E and M TIPERs Electricity and Magnetism Tasks Edition by Hieggelke Maloney OKuma Kanim

Full file at https://fratstock.eu 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 curth@jjc.edu

David P. Maloney Indiana University-Purdue University Fort Wayne Maloney@IPFW.EDU

Stephen E. Kanim New Mexico State University skanim@nmsu.edu

Thomas L. O'Kuma Lee College tokuma@Lee.Edu

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 https://fratstock.eu 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 © 2006 Pearson Prentice Hall

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Full file at https://fratstock.eu 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 openended 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. © 2006 Pearson Prentice Hall

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Full file at https://fratstock.eu 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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Full file at https://fratstock.eu List of the E & M TIPER Sets 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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Full file at https://fratstock.eu 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 currentcarrying 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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Full file at https://fratstock.eu Task Set Level1 ID

Task ID2

Alternate Table of Contents Electricity TIPERs Task Title Setup —Target Quantity

Page #

F F F F F F F F F F F I

eT1 eT1 eT1 eT1 eT1 eT1 eT1 eT1 eT1 eT1 eT1 eT1

RT1 RT2 RT3 QRT1 QRT2 QRT3 QRT4 CCT1 BCT1 WWT1 WWT2 PET1

Charge Density Charged Insulating Blocks—Charge Density Breaking a Charged Insulating Block—Charge Density Charged Insulating Blocks—Charge Breaking a Charged Insulating Block—Charge and Charge Density Charged Insulating Blocks—Original Block Charged Insulating Blocks—Charge and Charge Density Charged Insulating Rod—Charge and Charge Density Breaking a Charged Insulating Block—Charge Density Charged Insulating Blocks—Charge and Charge Density Breaking a Charged Insulating Block—Charge Density Breaking a Charged Insulating Block—Charge Density Two Insulating Rods—Charge Density

1 2 3 62 63 64 65 91 111 118 118 136

F I I F F F F F

eT1 eT1 eT1 eT10 eT1 eT1 eT1 eT1

RT7 QRT5 CCT2 CCT2 WWT3 WWT4 WWT5 PET2

Charges in Insulators and Conductors Charged Rod and Electroscope—Excess Charge Three Conducting Spheres—Charge Charged Insulators Connected with a Switch—Charge Charged Rod and Electroscope—Deflection Insulator and a Grounded Conductor—Induced Charge Balloon Sticking on a Wall—Charge Distribution Neutral Metal Sphere with a Charged Rod—Charge Distribution Electroscope—Charge

7 66 91 105 119 120 120 137

I F F F I I I I I I I I F I A F I F F F F F F I

eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3

RT2 RT3 RT4 RT5 RT8 QRT1 QRT2 QRT3 QRT4 QRT7 QRT8 QRT9 QRT10 LMCT1 LMCT2 CCT2 CCT6 BCT1 WWT1 WWT2 WWT3 TT1 TT2 PET2

Forces Exerted by/on Point Charges Charges Arranged in a Triangle—Force Charges in a Plane—Force Two Charges—Force Two and Three Charges in a Line—Force Three-Dimensional Locations near a Point Charge—Electric Force Two Unequal Charges—Force Three Charges in a Line—Force Three Charges in a Line—Force Three Charges in a Line—Force Force Direction on Charges in an Equilateral Triangle—Force Force Direction on Charges in a Right Triangle—Force Force Direction on Charges in a Square—Force Two Charges—Force on Each Charges Arranged in a Triangle—Force System of Charges—Electric Force on a Charge Two Charges—Force Conducting Cube Between Point Charges—Force Three Charges in a Line—Force Charges Arranged in a Triangle—Force Two Charges—Force Two Charged Objects—Force Charges Arranged in a Triangle—Force Two Charged Objects—Force Conducting Cube Between Point Charges—Force

9 10 11 12 15 67 68 69 70 73 73 74 75 80 81 93 95 112 122 123 123 130 130 138

1

F-Foundational Task, I-Intermediate Task, and A-Advanced Task 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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Full file at https://fratstock.eu F F F

eT2 eT2 eT2

WBT2 WBT10 WBT11

Charge Arrangement—Physical Situation Forces on Three Charges Along a Line—Charge Location Forces on Three Charges in Two Dimensions—Charge Locations

141 146 147

A I F I I I I F I F I F I F

eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3 eT3

RT6 RT7 RT9 CT1 QRT5 LMCT3 LMCT4 CCT3 CCT4 CCT5 WWT4 WWT5 TT3 TT4

Forces Exerted by/on Objects and Point Charges Charged Rods and Point Charges—Force Charged Curved Rod—Force Sphere and a Point Charge—Force Straight Charged Rod and Two Point Charges—Force Straight Charged Rod and Two Point Charges—Force Straight Charged Rod and Two Point Charges—Force Sphere and a Point Charge—Force Sphere and a Point Charge—Force Curved Charged Rod and Two Point Charges—Force Pairs of Charged Conductors—Force Straight Charged Rod and Two Point Charges—Force Sphere and a Point Charge—Force Straight Charged Rod and Two Point Charges—Force Sphere and a Point Charge—Force

13 14 16 57 71 82 83 93 94 94 124 124 131 131

F I F F I F F F I

eT3 eT5 eT5 eT3 eT5 eT3 eT5 eT3 eT2

RT10 RT1 RT15 LMCT5 LMCT1 CCT1 CCT5 WWT6 WBT9

Uniform Electric Field Three-Dimensional Locations in a Uniform Electric Field—Electric Force Charged Insulating Sheets—Electric Field Three-Dimensional Locations Within a Uniform Electric Field—Field Positive Charge in a Uniform Electric Field—Electric Force Charged Insulating Sheets—Electric Field Electron in a Uniform Electric Field—Electric Force Airplane Flying Between Two Charged Clouds—Electric Field Uniform Electric Field—Electric Force Charged Insulating Sheets—Electric Field

17 20 34 84 86 92 100 125 145

I I F F F F F F

eT5 eT5 eT5 eT5 eT5 eT5 eT5 eT2

RT6 RT8 RT12 CCT4 BCT2 WWT4 TT3 WBT1

Electric Fields of Point Charges Six Charges in Three Dimensions—Electric Field Three Charges in a Line—Electric Field Point Charges in Two Dimensions—Electric Field Three Charges in a Line—Electric Field Point Charge—Electric Field Three Charges in a Line—Electric Field Three Charges in a Line—Electric Field Three Charges—Physical Situation

25 27 31 99 114 126 133 141

F F A A A I I I A A I I I I A I

eT5 eT5 eT5 eT5 eT5 eT5 eT5 eT5 eT5 eT5 eT5 eT5 eT2 eT2 eT2 eT2

RT3 RT5 RT14 RT16 RT17 QRT2 CCT6 CCT8 CCT9 BCT3 WWT2 WWT6 WBT3 WBT4 WBT7 WBT12

Electric Fields of Insulators and Conductors Charged Solid Conducting Sphere—Electric Field Spherical Conducting Shell—Electric Field Charged Curved Rod—Electric Field Point Charge inside an Insulating Shell—Electric Field Point Charge inside a Conducting Shell—Electric Field Charged Insulating Rods—Electric Field Two Charged Spheres—Electric Field Point Charge in a Conducting Shell—Electric Field Field Outside a Sphere with a Cavity—Electric Field Charged Conducting Spherical Shells—Electric Field Hollow Conductors—Field Field Outside a Sphere with a Cavity—Electric Field Electric Field Graphs—Physical Situation Electric Field Graphs—Physical Situation Charged Rod with Electric Field Components—Length and Location Point Charge Inside a Shell—Shell Properties

22 24 33 35 36 78 100 101 102 115 121 127 142 142 144 147

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Full file at https://fratstock.eu I I A F I

eT5 eT5 eT5 eT5 eT5

RT2 RT4 RT13 CRT1 WWT1

Special or Unique Electric Field Situations Changing Electric Force on an Electron—Electric Field Three-Dimensional Locations in a Constant Electric Potential—Field Electric Field Lines—Electric Field Electric Force on an Electron—Electric Field Electric Force on an Electron—Electric Field

21 23 32 106 121

F I F F I I F F I I

eT8 eT8 eT8 eT8 eT8 eT8 eT7 eT7 eT8 eT2

RT1 RT2 RT6 RT8 RT10 CT1 LMCT1 LMCT2 LMCT1 WBT8

Electric Potential Near Point Charges Four Charges in Two Dimensions—Electric Potential Points near a Pair of Equal Opposite Charges—Potential Three-Dimensional Locations near a Point Charge—Electric Potential Six Charges in Three Dimensions—Electric Potential Systems of Eight Point Charges—Potential Points near Pair of Charges—Potential Difference Six Charges in Three Dimensions—Field and Potential at Origin Four Charges in Two Dimensions—Field and Potential Three Point Charge System—Electric Potential Potential near Two Charges—Physical Situation

42 43 47 49 51 61 87 88 89 145

I I I I A I I I I I I I I

eT1 eT1 eT1 eT8 eT8 eT8 eT8 eT8 eT8 eT8 eT7 eT8 eT2

RT4 RT5 RT6 RT3 RT4 RT5 RT9 CCT1 WWT1 WWT2 TT1 TT1 WBT5

Electric Potential Near Objects Pairs of Connected Charged Conductors—Charge Collection of Six Charged Connected Conductors—Charge Pairs of Outside and Inside Connected Charged Conductors—Charge Pairs of Charged Connected Conductors—Electric Potential Charged Curved Rod—Electric Potential Two Large Charged Parallel Sheets—Potential Difference Spherical Conducting Shell—Electric Potential Two Charged Spheres—Electric Potential Uniformly Charged Insulating Sphere—Electric Potential Two Large Charged Parallel Sheets—Potential Difference Two Connected Charged Spheres—Potential and Charge Two Large Charged Parallel Sheets—Potential Difference Electric Potential Difference—Physical Situation

4 5 6 44 45 46 50 103 128 129 134 134 143

F F I I I I F I I I I I I I F I I I I I I I I I

eT3 eT5 eT5 eT5 eT5 eT5 eT8 eT5 eT5 eT3 eT5 eT3 eT6 eT6 eT5 eT5 eT5 eT3 eT5 eT5 eT7 eT5 eT5 eT5

RT1 RT7 RT9 RT10 RT11 RT18 RT7 CT1 CT2 QRT6 QRT1 LMCT6 CCT1 CCT2 CCT3 CCT7 CRT2 CRT1 CRT3 BCT1 BCT1 WWT3 WWT5 TT1

Potential and Field/Force Relations Three-Dimensional Locations in a Constant Electric Potential—Force Potential near Charges—Electric Field Potential vs Position Graphs I—Electric Field Potential vs Position Graph II—Electric Field Potential vs Position Graph III—Electric Field Equipotential Surfaces—Electric Field Three-Dimensional Locations in a Uniform Electric Field—Potential Potential near Charges—Electric Field Potential vs Position Graph II—Electric Field Charge near Equipotential Surfaces—Force Direction Potential vs Position Graphs—Electric Field Potential vs Position Graph II—Force Electric Force on a Proton—Electric Field Electric Potential vs Distance Graph II—Electric Field Three-Dimensional Locations in a Constant Electric Potential—Field Potential near Charges—Electric Field Potential vs Position Graph II—Electric Field Direction Charges and Equipotentials—Force Potential vs Position Graph—Electric Field Graph Potential vs Position Graph II—Electric Field Potential near Two Charges—Electric Field and Potential Potential near Two Charges—Electric Field Potential vs Position Graph II—Electric Field Potential vs Position Graph II—Electric Field

8 26 28 29 30 37 48 58 59 72 77 85 96 97 98 101 107 107 108 113 116 126 127 132

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Full file at https://fratstock.eu I I

eT5 eT2

TT2 WBT6

Potential near Two Charges—Electric Field Electric Potential x and y Graphs—Electric Field

133 143

A I I A I I I I I

eT6 eT6 eT6 eT6 eT6 eT6 eT6 eT6 eT6

RT1 RT2 RT3 RT4 CT1 QRT1 CCT3 BCT1 WWT1

Work-Energy Issues Three-Dimensional Locations in a Constant Electric Potential—Work Three Charge System—Electric Potential Energy Electron in Equipotential Surfaces—Kinetic Energy Change Charges and Equipotentials—Work Three Charge System—Electric Potential Energy and Work Done Two Charged Objects—Work and Energy Systems of Point Charges—Work to Assemble Systems of Point Charges—Work to Assemble Moving Charged Particle in an Electric Field—Potential Energy

38 39 40 41 60 76 102 117 128

I I I A I F F F F I I

eT4 eT4 eT1 eT4 eT4 eT4 eT4 eT4 eT3 eT4 eT4

RT1 RT2 CT1 CT1 CCT1 WWT1 WWT2 TT1 PET1 PET1 PET2

Kinematic Issues Two Charged Objects—Acceleration Charges Between Charged Parallel Plates—Speed Charges in Electric Field—Charge Cart Approaching Sphere—Distance Cart Approaching Sphere—Distance Equipotential Lines—Direction of Proton’s Motion Electron in a Uniform Electric Field—Velocity Electron Moving into a Uniform Electric Field—Acceleration Two Charged Objects—Motion Straight Charged Rod and Two Point Charges—Acceleration Electric Potential vs Position Graph II—Motion of Charged Particles

18 19 57 58 95 119 125 132 138 139 139

I A A I I I I I I I

eT9 eT9 eT9 eT9 eT9 eT1 eT9 eT9 eT9 eT9

RT1 RT2 RT3 RT4 QRT1 CCT3 CCT1 CCT2 WWT1 TT1

Electric Flux Point Charges—Electric Flux Charged Insulator and Conductor—Electric Flux Insulator and Conductor—Electric Flux Gaussian Cubes in Non-Uniform Electric Fields—Electric Flux Charge Within a Hollow Conductor—Electric Flux Charged Sheet—Enclosed Charge Gaussian Cube near a Charge—Electric Flux Charges Inside Gaussian Sphere—Electric Flux and Electric Field Uniform Electric Field—Electric Flux Conducting Shell—Electric Flux

52 53 54 55 79 92 103 104 129 135

I I I I I

eT10 eT10 eT8 eT10 eT8

QRT1 LMCT1 CRT1 CRT1 PET1

Capacitance Graph of Charge vs Electric Potential—Capacitance Two Parallel Plates—Capacitance Parallel Plate Capacitor—Graph of Potential I Parallel Plate Capacitor—Graph of Potential II Parallel Plate Capacitor—Potential

78 90 109 110 140

I I I

eT10 eT10 eT10

RT1 CCT1 TT1

"Charged" Magnetic Poles Charged Rod near a Suspended Bar Magnet—Torque Charged Rod near a Suspended Bar Magnet—Rotation Charged Rod near a Suspended Bar Magnet—Rotation Direction

56 104 135

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Full file at https://fratstock.eu Task Set 3 Level ID

Task 4 ID

Alternate Table of Contents Magnetism TIPERs Task Title Setup —Target Quantity

Page #

I F F I A I F F F F F F F I I

mT9 mT1 mT1 mT5 mT5 mT9 mT1 mT1 mT5 mT5 mT5 mT5 mT1 mT9 mT9

RT1 QRT1 QRT2 QRT1 QRT2 LMCT1 CCT1 CCT2 CCT1 CCT2 BCT1 BCT2 WWT1 WWT1 WBT1

Forces on Charges and Wires in Non-uniform Magnetic Fields Parallel Current–Carrying Wires I—Magnetic Force on Wire Electric Charge near a Bar Magnet—Force Direction Charge near a Circular Current Loop—Force Direction Two Parallel Long Wires—Force Difference Suspended Permanent Magnet and Circular Coil—Scale Reading Three Parallel Current–Carrying Wires I—Magnetic Force on Wire Electric Charge near a Bar Magnet—Force Direction Charge near a Circular Current Loop—Magnetic Force Direction Moving Magnet and Circular Loop—Force Two Magnets—Force Two Long Straight Wires—Force Long Straight Wire and Rectangular Coil—Force Electric Charge near a Bar Magnet—Force Direction Three Parallel Current–Carrying Wires I—Magnetic Force Three Parallel Current–Carrying Wires I—Direction of Currents

159 176 177 182 183 203 209 209 210 211 221 222 225 227 240

F F I F F I F F F F F F A I I

mT2 mT2 mT2 mT2 mT2 mT2 mT2 mT2 mT2 mT2 mT2 mT2 mT2 mT2 mT2

RT1 RT2 RT3 QRT1 LMCT1 CRT1 WWT1 WWT2 TT1 PET1 PET2 PET3 WBT2 WBT1 WBT3

Charged Particle and a Uniform Magnetic Field Charge within a Uniform Magnetic Field—Magnetic Force Moving Charge Path—Direction and Strength of the Magnetic Field Proton in Magnetic and Electric Fields—Acceleration Charged Particle and a Uniform Magnetic Field—Path Moving Charge within a Uniform Magnetic Field—Force Charge in a Uniform Magnetic Field Equation—Acceleration Graph Moving Charge within a Uniform Magnetic Field—Force Direction Charged Particles and a Uniform Magnetic Field—Direction of Motion Path of a Moving Electron in a Uniform Magnetic Field Electron Moving into a Uniform Magnetic Field—Electron Proton at Rest in a Uniform Magnetic Field—Proton Proton Moving into a Uniform Magnetic Field—Proton Equation for a Charge and a Magnetic Field II—Physical Situation Equation for a Charge and a Magnetic Field I—Physical Situation Proton Moving Straight Through Magnetic Field—Cause

148 149 150 178 195 216 225 225 229 234 234 234 236 236 237

I I I F F I F F

mT3 mT3 mT3 mT3 mT3 mT3 mT3 mT3

RT1 QRT1 LMCT1 LMCT2 CCT1 CRT1 WWT1 TT1

Charges Near a Straight Current-Carrying Wire Moving Charge near a Straight Current–Carrying Wire—Acceleration Moving Charge near a Straight Current–Carrying Wire—Acceleration Moving Charge between Two Current–Carrying Wires—Acceleration Charge Moving Along Wire—Magnetic Force Charged Particle and Straight Current–Carrying Wire—Force Long Current–Carrying Wire II—Magnetic Field Moving Charge near a Straight Current–Carrying Wire—Force Moving Positive Charge near a Current–Carrying Wire—Force

151 179 196 197 210 217 226 229

F F I I

mT4 mT4 mT4 mT4

RT1 QRT1 QRT2 LMCT1

Current-Carrying Wire and a Uniform Magnetic Field Current–Carrying Wire in a Uniform Magnetic Field—Magnetic Force Current–Carrying Wire in a Uniform Magnetic Field—Magnetic Force Current–Carrying Wire in a Uniform Magnetic Field—“Bend” of Wire Current in a Uniform Magnetic Field—Magnetic Force

152 180 181 198

3

F-Foundational Task, I-Intermediate Task, and A-Advanced Task 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).

4

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Full file at https://fratstock.eu I F F I

mT4 mT4 mT4 mT4

CRT1 WWT1 TT1 WBT1

Force Equation—Diagram of the Current in a Magnetic Field Current–Carrying Wire in a Uniform Magnetic Field—Force Direction Current–Carrying Wire in a Uniform Magnetic Field—Force Equation for a Current and a Magnetic Field II—Physical Situation

217 226 230 237

F I F I I I F I I I F I I I I F I F F F I A I A I

mT6 mT6 mT7 mT8 mT8 mT8 mT6 mT8 mT8 mT6 mT7 mT8 mT8 mT8 mT6 mT6 mT8 mT6 mT6 mT7 mT8 mT7 mT8 mT8 mT8

RT1 RT2 RT1 RT1 RT2 RT3 QRT1 QRT1 QRT2 LMCT1 LMCT1 LMCT1 LMCT2 CCT1 CRT1 BCT1 BCT1 WWT1 TT1 TT1 PET1 WBT1 WBT1 WBT2 WBT3

Magnetic Fields of Straight Wires and Circular Loops Straight Current–Carrying Wire—Magnetic Field Three-Dimensional Locations near a Long Straight Wire—Magnetic Field Current–Carrying Circular Loops—Magnetic Field Current–Carrying Straight Wires—Magnetic Field Three Parallel Current–Carrying Wires I—Magnetic Field Three Parallel Current–Carrying Wires II—Magnetic Field at Wire Y Straight Current–Carrying Wire—Magnetic Field Three Parallel Current–Carrying Wires I—Magnetic Field Three Parallel Current–Carrying Wires II—Magnetic Field at a Wire Long Wire with a Current—Magnetic Field Current–Carrying Circular Loop—Magnetic Field Three Current–Carrying Wires—Magnetic Field between Wires Three Parallel Current–Carrying Wires I—Magnetic Field Three Parallel Current–Carrying Wires II—Force Magnetic Field Equation—Current and the Magnetic Field Diagram Straight Current–Carrying Wire—Magnetic Field Three Parallel Current–Carrying Wires I—Magnetic Field Current–Carrying Wire I—Magnetic Field Direction Current–Carrying Wire—Magnetic Field Current–Carrying Circular Loop—Magnetic Field Three Parallel Current–Carrying Wires I—Change Single Current Equation for a Current and a Magnetic Field—Physical Situation Equation for Three Currents—Physical Situation Three Parallel Current–Carrying Wires I—Direction of Currents Three Parallel Current–Carrying Wires II—Direction of Currents

153 154 155 156 157 158 184 185 186 199 200 201 202 211 218 223 223 226 230 231 235 238 238 239 239

I I I I I A

mT10 mT10 mT10 mT10 mT10 mT10

RT1 QRT1 BCT1 BCT2 PET1 WBT1

Energy of a Moving Charge in a Uniform Magnetic Field Moving Charge in a Uniform Magnetic Field—Change in Kinetic Energy Moving Charge in a Uniform Magnetic Field—Kinetic Energy Change Moving Charge in a Uniform Magnetic Field—Work and Kinetic Energy Moving Charge in a Uniform Magnetic Field—Work and Kinetic Energy Moving Charge in a Uniform Magnetic Field—Kinetic Energy Charge and a Magnetic Field—Physical Situation

160 187 224 224 235 240

I I I I F I I A F I A F A I I

mT11 mT11 mT11 mT11 mT11 mT11 mT11 mT11 mT11 mT11 mT11 mT11 mT11 mT11 mT11

RT1 RT2 RT3 RT4 CT1 CT2 QRT1 QRT2 CCT1 CRT1 CRT2 TT1 WBT2 WBT1 WBT3

Magnetic Flux or Magnetic Flux Change Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux and Flux Change Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux and Flux Change Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Moving Parallelogram Loop in Uniform Magnetic Fields—Magnetic Flux Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change Magnetic Flux versus Time Graph—Loop Characteristics Moving Rectangular Loops in Uniform Magnetic Fields—Situation Moving Rectangular Loops in Uniform Magnetic Fields—Situation

161 162 163 164 174 174 188 189 212 218 219 231 241 241 242

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Full file at https://fratstock.eu F I I I I I I I A A I A A I F A I I I I A I F I I F I I I F I A I I I I

mT12 mT13 mT13 mT14 mT14 mT14 mT14 mT14 mT15 mT13 mT13 mT13 mT13 mT14 mT14 mT15 mT12 mT12 mT13 mT13 mT15 mT12 mT13 mT13 mT14 mT14 mT12 mT13 mT13 mT14 mT14 mT12 mT13 mT14 mT13 mT12

RT1 RT1 RT2 RT1 RT2 RT3 RT4 RT5 RT1 CT2 CT1 QRT1 QRT2 QRT1 QRT2 QRT1 LMCT1 LMCT2 LMCT1 LMCT2 LMCT1 CCT1 CCT1 CCT2 CCT1 CCT2 CRT1 CRT1 WWT1 WWT1 WWT2 TT1 TT1 TT1 PET1 WBT1

© 2006 Pearson Prentice Hall

Electromagnetic Induction Moving Rectangular Loops in Uniform Magnetic Fields—Voltage Moving Rectangular Loops in Uniform Magnetic Fields—Current Changing Current—Bulb Brightness Wire on a Loop Moving in a Magnetic Field—Magnetic Field Loop Moving into a Uniform Magnetic Field—Magnetic Field Loops and Uniform Magnetic Fields—Magnetic Field Wire on a Loop Moving in a Magnetic Field—Induced Magnetic Field Loops and Uniform Magnetic Field—Induced Magnetic Field Wire Loops and Moving Magnets—Loop Motion Moving Rectangular Loops in Uniform Magnetic Fields—Current Moving Rectangular Loops in Uniform Magnetic Fields—Current Changing Current—Bulb Brightness Circular Loop outside a Long Solenoid—Induced Current Loop Moving in a Uniform Magnetic Field—Induced and Total Magnetic Field Loops and Magnetic Field—Direction of Induced Magnetic Field Wire Loops and Moving Magnets—Motion of the System Moving Rectangular Loops in Uniform Magnetic Fields—Emf Rectangular Loop in a Uniform Magnetic Field—Velocity Moving Rectangular Loops in Uniform Magnetic Fields—Current Loops with Bulbs near a Current—Bulb Lighting Wire Loops and Moving Magnets—Loop Behavior Moving Rectangular Loops in Uniform Magnetic Fields—Emf Moving Rectangular Loops in Uniform Magnetic Fields—Current Changing Current—Bulb Brightness Moving Loops in Uniform Magnetic Fields—Magnetic Field Loop Moving into a Uniform Magnetic Field—Induced Magnetic Field Magnetic Flux vs Time Graph—Emf vs Time Graph Moving Rectangular Loops in Uniform Magnetic Fields—Current Changing Current—Bulb Brightness Moving Loop in Uniform Magnetic Field—Induced Magnetic Field Loop Moving into a Uniform Magnetic Field—Induced Magnetic Field Moving Rectangular Loops in Uniform Magnetic Fields—Voltage Changing Current—Bulb Brightness Moving Loops in Uniform Magnetic Fields—Magnetic Field Circular Loops within a Solenoid—Ammeter Moving Rectangular Loops in Uniform Magnetic Fields—Situation

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165 166 167 168 169 170 171 172 173 175 175 190 191 192 193 194 204 205 206 207 208 212 213 213 214 215 219 220 227 228 228 232 232 233 235 242

Instructors Manual Part 1 E & M TIPERs

Full file at https://fratstock.eu 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

12 m/s

m = 1200 kg

m = 1200 kg

Greatest

1 B

2 AF

m = 1600 kg

3

4 H

m = 1500 kg

G

5 m/s

6 C

7 DG

8

H

10 m/s

m = 1500 kg

5 E

D

5 m/s

m = 1600 kg

F

12 m/s

C

8 m/s

m = 1000 kg

E

9 m/s

B

16 m/s

m = 1100 kg

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) Basically Guessed 1 2 3 4

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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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Instructors Manual Part 1 E & M TIPERs

Full file at https://fratstock.eu 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 60 N

D 75 g

40 g

C 48 N

E 60 N

50 g

48 N

60 g

F 40 N

40 N

40 g

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) Basically Guessed 1 2 3 4

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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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Full file at https://fratstock.eu ELECTROSTATICS RANKING TASKS (RT) 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.

Vo

Qo

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.

Vo

2Vo 2Qo Block A

2Vo 2Qo

Block B

2Vo

Vo

ρo

Qo Block C

Block D

2Vo 2ρo

2ρo Block E

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.

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Full file at https://fratstock.eu 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.

2w/3

A O

w/3

B

h/3

C

2h/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.

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Full file at https://fratstock.eu 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.

Vo

Qo

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.

Vo

2Vo 2Qo Block A

2Vo 2Qo

Block B

2Vo

Vo

ρo

Qo Block C

Block D

2Vo 2ρo

2ρo Block E

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.

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Full file at https://fratstock.eu 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.

A

B +20 nC

+70 nC

D

C +20 nC

+70 nC

E

F +20 nC

+70 nC

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.

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Full file at https://fratstock.eu 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.

A

B +20 nC

+70 nC

D

C +20 nC

+70 nC

E

F +20 nC

+70 nC

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.

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Full file at https://fratstock.eu 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.

B

A

+60 nC

+20 nC

C D +20 nC

+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.

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Full file at https://fratstock.eu 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.

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Full file at https://fratstock.eu 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.

z H G

D

E B C F

y

A x

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.

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Full file at https://fratstock.eu 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.)

2q

2q

A

0

B

2q

C

q

q

2q

2q

2q

2q

D

–q

2q

E

q

–2q

F

2q

2q

2q

–2q

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.

2q

2q

A 2q

B q

q

2q

2q

2q

E –2q

2q

F 2q

9

–q

2q

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C 2q

D q

0

7

2q

8

–2q

9

Very Sure 10 E & M TIPERs Key

Full file at https://fratstock.eu 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.

F

A q

–4Q

q +4Q

B q

+8Q

G

–2Q

C +2Q

q

+2Q +2Q

D

q

H

–2Q

q

q

+2Q

E –Q

q

+8Q

–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.

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E & M TIPERs Key