charged Rod and Two Point Charges—Force 124 F eT3 WWT5 Sphere and a Point Charge—Force 124 I eT3 TT3 Straight Charged Rod and Two Point Charges—Force 131 F eT3 TT4 Sphere and a Point Charge—Force 131
Uniform Electric Field F eT3 RT10 Three-Dimensional Locations in a Uniform Electric Field—Electric Force 17 I eT5 RT1 Charged Insulating Sheets—Electric Field 20 F eT5 RT15 Three-Dimensional Locations Within a Uniform Electric Field—Field 34 F eT3 LMCT5 Positive Charge in a Uniform Electric Field—Electric Force 84 I eT5 LMCT1 Charged Insulating Sheets—Electric Field 86 F eT3 CCT1 Electron in a Uniform Electric Field—Electric Force 92 F eT5 CCT5 Airplane Flying Between Two Charged Clouds—Electric Field 100 F eT3 WWT6 Uniform Electric Field—Electric Force 125 I eT2 WBT9 Charged Insulating Sheets—Electric Field 145
Electric Fields of Point Charges I eT5 RT6 Six Charges in Three Dimensions—Electric Field 25 I eT5 RT8 Three Charges in a Line—Electric Field 27 F eT5 RT12 Point Charges in Two Dimensions—Electric Field 31 F eT5 CCT4 Three Charges in a Line—Electric Field 99 F eT5 BCT2 Point Charge—Electric Field 114 F eT5 WWT4 Three Charges in a Line—Electric Field 126 F eT5 TT3 Three Charges in a Line—Electric Field 133 F eT2 WBT1 Three Charges—Physical Situation 141
Electric Fields of Insulators and Conductors F eT5 RT3 Charged Solid Conducting Sphere—Electric Field 22 F eT5 RT5 Spherical Conducting Shell—Electric Field 24 A eT5 RT14 Charged Curved Rod—Electric Field 33 A eT5 RT16 Point Charge inside an Insulating Shell—Electric Field 35 A eT5 RT17 Point Charge inside a Conducting Shell—Electric Field 36 I eT5 QRT2 Charged Insulating Rods—Electric Field 78 I eT5 CCT6 Two Charged Spheres—Electric Field 100 I eT5 CCT8 Point Charge in a Conducting Shell—Electric Field 101 A eT5 CCT9 Field Outside a Sphere with a Cavity—Electric Field 102 A eT5 BCT3 Charged Conducting Spherical Shells—Electric Field 115 I eT5 WWT2 Hollow Conductors—Field 121 I eT5 WWT6 Field Outside a Sphere with a Cavity—Electric Field 127 I eT2 WBT3 Electric Field Graphs—Physical Situation 142 I eT2 WBT4 Electric Field Graphs—Physical Situation 142 A eT2 WBT7 Charged Rod with Electric Field Components—Length and Location 144 I eT2 WBT12 Point Charge Inside a Shell—Shell Properties 147
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Special or Unique Electric Field Situations I eT5 RT2 Changing Electric Force on an Electron—Electric Field 21 I eT5 RT4 Three-Dimensional Locations in a Constant Electric Potential—Field 23 A eT5 RT13 Electric Field Lines—Electric Field 32 F eT5 CRT1 Electric Force on an Electron—Electric Field 106 I eT5 WWT1 Electric Force on an Electron—Electric Field 121
Electric Potential Near Point Charges F eT8 RT1 Four Charges in Two Dimensions—Electric Potential 42 I eT8 RT2 Points near a Pair of Equal Opposite Charges—Potential 43 F eT8 RT6 Three-Dimensional Locations near a Point Charge—Electric Potential 47 F eT8 RT8 Six Charges in Three Dimensions—Electric Potential 49 I eT8 RT10 Systems of Eight Point Charges—Potential 51 I eT8 CT1 Points near Pair of Charges—Potential Difference 61 F eT7 LMCT1 Six Charges in Three Dimensions—Field and Potential at Origin 87 F eT7 LMCT2 Four Charges in Two Dimensions—Field and Potential 88 I eT8 LMCT1 Three Point Charge System—Electric Potential 89 I eT2 WBT8 Potential near Two Charges—Physical Situation 145
Electric Potential Near Objects I eT1 RT4 Pairs of Connected Charged Conductors—Charge 4 I eT1 RT5 Collection of Six Charged Connected Conductors—Charge 5 I eT1 RT6 Pairs of Outside and Inside Connected Charged Conductors—Charge 6 I eT8 RT3 Pairs of Charged Connected Conductors—Electric Potential 44 A eT8 RT4 Charged Curved Rod—Electric Potential 45 I eT8 RT5 Two Large Charged Parallel Sheets—Potential Difference 46 I eT8 RT9 Spherical Conducting Shell—Electric Potential 50 I eT8 CCT1 Two Charged Spheres—Electric Potential 103 I eT8 WWT1 Uniformly Charged Insulating Sphere—Electric Potential 128 I eT8 WWT2 Two Large Charged Parallel Sheets—Potential Difference 129 I eT7 TT1 Two Connected Charged Spheres—Potential and Charge 134 I eT8 TT1 Two Large Charged Parallel Sheets—Potential Difference 134 I eT2 WBT5 Electric Potential Difference—Physical Situation 143
Potential and Field/Force Relations F eT3 RT1 Three-Dimensional Locations in a Constant Electric Potential—Force 8 F eT5 RT7 Potential near Charges—Electric Field 26 I eT5 RT9 Potential vs Position Graphs I—Electric Field 28 I eT5 RT10 Potential vs Position Graph II—Electric Field 29 I eT5 RT11 Potential vs Position Graph III—Electric Field 30 I eT5 RT18 Equipotential Surfaces—Electric Field 37 F eT8 RT7 Three-Dimensional Locations in a Uniform Electric Field—Potential 48 I eT5 CT1 Potential near Charges—Electric Field 58 I eT5 CT2 Potential vs Position Graph II—Electric Field 59 I eT3 QRT6 Charge near Equipotential Surfaces—Force Direction 72 I eT5 QRT1 Potential vs Position Graphs—Electric Field 77 I eT3 LMCT6 Potential vs Position Graph II—Force 85 I eT6 CCT1 Electric Force on a Proton—Electric Field 96 I eT6 CCT2 Electric Potential vs Distance Graph II—Electric Field 97 F eT5 CCT3 Three-Dimensional Locations in a Constant Electric Potential—Field 98 I eT5 CCT7 Potential near Charges—Electric Field 101 I eT5 CRT2 Potential vs Position Graph II—Electric Field Direction 107 I eT3 CRT1 Charges and Equipotentials—Force 107 I eT5 CRT3 Potential vs Position Graph—Electric Field Graph 108 I eT5 BCT1 Potential vs Position Graph II—Electric Field 113 I eT7 BCT1 Potential near Two Charges—Electric Field and Potential 116 I eT5 WWT3 Potential near Two Charges—Electric Field 126 I eT5 WWT5 Potential vs Position Graph II—Electric Field 127 I eT5 TT1 Potential vs Position Graph II—Electric Field 132
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I eT5 TT2 Potential near Two Charges—Electric Field 133 I eT2 WBT6 Electric Potential x and y Graphs—Electric Field 143
Work-Energy Issues A eT6 RT1 Three-Dimensional Locations in a Constant Electric Potential—Work 38 I eT6 RT2 Three Charge System—Electric Potential Energy 39 I eT6 RT3 Electron in Equipotential Surfaces—Kinetic Energy Change 40 A eT6 RT4 Charges and Equipotentials—Work 41 I eT6 CT1 Three Charge System—Electric Potential Energy and Work Done 60 I eT6 QRT1 Two Charged Objects—Work and Energy 76 I eT6 CCT3 Systems of Point Charges—Work to Assemble 102 I eT6 BCT1 Systems of Point Charges—Work to Assemble 117 I eT6 WWT1 Moving Charged Particle in an Electric Field—Potential Energy 128
Kinematic Issues I eT4 RT1 Two Charged Objects—Acceleration 18 I eT4 RT2 Charges Between Charged Parallel Plates—Speed 19 I eT1 CT1 Charges in Electric Field—Charge 57 A eT4 CT1 Cart Approaching Sphere—Distance 58 I eT4 CCT1 Cart Approaching Sphere—Distance 95 F eT4 WWT1 Equipotential Lines—Direction of Proton’s Motion 119 F eT4 WWT2 Electron in a Uniform Electric Field—Velocity 125 F eT4 TT1 Electron Moving into a Uniform Electric Field—Acceleration 132 F eT3 PET1 Two Charged Objects—Motion 138 I eT4 PET1 Straight Charged Rod and Two Point Charges—Acceleration 139 I eT4 PET2 Electric Potential vs Position Graph II—Motion of Charged Particles 139
Electric Flux I eT9 RT1 Point Charges—Electric Flux 52 A eT9 RT2 Charged Insulator and Conductor—Electric Flux 53 A eT9 RT3 Insulator and Conductor—Electric Flux 54 I eT9 RT4 Gaussian Cubes in Non-Uniform Electric Fields—Electric Flux 55 I eT9 QRT1 Charge Within a Hollow Conductor—Electric Flux 79 I eT1 CCT3 Charged Sheet—Enclosed Charge 92 I eT9 CCT1 Gaussian Cube near a Charge—Electric Flux 103 I eT9 CCT2 Charges Inside Gaussian Sphere—Electric Flux and Electric Field 104 I eT9 WWT1 Uniform Electric Field—Electric Flux 129 I eT9 TT1 Conducting Shell—Electric Flux 135
Capacitance I eT10 QRT1 Graph of Charge vs Electric Potential—Capacitance 78 I eT10 LMCT1 Two Parallel Plates—Capacitance 90 I eT8 CRT1 Parallel Plate Capacitor—Graph of Potential I 109 I eT10 CRT1 Parallel Plate Capacitor—Graph of Potential II 110 I eT8 PET1 Parallel Plate Capacitor—Potential 140
"Charged" Magnetic Poles I eT10 RT1 Charged Rod near a Suspended Bar Magnet—Torque 56 I eT10 CCT1 Charged Rod near a Suspended Bar Magnet—Rotation 104 I eT10 TT1 Charged Rod near a Suspended Bar Magnet—Rotation Direction 135
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Task Set Task Task Title Page Level3 ID ID4 Setup —Target Quantity #
Forces on Charges and Wires in Non-uniform Magnetic Fields I mT9 RT1 Parallel Current–Carrying Wires I—Magnetic Force on Wire 159 F mT1 QRT1 Electric Charge near a Bar Magnet—Force Direction 176 F mT1 QRT2 Charge near a Circular Current Loop—Force Direction 177 I mT5 QRT1 Two Parallel Long Wires—Force Difference 182 A mT5 QRT2 Suspended Permanent Magnet and Circular Coil—Scale Reading 183 I mT9 LMCT1 Three Parallel Current–Carrying Wires I—Magnetic Force on Wire 203 F mT1 CCT1 Electric Charge near a Bar Magnet—Force Direction 209 F mT1 CCT2 Charge near a Circular Current Loop—Magnetic Force Direction 209 F mT5 CCT1 Moving Magnet and Circular Loop—Force 210 F mT5 CCT2 Two Magnets—Force 211 F mT5 BCT1 Two Long Straight Wires—Force 221 F mT5 BCT2 Long Straight Wire and Rectangular Coil—Force 222 F mT1 WWT1 Electric Charge near a Bar Magnet—Force Direction 225 I mT9 WWT1 Three Parallel Current–Carrying Wires I—Magnetic Force 227 I mT9 WBT1 Three Parallel Current–Carrying Wires I—Direction of Currents 240
Charged Particle and a Uniform Magnetic Field F mT2 RT1 Charge within a Uniform Magnetic Field—Magnetic Force 148 F mT2 RT2 Moving Charge Path—Direction and Strength of the Magnetic Field 149 I mT2 RT3 Proton in Magnetic and Electric Fields—Acceleration 150 F mT2 QRT1 Charged Particle and a Uniform Magnetic Field—Path 178 F mT2 LMCT1 Moving Charge within a Uniform Magnetic Field—Force 195 I mT2 CRT1 Charge in a Uniform Magnetic Field Equation—Acceleration Graph 216 F mT2 WWT1 Moving Charge within a Uniform Magnetic Field—Force Direction 225 F mT2 WWT2 Charged Particles and a Uniform Magnetic Field—Direction of Motion 225 F mT2 TT1 Path of a Moving Electron in a Uniform Magnetic Field 229 F mT2 PET1 Electron Moving into a Uniform Magnetic Field—Electron 234 F mT2 PET2 Proton at Rest in a Uniform Magnetic Field—Proton 234 F mT2 PET3 Proton Moving into a Uniform Magnetic Field—Proton 234 A mT2 WBT2 Equation for a Charge and a Magnetic Field II—Physical Situation 236 I mT2 WBT1 Equation for a Charge and a Magnetic Field I—Physical Situation 236 I mT2 WBT3 Proton Moving Straight Through Magnetic Field—Cause 237
Charges Near a Straight Current-Carrying Wire I mT3 RT1 Moving Charge near a Straight Current–Carrying Wire—Acceleration 151 I mT3 QRT1 Moving Charge near a Straight Current–Carrying Wire—Acceleration 179 I mT3 LMCT1 Moving Charge between Two Current–Carrying Wires—Acceleration 196 F mT3 LMCT2 Charge Moving Along Wire—Magnetic Force 197 F mT3 CCT1 Charged Particle and Straight Current–Carrying Wire—Force 210 I mT3 CRT1 Long Current–Carrying Wire II—Magnetic Field 217 F mT3 WWT1 Moving Charge near a Straight Current–Carrying Wire—Force 226 F mT3 TT1 Moving Positive Charge near a Current–Carrying Wire—Force 229
Current-Carrying Wire and a Uniform Magnetic Field F mT4 RT1 Current–Carrying Wire in a Uniform Magnetic Field—Magnetic Force 152 F mT4 QRT1 Current–Carrying Wire in a Uniform Magnetic Field—Magnetic Force 180 I mT4 QRT2 Current–Carrying Wire in a Uniform Magnetic Field—“Bend” of Wire 181 I mT4 LMCT1 Current in a Uniform Magnetic Field—Magnetic Force 198
3 F-Foundational Task, I-Intermediate Task, and A-Advanced Task 4 Ranking Tasks (RT); Working Backwards Tasks (WBT); What, if anything, is Wrong Tasks (WWT); Troubleshooting Tasks (TT); Bar Chart Tasks (BCT); Conflicting Contentions Tasks (CCT); Linked Multiple Choice Tasks (LMCT); Changing Representations Tasks (CRT); Predict and Explain Tasks (PET); and Qualitative Reasoning Tasks (QRT).
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I mT4 CRT1 Force Equation—Diagram of the Current in a Magnetic Field 217 F mT4 WWT1 Current–Carrying Wire in a Uniform Magnetic Field—Force Direction 226 F mT4 TT1 Current–Carrying Wire in a Uniform Magnetic Field—Force 230 I mT4 WBT1 Equation for a Current and a Magnetic Field II—Physical Situation 237
Magnetic Fields of Straight Wires and Circular Loops F mT6 RT1 Straight Current–Carrying Wire—Magnetic Field 153 I mT6 RT2 Three-Dimensional Locations near a Long Straight Wire—Magnetic Field 154 F mT7 RT1 Current–Carrying Circular Loops—Magnetic Field 155 I mT8 RT1 Current–Carrying Straight Wires—Magnetic Field 156 I mT8 RT2 Three Parallel Current–Carrying Wires I—Magnetic Field 157 I mT8 RT3 Three Parallel Current–Carrying Wires II—Magnetic Field at Wire Y 158 F mT6 QRT1 Straight Current–Carrying Wire—Magnetic Field 184 I mT8 QRT1 Three Parallel Current–Carrying Wires I—Magnetic Field 185 I mT8 QRT2 Three Parallel Current–Carrying Wires II—Magnetic Field at a Wire 186 I mT6 LMCT1 Long Wire with a Current—Magnetic Field 199 F mT7 LMCT1 Current–Carrying Circular Loop—Magnetic Field 200 I mT8 LMCT1 Three Current–Carrying Wires—Magnetic Field between Wires 201 I mT8 LMCT2 Three Parallel Current–Carrying Wires I—Magnetic Field 202 I mT8 CCT1 Three Parallel Current–Carrying Wires II—Force 211 I mT6 CRT1 Magnetic Field Equation—Current and the Magnetic Field Diagram 218 F mT6 BCT1 Straight Current–Carrying Wire—Magnetic Field 223 I mT8 BCT1 Three Parallel Current–Carrying Wires I—Magnetic Field 223 F mT6 WWT1 Current–Carrying Wire I—Magnetic Field Direction 226 F mT6 TT1 Current–Carrying Wire—Magnetic Field 230 F mT7 TT1 Current–Carrying Circular Loop—Magnetic Field 231 I mT8 PET1 Three Parallel Current–Carrying Wires I—Change Single Current 235 A mT7 WBT1 Equation for a Current and a Magnetic Field—Physical Situation 238 I mT8 WBT1 Equation for Three Currents—Physical Situation 238 A mT8 WBT2 Three Parallel Current–Carrying Wires I—Direction of Currents 239 I mT8 WBT3 Three Parallel Current–Carrying Wires II—Direction of Currents 239
Energy of a Moving Charge in a Uniform Magnetic Field I mT10 RT1 Moving Charge in a Uniform Magnetic Field—Change in Kinetic Energy 160 I mT10 QRT1 Moving Charge in a Uniform Magnetic Field—Kinetic Energy Change 187 I mT10 BCT1 Moving Charge in a Uniform Magnetic Field—Work and Kinetic Energy 224 I mT10 BCT2 Moving Charge in a Uniform Magnetic Field—Work and Kinetic Energy 224 I mT10 PET1 Moving Charge in a Uniform Magnetic Field—Kinetic Energy 235 A mT10 WBT1 Charge and a Magnetic Field—Physical Situation 240
Magnetic Flux or Magnetic Flux Change I mT11 RT1 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux 161 I mT11 RT2 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux 162 I mT11 RT3 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change 163 I mT11 RT4 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change 164 F mT11 CT1 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux 174 I mT11 CT2 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change 174 I mT11 QRT1 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux and Flux Change 188 A mT11 QRT2 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux and Flux Change 189 F mT11 CCT1 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change 212 I mT11 CRT1 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux 218 A mT11 CRT2 Moving Parallelogram Loop in Uniform Magnetic Fields—Magnetic Flux 219 F mT11 TT1 Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change 231 A mT11 WBT2 Magnetic Flux versus Time Graph—Loop Characteristics 241 I mT11 WBT1 Moving Rectangular Loops in Uniform Magnetic Fields—Situation 241 I mT11 WBT3 Moving Rectangular Loops in Uniform Magnetic Fields—Situation 242
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Electromagnetic Induction F mT12 RT1 Moving Rectangular Loops in Uniform Magnetic Fields—Voltage 165 I mT13 RT1 Moving Rectangular Loops in Uniform Magnetic Fields—Current 166 I mT13 RT2 Changing Current—Bulb Brightness 167 I mT14 RT1 Wire on a Loop Moving in a Magnetic Field—Magnetic Field 168 I mT14 RT2 Loop Moving into a Uniform Magnetic Field—Magnetic Field 169 I mT14 RT3 Loops and Uniform Magnetic Fields—Magnetic Field 170 I mT14 RT4 Wire on a Loop Moving in a Magnetic Field—Induced Magnetic Field 171 I mT14 RT5 Loops and Uniform Magnetic Field—Induced Magnetic Field 172 A mT15 RT1 Wire Loops and Moving Magnets—Loop Motion 173 A mT13 CT2 Moving Rectangular Loops in Uniform Magnetic Fields—Current 175 I mT13 CT1 Moving Rectangular Loops in Uniform Magnetic Fields—Current 175 A mT13 QRT1 Changing Current—Bulb Brightness 190 A mT13 QRT2 Circular Loop outside a Long Solenoid—Induced Current 191 I mT14 QRT1 Loop Moving in a Uniform Magnetic Field—Induced and Total Magnetic Field 192 F mT14 QRT2 Loops and Magnetic Field—Direction of Induced Magnetic Field 193 A mT15 QRT1 Wire Loops and Moving Magnets—Motion of the System 194 I mT12 LMCT1 Moving Rectangular Loops in Uniform Magnetic Fields—Emf 204 I mT12 LMCT2 Rectangular Loop in a Uniform Magnetic Field—Velocity 205 I mT13 LMCT1 Moving Rectangular Loops in Uniform Magnetic Fields—Current 206 I mT13 LMCT2 Loops with Bulbs near a Current—Bulb Lighting 207 A mT15 LMCT1 Wire Loops and Moving Magnets—Loop Behavior 208 I mT12 CCT1 Moving Rectangular Loops in Uniform Magnetic Fields—Emf 212 F mT13 CCT1 Moving Rectangular Loops in Uniform Magnetic Fields—Current 213 I mT13 CCT2 Changing Current—Bulb Brightness 213 I mT14 CCT1 Moving Loops in Uniform Magnetic Fields—Magnetic Field 214 F mT14 CCT2 Loop Moving into a Uniform Magnetic Field—Induced Magnetic Field 215 I mT12 CRT1 Magnetic Flux vs Time Graph—Emf vs Time Graph 219 I mT13 CRT1 Moving Rectangular Loops in Uniform Magnetic Fields—Current 220 I mT13 WWT1 Changing Current—Bulb Brightness 227 F mT14 WWT1 Moving Loop in Uniform Magnetic Field—Induced Magnetic Field 228 I mT14 WWT2 Loop Moving into a Uniform Magnetic Field—Induced Magnetic Field 228 A mT12 TT1 Moving Rectangular Loops in Uniform Magnetic Fields—Voltage 232 I mT13 TT1 Changing Current—Bulb Brightness 232 I mT14 TT1 Moving Loops in Uniform Magnetic Fields—Magnetic Field 233 I mT13 PET1 Circular Loops within a Solenoid—Ammeter 235 I mT12 WBT1 Moving Rectangular Loops in Uniform Magnetic Fields—Situation 242
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Ranking Task Sample I For a ranking task, each item will have a number of situations as illustrated. Your task will be to rank the items in a specific order. After ranking them you will be asked to identify the basis you used for the ranking and the reasoning behind your choice. It is extremely important that you are careful to write out the proper ranking once you have determined what basis you are going to use, i.e., make sure all of the situations are ranked in the proper order according to your basis. The sample below shows how to rank items and what your explanation should be like. NOTE: Although the procedure for working the item is correct, the particular answer, which was chosen at random from actual student responses, may not be correct. Example: Shown below are eight cars that are moving along horizontal roads at specified speeds. Also given are the masses of the cars. All of the cars are the same size and shape, but they are carrying loads with different masses. All of these cars are going to be stopped by plowing into barrel barriers. All of the cars are going to be stopped in the same distance. Rank these situations from greatest to least on the basis of the strength of the forces that will be needed to stop the cars in the same distance. That is, put first the car on which the strongest force will have to be applied to stop it in x meters, and put last the car on which the weakest force will be applied to stop the car in the same distance.
A
m = 1200 kg
B
m = 1000 kg
C8 m/s
m = 1600 kg
D
m = 1500 kg
5 m/s16 m/s12 m/s
E
m = 1200 kg
F
m = 1600 kg
G5 m/s
m = 1500 kg
H
m = 1100 kg
10 m/s12 m/s9 m/s
Greatest 1 B 2 A F 3 4 H 5 E 6 C 7 D G 8 Least
Or, all cars require the same force. ________
Please carefully explain your reasoning.
Since acceleration is the change in velocity divided by the change in time and all the changes in times are the same, then I
used the change in velocity. How sure were you of your ranking? (circle one)
Notice in this example that two situations produced the same result for the ranking and that these were listed in the same answer blank. Such a possibility exists for all items. In the same way, it is possible that all of the situations will give the same result. If that occurs, and only if that occurs, the option of all equal, or all the same, should be chosen.
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Ranking Task Sample II Each ranking task will have a number of situations, or variations of a situation, that have varying values for two or three variables. Your task is to rank these variations on a specified basis. After ranking the items, you will be asked to explain how you determined your ranking sequence and the reasoning behind the way you used the values of the variables to reach your answer. An example of how to work the ranking tasks follows. Example: Shown below are six situations where a cart, which is initially moving to the right, has a force applied to it such that the force will cause the cart to come to a stop. All of the carts have the same initial speed, but the masses of the carts vary, as do the forces acting upon them. Rank these situations, from greatest to least, on the basis of how long it will take each cart to stop.
A
60 g
B
40 g
C
60 g
D
75 g
E
50 g
F
40 g
60 N
60 N
48 N 48 N
40 N 40 N
Greatest 1___B___ 2___A___ 3___F____ 4___C __ 5___D____ 6____E____ Least Or, all of these carts will require the same time to stop. _______ Please carefully explain your reasoning. I think the time depends on the acceleration, so I divided the forces by the masses. How sure were you of your ranking? (circle one)
Notice in this example that in one instance, two of the situations produced the same value of the ratio used to determine the ranking, and that the letters for the ones that tied are circled showing they were ranked equally (A and F). In another instance, three of the remaining situations have the same ranking and they are circled together (C and D and E), showing this result. In the same way, it is possible that all of the arrangements will give the same result for a particular basis. If that occurs, and only if that occurs, the option of all equal, or all the same, should be chosen.
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ET1-RT1: CHARGED INSULATING BLOCKS—CHARGE DENSITY The block of insulating material shown at right has a volume Vo. An overall charge Qo is spread evenly throughout the volume of the block so that the block has a uniform charge density ρo. Six additional charged insulating blocks are shown below. For each block, the volume is given as well as either the charge or the charge density.
Vo2Qo
2Vo
2Qo
2Vo
Qo
2Vo
ρo
2Vo
2ρo
Block A Block B Block C
Vo2ρo
Block EBlock D Block F
Rank the charge densities of the six blocks.
Greatest 1 ___ AEF ____ 2 _______ 3 _______ 4 ___ BD ____ 5 _______ 6 ___ C ____ Least OR, the charge density is the same for all six blocks. ____ OR, the ranking for the charge density cannot be determined. ____ Carefully explain your reasoning. Charge density is defined as the ratio of total charge divided by volume, so you compute that for each block if not already given. How sure were you of your ranking? (circle one)
ET1-RT2: BREAKING A CHARGED INSULATING BLOCK—CHARGE DENSITY A block of insulating material (labeled O in the diagram) with a width w, height h, and thickness t has a positive charge +Qo distributed uniformly throughout its volume. The block is then broken into three pieces, A, B, and C, as shown.
AB
CO
h/3
2h/3
w/3
2w/3
Rank the charge densities of the original block O, piece A, piece B, and piece C.
Greatest 1 _____ 2 _____ 3 _____ 4 _____ Least OR, the charge density is the same for all four pieces. __ X __ OR, the ranking for the charge densities cannot be determined. ____
Carefully explain your reasoning. The charge density is not going to change because each block will have a charge proportional to its volume since the charge is uniformly distributed. How sure were you of your ranking? (circle one)
ET1-RT3: CHARGED INSULATING BLOCKS—CHARGE The block of insulating material shown at right has a volume Vo. An overall charge Qo is spread uniformly throughout the volume of the block so that the block has a charge density ρo. Six additional charged insulating blocks are shown below. For each block, the volume is given as well as either the charge or the charge density of the block.
Vo2Qo
2Vo
2Qo
2Vo
Qo
2Vo
ρo
2Vo
2ρo
Block A Block B Block C
Vo2ρo
Block EBlock D Block F
Rank the overall charge of the six blocks.
Greatest 1 ___ F ____ 2 ___ ABDE ____ 3 _______ 4 _______ 5 _______ 6 ___ C ____ Least OR, the charge is the same for all six blocks. ____ OR, the ranking for the charge cannot be determined. ____ Carefully explain your reasoning. To determine the total charge for the blocks where it is not given we need to multiply the charge density by the volume and then rank the blocks. How sure were you of your ranking? (circle one)
ET1-RT4: PAIRS OF CONNECTED CHARGED CONDUCTORS—CHARGE Three pairs of charged, isolated, conducting spheres are connected with wires and switches. The spheres are very far apart. The large spheres have twice the radius of the small spheres. Each sphere on the left has a charge of +20 nC and each sphere on the right has a charge of +70 nC before the switches are closed.
+20 nC +70 nC
A B
+20 nC +70 nC
CD
+20 nC +70 nC
E F
Rank the electric charge of the spheres after all of the switches are closed.
Greatest 1 ___ D ____ 2 ___ ABEF ____ 3 _______ 4 _______ 5 _______ 6 ___ C ____ Least OR, the electric charge is the same for all six spheres. _____ OR, the ranking of the electric charge cannot be determined. _____ Carefully explain your reasoning. The charges will move until the potential of each sphere will be the same. Equal size spheres will share the charge equally, but where the sizes differ the larger sphere will have the larger charge. How sure were you of your ranking? (circle one)
ET1-RT5: COLLECTION OF SIX CHARGED CONNECTED CONDUCTORS—CHARGE Six charged conducting spheres are connected with wires and switches. The large spheres have twice the radius of the small spheres. Each sphere on the left has a charge of +20 nC and each sphere on the right has a charge of +70 nC before the switches are closed.
+20 nC +70 nC
A B
+20 nC +70 nC
CD
+20 nC +70 nC
E F
Rank the electric charge of the spheres after all of the switches are closed.
Greatest 1 ___ ABD ____ 2 _______ 3 _______ 4 ___ CEF ____ 5 _______ 6 _______ Least OR, the electric charge is the same for all six spheres. _____ OR, the ranking of the electric charge cannot be determined. _____ Carefully explain your reasoning. The charges will move until the potential of each sphere is the same, so the larger spheres will all have the same charge, as will the three smaller spheres. How sure were you of your ranking? (circle one)
ET1-RT6: PAIRS OF OUTSIDE AND INSIDE CONNECTED CHARGED CONDUCTORS—CHARGE Two pairs of charged, hollow, spherical conducting shells are connected with wires and switches. The system AB is very far from CD. The large shells have four times the radius of the small shells. Each pair has a charge of +20 nC on the small shell and +60 nC on the large shell before the switches are closed.
+60 nC
A B
+20 nC
C
+20 nC
D
+60 nC
Rank the electric charge on the shells A-D after the switches are closed.
Greatest 1 ___ C ____ 2 ___ B ____ 3 ___ A ____ 4 ___ D ____ Least OR, the electric charge is the same for all four shells. _____ OR, the ranking of the electric charge cannot be determined. _____ Carefully explain your reasoning. The charge flows until the potential is the same of each sphere for A and B but all the charge on D flows to the outside sphere since there is no charge inside a conducting object giving C the largest charge.
ET1-RT7: CHARGED ROD AND ELECTROSCOPE—EXCESS CHARGE In each of the four cases below, a charged rod is brought close to an electroscope that is initially uncharged. In cases A and B, the rod is positively charged; in cases C and D, the rod is negatively charged. In cases A and C, the leaf of the electroscope is deflected the same amount, which is more than it is deflected in cases B and D.
A B C D Rank the net charge on the electroscope while the charged rod is near. (This will be a negative value if there is more negative than positive charge on the electroscope.)
Greatest positive 1 _______ 2 _______ 3 _______ 4 _______ Greatest negative OR, the net charge is the same for all four situations but it is not zero. _______ OR, the net charge is zero for all of these situations. ___ X ____ OR, the ranking for the net charge cannot be determined from the information given. _______
Carefully explain your reasoning. The net charge on the electroscope, assuming the rod does not touch it, is zero in all four cases since no charge is transferred.
ET3-RT1: THREE-DIMENSIONAL LOCATIONS IN A CONSTANT ELECTRIC POTENTIAL—FORCE The electric potential has a constant value of six volts everywhere in a three-dimensional region, part of which is shown below.
x
y
z
A
BC
E
F
D
G
H
Rank the strength (magnitude) of the electric force on a charge of +2 µC if it is placed at the labeled points.
Greatest 1 ______ 2 ______ 3 ______ 4 ______ 5 ______ 6 ______ 7 ______ 8 ______ Least OR, the electric force is the same but not zero for all of these points. ____ OR, the electric force is zero for all of these points. __ X __ OR, the ranking for the electric force cannot be determined for all of these points. ____ Carefully explain your reasoning. The field is zero since the potential does not change, thus the force is zero. How sure were you of your ranking? (circle one)
ET3-RT2: CHARGES ARRANGED IN A TRIANGLE—FORCE In each case below, three particles are fixed in place at the vertices of an equilateral triangle. The triangles are all the same size. The particles are charged as shown. (In case C, the top particle has no charge.)
q2q
2q
A2qq
2q
B–q2q
0
C
–2qq
2q
D2q2q
2q
E–2q2q
2q
F
Rank the magnitude of the net electric force on the lower left particle.
Greatest 1 __ E ___ 2 __ A ___ 3 __ F ___ 4 __ B ___ 5 ___ CD __ 6 _____ Least OR, the net electric force on the lower left particle is the same for all six cases. ____ OR, the ranking for the net electric force on the lower left particle cannot be determined. ____ Carefully explain your reasoning.
We apply Coulomb’s Law to the interaction between the lower left charge and the other two, taking account of the vector process of adding the forces.
ET3-RT3: CHARGES IN A PLANE—FORCE In each case shown below, small charged particles are fixed on grids having the same spacing. Each charge q is identical, and all other charges have a magnitude that is an integer multiple of Q.
A
B
C
D
E
F
G
Hq
q+2Q
–2Q
+4Q
q–4Qq
–Q
+2Q
+8Q
+8Q
q
+2Qq
–2Q +2Qq
q –2Q
Rank the magnitude of the electric force on the charge labeled q due to the other charges.
Greatest 1 __ ADEH _ 2 ______ 3 ______ 4 ______ 5 _ F ___ 6 ___G___ 7 ___ B __ 8 ___ C ___ Least OR, the electric force on q is the same but not zero for all eight cases. ____ OR, the electric force on q is zero for all eight cases. ____ OR, the ranking for the electric force on q cannot be determined. ____ Carefully explain your reasoning.
Apply Coulomb’s Law to the interaction between each charge and q and then perform the vector sum when more than one charge is involved.
How sure were you of your ranking? (circle one) Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10
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