Solution Manual for E and M TIPERs Electricity And Magnetism: Electricity And Magnetism Tasks: Inspried By Physics Education Research, 1st Edition

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Instructors Manual including Answer Key with SolutionsforE & M TIPERs:Electricity and Magnetism Tasks(Inspired by Physics Education Research)Curtis J. HieggelkeJoliet Junior Collegecurth@jjc.eduDavid P. MaloneyIndiana University-Purdue University Fort WayneMaloney@IPFW.EDUStephen E. KanimNew Mexico State Universityskanim@nmsu.eduThomas L. O'KumaLee Collegetokuma@Lee.EduNovember 1, 2005

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iiE & M TIPER Sets OverviewTIPERs tasks are instructional materials based on formats that are inspired by the insights provided by education researchinto students’ reasoning. Good research tasks and questions often make good instructional materials. These TIPERs aredesigned to target important concepts and reasoning skills in order to promote and establish a strong functionalunderstanding of physics. This understanding provides a base upon which physics students can solve problems with betterunderstanding. These tasks can be used as tools for learning and informative assessment. They are designed to providesmall 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 partiallyconsistent with the physically correct perception. The goal of these tasks is to help students change their ideas whennecessary. In many cases, it is very difficult to modify the students’ thinking. There is some evidence that instructionalapproaches which emphasize putting the students into confrontations with phenomena and their peers while debatingpredictions, testing ideas, and explanations leads to more productive learning. One aspect of this approach is theimportance of asking questions in different ways and asking very similar questions that are interrelated. TIPERs providetasks that encourage using and support active learning and they require little learning on the part of students to handle thetask formats effectively.TIPER formatsin this book include: Ranking Tasks (RT); Working Backwards Tasks (WBT); What, if anything, isWrong 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 butthere usually are three or four different formats depending on the focus of the set. The sets are much broader in electricityand 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 thesame question or issue. Each title task has a part that describes briefly the setup and a second part that indicates the targetaspect of the task such as force or field. Tasks with identical task setups often are part of the same set. Each task has ashort 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 specialcolorindicating a solution. Thesolution pages match the student edition.Several common conventions are employed in these tasks. All electric currents are conventional currents unless otherwisespecified. 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 inthe center is used to represent a vector pointing into the page. Uniform fields, electric or magnetic, will be constant both inspace 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 mosttextbooks to help educators select tasks for their students. This alternative table also includes a task level whereFrepresents a Foundational Task level suitable for all students,Irepresents an Intermediate Task, andArepresents anAdvanced 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 withother students and finally have a class discussion on the issues. Students are encouraged to discuss what they did and therationale for their responses. It is the expectation that they will eventually come to a correct consensus viewpoint in theirgroup or class. Another way of using them is to place students in small groups where each person can work on a differenttask from the same set and eventually the issues with each task can be discussed and resolved in the group. There areseveral 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 thinkwould 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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iiiindividual task. TIPERs can be used to introduce new material, to review previous material or ideas, to introduce labwork, as test items, as homework, as group work in class, or as class discussion items. The various formats providealternative 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 FormatsRanking Tasks (RT)A Ranking Task is an exercise that presents students with a set of variations, ranging from four to eight, on a basicphysical situation. The variations differ in the values (numeric or symbolic) for the variables involved but also frequentlyinclude variables that are not important to the task. The students’ task is to rank the variations on the basis of a specifiedphysical quantity. Students must also explain the reasoning for their ranking scheme and rate their confidence in theirranking. 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 targetquantity. In these cases, answers need to explicitly show that they are tied either by putting tied answers in the sameanswer blank or placing a circle surrounding the ones that are tied. Examples of these are found at the end of thisdocument. In addition, one of the options often available is the ranking for (whatever quantity is designated) cannot bedetermined. With ranking tasks, it may not be possible to figure out specific values for a quantity, but you may still beable 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), essentiallyreverse the order of the problem steps. For example, the given information could be an equation with specific values forall, or all but one, of the variables. The students then have to construct a physical situation for which the given equationwould apply. Such working backwards tasks require students to take numerical values, including units, and translate theminto physical variables. Working backwards problems also require students to reason about these situations in an unusualway 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, todetermine if it is correct or not. If everything is correct the student is asked to explain what is going on and why it worksas 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 acceptingincorrect situations and for rejecting legitimate situations;and often students’ responses provide ideas for generating newitems.Troubleshooting Tasks (TT)Troubleshooting Tasks are variations on the What, if anything, is Wrong Tasks. In these items, the students are explicitlytold 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 correctaspect of the situation as erroneous. Once again, this outcome helps develop new items.Bar Chart Tasks (BCT)Bar Chart Taskshave histograms for one or more quantities. Frequently histograms are given for before and after somephysical process with one bar left off. Students are asked to complete the bar chart by supplying the value for the missingquantity. Requiring the students to translate between representations they are using and this one is usually quiteproductive in developing a better understanding. These items can be especially useful since most students seem to adapt toand 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. Thestudents have to decide which contention they agree with and explain why. These tasks are very useful for contrastingalternate conceptions with physically accepted statements. This process is facilitated in these tasks because they can bephrased as “which statement do you agree with and why” rather than asking which statement is correct or true. Thesetasks compliment the WWTs.

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ivLinked Multiple Choice Tasks (LMCT)Linked Multiple Choice Tasks have one set of answer possibilities that apply to a collection of questions about a relatedset of cases. In these tasks, different variations of the situation are described and the students choose from a limited set ofpossible outcomes. These items allow for the comparison of how students think about various aspects and/or variations ofa situation. These tasks have the nice feature that one gets both the student’s answer to a particular question and theirpattern 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 musthave situations with which the students are familiar, or have sufficient background information, to enable the students tounderstand 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., anequipotential curves or surfaces diagram). Students often learn how to cope with one representation without reallylearning the role and value of representations and their relationship to problem solving. Getting students to go back andforth 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 asa 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. Frequentlystudents are presented with an initial and final situation and asked how some quantity, or aspect, will change. Qualitativecomparisons (e.g., the quantity increases, decreases, or stays the same) are often the appropriate answer. Qualitativereasoning tasks can frequently contain elements found in some of the other task formats (e.g., different qualitativerepresentations 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 thatquantity in a second situation along with the reasoning for the decision. These situations may be complicated or difficultbut they can be answered without detailed equations and computations. They are useful in eliciting student ideas aboutunderlying concepts. A sequence of related comparison tasks can help in connecting or bridging related concepts andprovide for information for assessing and/or guiding future instruction.

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vList of the E & M TIPER SetsCategory 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 chargedensities for continuous distributions.Category eT2: Working Backwards TasksThis category contains all of the working backwards tasks since they normally have the identification/construction of aphysical situation as their target, rather than some physical quantity.Category eT3: ForceThis category contains the tasks where the Coulomb force between charges, charge distributions, and/or objects is thequantity that is asked about.Category eT4: Kinematic QuantitiesThis category contains the tasks that have acceleration, speed, velocity or some other aspect of the motion of chargedobjects as their target quantities.Category eT5: Electric FieldThis category is for tasks that ask about various aspects, such as magnitudes and directions, of individual or net electricfields.Category eT6: Work & Electric Potential EnergyThis category contains items that ask about the work done to move charges or charged objects to locations near othercharges or charge configurations.Category eT7: Multiple Electrostatic QuantitiesTasks in this category ask about more than one electrostatic quantity. An example would be a task that asks about both theelectric field and the electric potential at a point.Category eT8: Electric PotentialTasks in this category ask about the electric potential at points near charges, charge distributions or charged objects.Category eT9: Electric FluxThese tasks have electric flux as the target quantity so they normally relate to situations where Gauss’ Law is involved.Category eT10: MiscellaneousThis is the catch-all category where quantities such as capacitance, torque, or any other non-electrostatic quantity is thetarget that the task asks about.Category mT1: Electric Charge near a Bar Magnet or a Current LoopThis set has electric charges sitting at rest near the poles of permanent magnets or moving along the axial line of a circularcoil 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, andthat 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 turnedoff, some of the situations in this set are problematic since they are experimentally unrealizable.Category mT2: Charges Moving in a Uniform Magnetic FieldThis set deals with charges moving in magnetic fields. There is some variation among the items in the actual physicalarrangements, but all of the items in the set ask about the force on and/or motion of electric charges moving in magneticfields.Category mT3: Charges near a Straight Current-Carrying WireThis set deals with electric charges moving near straight current-carrying wires. The questions in the items in the set askabout the force on or acceleration of the particle.

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viCategory mT4: Straight Current-Carrying Wire in a Uniform Magnetic FieldThis set deals with only one question. This set deals with the force on a current-carrying wire segment when placed in amagnetic field.Category mT5: Magnetic ForcesThis set probes an important aspect of the magnetic interactions between varieties of pairs of objects. Students are askedabout the relative magnitudes of the forces the two objects exert on each other.Category mT6: Magnetic Field near Straight Current-Carrying WireThis set focuses on the magnetic field associated with a long straight current carrying wire. Items ask about magnitudeand/or direction of the field at specified points.Category mT7: Magnetic Field near a Current-Carrying Circular LoopThis set focuses on the magnetic field at the center of a circular current-carrying coil of wire. Again the questions in theitems ask about magnitude and/or direction of the field.Category mT8: Magnetic Field near Three Parallel Current-Carrying WiresThis 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 WiresThis 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 FieldThis set focuses on the issue that a constant and uniform magnetic field does no work on a moving charge since the forceand velocity are always perpendicular to each other.Category mT11: Flux or Flux Change in Loops in Uniform Magnetic FieldsThis set deals with moving rectangular wire loops that travel into, through, and/or out of a region that contains a uniformmagnetic field. The issue targeted is the total flux or the change in flux passing through the loops in the differentsituations.Category mT12: Voltage Induced in Loops in Uniform Magnet FieldsThe induced emf in a rectangular wire loop that is being moved into, through and/or out of a uniform magnetic field is thefocus of this set.Category mT13: Induced Current or Current Changing in Wires near Coils with BulbsThis set is a variation on the theme of mT12 set since the physical situation is the same (a rectangular wire loop beingmoved into, through and/or out of a uniform magnetic field) but this time the question is about the current in the loopinstead 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 comparativebrightness of the bulbs. In addition, this set has a physical situation where a circular loop of wire is outside and concentricwith 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 FieldThis set deals with rectangular wire loops that travel into, through, and/or out of a region that contains a uniform magneticfield. The issue targeted is the total magnetic field at the center point or the induced magnetic field at the center point ofthe loops in different situations.Category mT15: Wire Coils and Moving MagnetsThis set deals with a permanent magnet moving toward, or away, from a circular coil of wire that is suspended from astring. The issue explored is how the induced magnetic field interacts with the changing field from the moving magnet.

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viiAlternate Table of ContentsElectricity TIPERsTaskSetTaskTask TitlePageLevel1IDID2Setup—Target Quantity#Charge DensityFeT1RT1Charged Insulating Blocks—Charge Density1FeT1RT2Breaking a Charged Insulating Block—Charge Density2FeT1RT3Charged Insulating Blocks—Charge3FeT1QRT1Breaking a Charged Insulating Block—Charge and Charge Density62FeT1QRT2Charged Insulating Blocks—Original Block63FeT1QRT3Charged Insulating Blocks—Charge and Charge Density64FeT1QRT4Charged Insulating Rod—Charge and Charge Density65FeT1CCT1Breaking a Charged Insulating Block—Charge Density91FeT1BCT1Charged Insulating Blocks—Charge and Charge Density111FeT1WWT1Breaking a Charged Insulating Block—Charge Density118FeT1WWT2Breaking a Charged Insulating Block—Charge Density118IeT1PET1Two Insulating Rods—Charge Density136Charges in Insulators and ConductorsFeT1RT7Charged Rod and Electroscope—Excess Charge7IeT1QRT5Three Conducting Spheres—Charge66IeT1CCT2Charged Insulators Connected with a Switch—Charge91FeT10CCT2Charged Rod and Electroscope—Deflection105FeT1WWT3Insulator and a Grounded Conductor—Induced Charge119FeT1WWT4Balloon Sticking on a Wall—Charge Distribution120FeT1WWT5Neutral Metal Sphere with a Charged Rod—Charge Distribution120FeT1PET2Electroscope—Charge137Forces Exerted by/on Point ChargesIeT3RT2Charges Arranged in a Triangle—Force9FeT3RT3Charges in a Plane—Force10FeT3RT4Two Charges—Force11FeT3RT5Two and Three Charges in a Line—Force12IeT3RT8Three-Dimensional Locations near a Point Charge—Electric Force15IeT3QRT1Two Unequal Charges—Force67IeT3QRT2Three Charges in a Line—Force68IeT3QRT3Three Charges in a Line—Force69IeT3QRT4Three Charges in a Line—Force70IeT3QRT7Force Direction on Charges in an Equilateral Triangle—Force73IeT3QRT8Force Direction on Charges in a Right Triangle—Force73IeT3QRT9Force Direction on Charges in a Square—Force74FeT3QRT10Two Charges—Force on Each75IeT3LMCT1Charges Arranged in a Triangle—Force80AeT3LMCT2System of Charges—Electric Force on a Charge81FeT3CCT2Two Charges—Force93IeT3CCT6Conducting Cube Between Point Charges—Force95FeT3BCT1Three Charges in a Line—Force112FeT3WWT1Charges Arranged in a Triangle—Force122FeT3WWT2Two Charges—Force123FeT3WWT3Two Charged Objects—Force123FeT3TT1Charges Arranged in a Triangle—Force130FeT3TT2Two Charged Objects—Force130IeT3PET2Conducting Cube Between Point Charges—Force1381F-Foundational Task, I-Intermediate Task, and A-Advanced Task2Ranking 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 RepresentationsTasks (CRT); Predict and Explain Tasks (PET); and Qualitative Reasoning Tasks (QRT).

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viiiFeT2WBT2Charge Arrangement—Physical Situation141FeT2WBT10Forces on Three Charges Along a Line—Charge Location146FeT2WBT11Forces on Three Charges in Two Dimensions—Charge Locations147Forces Exerted by/on Objects and Point ChargesAeT3RT6Charged Rods and Point Charges—Force13IeT3RT7Charged Curved Rod—Force14FeT3RT9Sphere and a Point Charge—Force16IeT3CT1Straight Charged Rod and Two Point Charges—Force57IeT3QRT5Straight Charged Rod and Two Point Charges—Force71IeT3LMCT3Straight Charged Rod and Two Point Charges—Force82IeT3LMCT4Sphere and a Point Charge—Force83FeT3CCT3Sphere and a Point Charge—Force93IeT3CCT4Curved Charged Rod and Two Point Charges—Force94FeT3CCT5Pairs of Charged Conductors—Force94IeT3WWT4Straight Charged Rod and Two Point Charges—Force124FeT3WWT5Sphere and a Point Charge—Force124IeT3TT3Straight Charged Rod and Two Point Charges—Force131FeT3TT4Sphere and a Point Charge—Force131Uniform Electric FieldFeT3RT10Three-Dimensional Locations in a Uniform Electric Field—Electric Force17IeT5RT1Charged Insulating Sheets—Electric Field20FeT5RT15Three-Dimensional Locations Within a Uniform Electric Field—Field34FeT3LMCT5Positive Charge in a Uniform Electric Field—Electric Force84IeT5LMCT1Charged Insulating Sheets—Electric Field86FeT3CCT1Electron in a Uniform Electric Field—Electric Force92FeT5CCT5Airplane Flying Between Two Charged Clouds—Electric Field100FeT3WWT6Uniform Electric Field—Electric Force125IeT2WBT9Charged Insulating Sheets—Electric Field145Electric Fields of Point ChargesIeT5RT6Six Charges in Three Dimensions—Electric Field25IeT5RT8Three Charges in a Line—Electric Field27FeT5RT12Point Charges in Two Dimensions—Electric Field31FeT5CCT4Three Charges in a Line—Electric Field99FeT5BCT2Point Charge—Electric Field114FeT5WWT4Three Charges in a Line—Electric Field126FeT5TT3Three Charges in a Line—Electric Field133FeT2WBT1Three Charges—Physical Situation141Electric Fields of Insulators and ConductorsFeT5RT3Charged Solid Conducting Sphere—Electric Field22FeT5RT5Spherical Conducting Shell—Electric Field24AeT5RT14Charged Curved Rod—Electric Field33AeT5RT16Point Charge inside an Insulating Shell—Electric Field35AeT5RT17Point Charge inside a Conducting Shell—Electric Field36IeT5QRT2Charged Insulating Rods—Electric Field78IeT5CCT6Two Charged Spheres—Electric Field100IeT5CCT8Point Charge in a Conducting Shell—Electric Field101AeT5CCT9Field Outside a Sphere with a Cavity—Electric Field102AeT5BCT3Charged Conducting Spherical Shells—Electric Field115IeT5WWT2Hollow Conductors—Field121IeT5WWT6Field Outside a Sphere with a Cavity—Electric Field127IeT2WBT3Electric Field Graphs—Physical Situation142IeT2WBT4Electric Field Graphs—Physical Situation142AeT2WBT7Charged Rod with Electric Field Components—Length and Location144IeT2WBT12Point Charge Inside a Shell—Shell Properties147

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ixSpecial or Unique Electric Field SituationsIeT5RT2Changing Electric Force on an Electron—Electric Field21IeT5RT4Three-Dimensional Locations in a Constant Electric Potential—Field23AeT5RT13Electric Field Lines—Electric Field32FeT5CRT1Electric Force on an Electron—Electric Field106IeT5WWT1Electric Force on an Electron—Electric Field121Electric Potential Near Point ChargesFeT8RT1Four Charges in Two Dimensions—Electric Potential42IeT8RT2Points near a Pair of Equal Opposite Charges—Potential43FeT8RT6Three-Dimensional Locations near a Point Charge—Electric Potential47FeT8RT8Six Charges in Three Dimensions—Electric Potential49IeT8RT10Systems of Eight Point Charges—Potential51IeT8CT1Points near Pair of Charges—Potential Difference61FeT7LMCT1Six Charges in Three Dimensions—Field and Potential at Origin87FeT7LMCT2Four Charges in Two Dimensions—Field and Potential88IeT8LMCT1Three Point Charge System—Electric Potential89IeT2WBT8Potential near Two Charges—Physical Situation145Electric Potential Near ObjectsIeT1RT4Pairs of Connected Charged Conductors—Charge4IeT1RT5Collection of Six Charged Connected Conductors—Charge5IeT1RT6Pairs of Outside and Inside Connected Charged Conductors—Charge6IeT8RT3Pairs of Charged Connected Conductors—Electric Potential44AeT8RT4Charged Curved Rod—Electric Potential45IeT8RT5Two Large Charged Parallel Sheets—Potential Difference46IeT8RT9Spherical Conducting Shell—Electric Potential50IeT8CCT1Two Charged Spheres—Electric Potential103IeT8WWT1Uniformly Charged Insulating Sphere—Electric Potential128IeT8WWT2Two Large Charged Parallel Sheets—Potential Difference129IeT7TT1Two Connected Charged Spheres—Potential and Charge134IeT8TT1Two Large Charged Parallel Sheets—Potential Difference134IeT2WBT5Electric Potential Difference—Physical Situation143Potential and Field/Force RelationsFeT3RT1Three-Dimensional Locations in a Constant Electric Potential—Force8FeT5RT7Potential near Charges—Electric Field26IeT5RT9Potential vs Position Graphs I—Electric Field28IeT5RT10Potential vs Position Graph II—Electric Field29IeT5RT11Potential vs Position Graph III—Electric Field30IeT5RT18Equipotential Surfaces—Electric Field37FeT8RT7Three-Dimensional Locations in a Uniform Electric Field—Potential48IeT5CT1Potential near Charges—Electric Field58IeT5CT2Potential vs Position Graph II—Electric Field59IeT3QRT6Charge near Equipotential Surfaces—Force Direction72IeT5QRT1Potential vs Position Graphs—Electric Field77IeT3LMCT6Potential vs Position Graph II—Force85IeT6CCT1Electric Force on a Proton—Electric Field96IeT6CCT2Electric Potential vs Distance Graph II—Electric Field97FeT5CCT3Three-Dimensional Locations in a Constant Electric Potential—Field98IeT5CCT7Potential near Charges—Electric Field101IeT5CRT2Potential vs Position Graph II—Electric Field Direction107IeT3CRT1Charges and Equipotentials—Force107IeT5CRT3Potential vs Position Graph—Electric Field Graph108IeT5BCT1Potential vs Position Graph II—Electric Field113IeT7BCT1Potential near Two Charges—Electric Field and Potential116IeT5WWT3Potential near Two Charges—Electric Field126IeT5WWT5Potential vs Position Graph II—Electric Field127IeT5TT1Potential vs Position Graph II—Electric Field132

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xIeT5TT2Potential near Two Charges—Electric Field133IeT2WBT6Electric Potential x and y Graphs—Electric Field143Work-Energy IssuesAeT6RT1Three-Dimensional Locations in a Constant Electric Potential—Work38IeT6RT2Three Charge System—Electric Potential Energy39IeT6RT3Electron in Equipotential Surfaces—Kinetic Energy Change40AeT6RT4Charges and Equipotentials—Work41IeT6CT1Three Charge System—Electric Potential Energy and Work Done60IeT6QRT1Two Charged Objects—Work and Energy76IeT6CCT3Systems of Point Charges—Work to Assemble102IeT6BCT1Systems of Point Charges—Work to Assemble117IeT6WWT1Moving Charged Particle in an Electric Field—Potential Energy128Kinematic IssuesIeT4RT1Two Charged Objects—Acceleration18IeT4RT2Charges Between Charged Parallel Plates—Speed19IeT1CT1Charges in Electric Field—Charge57AeT4CT1Cart Approaching Sphere—Distance58IeT4CCT1Cart Approaching Sphere—Distance95FeT4WWT1Equipotential Lines—Direction of Proton’s Motion119FeT4WWT2Electron in a Uniform Electric Field—Velocity125FeT4TT1Electron Moving into a Uniform Electric Field—Acceleration132FeT3PET1Two Charged Objects—Motion138IeT4PET1Straight Charged Rod and Two Point Charges—Acceleration139IeT4PET2Electric Potential vs Position Graph II—Motion of Charged Particles139Electric FluxIeT9RT1Point Charges—Electric Flux52AeT9RT2Charged Insulator and Conductor—Electric Flux53AeT9RT3Insulator and Conductor—Electric Flux54IeT9RT4Gaussian Cubes in Non-Uniform Electric Fields—Electric Flux55IeT9QRT1Charge Within a Hollow Conductor—Electric Flux79IeT1CCT3Charged Sheet—Enclosed Charge92IeT9CCT1Gaussian Cube near a Charge—Electric Flux103IeT9CCT2Charges Inside Gaussian Sphere—Electric Flux and Electric Field104IeT9WWT1Uniform Electric Field—Electric Flux129IeT9TT1Conducting Shell—Electric Flux135CapacitanceIeT10QRT1Graph of Charge vs Electric Potential—Capacitance78IeT10LMCT1Two Parallel Plates—Capacitance90IeT8CRT1Parallel Plate Capacitor—Graph of Potential I109IeT10CRT1Parallel Plate Capacitor—Graph of Potential II110IeT8PET1Parallel Plate Capacitor—Potential140"Charged" Magnetic PolesIeT10RT1Charged Rod near a Suspended Bar Magnet—Torque56IeT10CCT1Charged Rod near a Suspended Bar Magnet—Rotation104IeT10TT1Charged Rod near a Suspended Bar Magnet—Rotation Direction135

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xiAlternate Table of ContentsMagnetism TIPERsTaskSetTaskTask TitlePageLevel3IDID4Setup —Target Quantity#Forces on Charges and Wires in Non-uniform Magnetic FieldsImT9RT1Parallel Current–Carrying Wires I—Magnetic Force on Wire159FmT1QRT1Electric Charge near a Bar Magnet—Force Direction176FmT1QRT2Charge near a Circular Current Loop—Force Direction177ImT5QRT1Two Parallel Long Wires—Force Difference182AmT5QRT2Suspended Permanent Magnet and Circular Coil—Scale Reading183ImT9LMCT1Three Parallel Current–Carrying Wires I—Magnetic Force on Wire203FmT1CCT1Electric Charge near a Bar Magnet—Force Direction209FmT1CCT2Charge near a Circular Current Loop—Magnetic Force Direction209FmT5CCT1Moving Magnet and Circular Loop—Force210FmT5CCT2Two Magnets—Force211FmT5BCT1Two Long Straight Wires—Force221FmT5BCT2Long Straight Wire and Rectangular Coil—Force222FmT1WWT1Electric Charge near a Bar Magnet—Force Direction225ImT9WWT1Three Parallel Current–Carrying Wires I—Magnetic Force227ImT9WBT1Three Parallel Current–Carrying Wires I—Direction of Currents240Charged Particle and a Uniform Magnetic FieldFmT2RT1Charge within a Uniform Magnetic Field—Magnetic Force148FmT2RT2Moving Charge Path—Direction and Strength of the Magnetic Field149ImT2RT3Proton in Magnetic and Electric Fields—Acceleration150FmT2QRT1Charged Particle and a Uniform Magnetic Field—Path178FmT2LMCT1Moving Charge within a Uniform Magnetic Field—Force195ImT2CRT1Charge in a Uniform Magnetic Field Equation—Acceleration Graph216FmT2WWT1Moving Charge within a Uniform Magnetic Field—Force Direction225FmT2WWT2Charged Particles and a Uniform Magnetic Field—Direction of Motion225FmT2TT1Path of a Moving Electron in a Uniform Magnetic Field229FmT2PET1Electron Moving into a Uniform Magnetic Field—Electron234FmT2PET2Proton at Rest in a Uniform Magnetic Field—Proton234FmT2PET3Proton Moving into a Uniform Magnetic Field—Proton234AmT2WBT2Equation for a Charge and a Magnetic Field II—Physical Situation236ImT2WBT1Equation for a Charge and a Magnetic Field I—Physical Situation236ImT2WBT3Proton Moving Straight Through Magnetic Field—Cause237Charges Near a Straight Current-Carrying WireImT3RT1Moving Charge near a Straight Current–Carrying Wire—Acceleration151ImT3QRT1Moving Charge near a Straight Current–Carrying Wire—Acceleration179ImT3LMCT1Moving Charge between Two Current–Carrying Wires—Acceleration196FmT3LMCT2Charge Moving Along Wire—Magnetic Force197FmT3CCT1Charged Particle and Straight Current–Carrying Wire—Force210ImT3CRT1Long Current–Carrying Wire II—Magnetic Field217FmT3WWT1Moving Charge near a Straight Current–Carrying Wire—Force226FmT3TT1Moving Positive Charge near a Current–Carrying Wire—Force229Current-Carrying Wire and a Uniform Magnetic FieldFmT4RT1Current–Carrying Wire in a Uniform Magnetic Field—Magnetic Force152FmT4QRT1Current–Carrying Wire in a Uniform Magnetic Field—Magnetic Force180ImT4QRT2Current–Carrying Wire in a Uniform Magnetic Field—“Bend” of Wire181ImT4LMCT1Current in a Uniform Magnetic Field—Magnetic Force1983F-Foundational Task, I-Intermediate Task, and A-Advanced Task4Ranking 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 RepresentationsTasks (CRT); Predict and Explain Tasks (PET); and Qualitative Reasoning Tasks (QRT).

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xiiImT4CRT1Force Equation—Diagram of the Current in a Magnetic Field217FmT4WWT1Current–Carrying Wire in a Uniform Magnetic Field—Force Direction226FmT4TT1Current–Carrying Wire in a Uniform Magnetic Field—Force230ImT4WBT1Equation for a Current and a Magnetic Field II—Physical Situation237Magnetic Fields of Straight Wires and Circular LoopsFmT6RT1Straight Current–Carrying Wire—Magnetic Field153ImT6RT2Three-Dimensional Locations near a Long Straight Wire—Magnetic Field154FmT7RT1Current–Carrying Circular Loops—Magnetic Field155ImT8RT1Current–Carrying Straight Wires—Magnetic Field156ImT8RT2Three Parallel Current–Carrying Wires I—Magnetic Field157ImT8RT3Three Parallel Current–Carrying Wires II—Magnetic Field at Wire Y158FmT6QRT1Straight Current–Carrying Wire—Magnetic Field184ImT8QRT1Three Parallel Current–Carrying Wires I—Magnetic Field185ImT8QRT2Three Parallel Current–Carrying Wires II—Magnetic Field at a Wire186ImT6LMCT1Long Wire with a Current—Magnetic Field199FmT7LMCT1Current–Carrying Circular Loop—Magnetic Field200ImT8LMCT1Three Current–Carrying Wires—Magnetic Field between Wires201ImT8LMCT2Three Parallel Current–Carrying Wires I—Magnetic Field202ImT8CCT1Three Parallel Current–Carrying Wires II—Force211ImT6CRT1Magnetic Field Equation—Current and the Magnetic Field Diagram218FmT6BCT1Straight Current–Carrying Wire—Magnetic Field223ImT8BCT1Three Parallel Current–Carrying Wires I—Magnetic Field223FmT6WWT1Current–Carrying Wire I—Magnetic Field Direction226FmT6TT1Current–Carrying Wire—Magnetic Field230FmT7TT1Current–Carrying Circular Loop—Magnetic Field231ImT8PET1Three Parallel Current–Carrying Wires I—Change Single Current235AmT7WBT1Equation for a Current and a Magnetic Field—Physical Situation238ImT8WBT1Equation for Three Currents—Physical Situation238AmT8WBT2Three Parallel Current–Carrying Wires I—Direction of Currents239ImT8WBT3Three Parallel Current–Carrying Wires II—Direction of Currents239Energy of a Moving Charge in a Uniform Magnetic FieldImT10RT1Moving Charge in a Uniform Magnetic Field—Change in Kinetic Energy160ImT10QRT1Moving Charge in a Uniform Magnetic Field—Kinetic Energy Change187ImT10BCT1Moving Charge in a Uniform Magnetic Field—Work and Kinetic Energy224ImT10BCT2Moving Charge in a Uniform Magnetic Field—Work and Kinetic Energy224ImT10PET1Moving Charge in a Uniform Magnetic Field—Kinetic Energy235AmT10WBT1Charge and a Magnetic Field—Physical Situation240Magnetic Flux or Magnetic Flux ChangeImT11RT1Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux161ImT11RT2Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux162ImT11RT3Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change163ImT11RT4Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change164FmT11CT1Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux174ImT11CT2Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change174ImT11QRT1Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux and Flux Change188AmT11QRT2Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux and Flux Change189FmT11CCT1Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change212ImT11CRT1Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux218AmT11CRT2Moving Parallelogram Loop in Uniform Magnetic Fields—Magnetic Flux219FmT11TT1Moving Rectangular Loops in Uniform Magnetic Fields—Magnetic Flux Change231AmT11WBT2Magnetic Flux versus Time Graph—Loop Characteristics241ImT11WBT1Moving Rectangular Loops in Uniform Magnetic Fields—Situation241ImT11WBT3Moving Rectangular Loops in Uniform Magnetic Fields—Situation242

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xiiiElectromagnetic InductionFmT12RT1Moving Rectangular Loops in Uniform Magnetic Fields—Voltage165ImT13RT1Moving Rectangular Loops in Uniform Magnetic Fields—Current166ImT13RT2Changing Current—Bulb Brightness167ImT14RT1Wire on a Loop Moving in a Magnetic Field—Magnetic Field168ImT14RT2Loop Moving into a Uniform Magnetic Field—Magnetic Field169ImT14RT3Loops and Uniform Magnetic Fields—Magnetic Field170ImT14RT4Wire on a Loop Moving in a Magnetic Field—Induced Magnetic Field171ImT14RT5Loops and Uniform Magnetic Field—Induced Magnetic Field172AmT15RT1Wire Loops and Moving Magnets—Loop Motion173AmT13CT2Moving Rectangular Loops in Uniform Magnetic Fields—Current175ImT13CT1Moving Rectangular Loops in Uniform Magnetic Fields—Current175AmT13QRT1Changing Current—Bulb Brightness190AmT13QRT2Circular Loop outside a Long Solenoid—Induced Current191ImT14QRT1Loop Moving in a Uniform Magnetic Field—Induced and Total Magnetic Field192FmT14QRT2Loops and Magnetic Field—Direction of Induced Magnetic Field193AmT15QRT1Wire Loops and Moving Magnets—Motion of the System194ImT12LMCT1Moving Rectangular Loops in Uniform Magnetic Fields—Emf204ImT12LMCT2Rectangular Loop in a Uniform Magnetic Field—Velocity205ImT13LMCT1Moving Rectangular Loops in Uniform Magnetic Fields—Current206ImT13LMCT2Loops with Bulbs near a Current—Bulb Lighting207AmT15LMCT1Wire Loops and Moving Magnets—Loop Behavior208ImT12CCT1Moving Rectangular Loops in Uniform Magnetic Fields—Emf212FmT13CCT1Moving Rectangular Loops in Uniform Magnetic Fields—Current213ImT13CCT2Changing Current—Bulb Brightness213ImT14CCT1Moving Loops in Uniform Magnetic Fields—Magnetic Field214FmT14CCT2Loop Moving into a Uniform Magnetic Field—Induced Magnetic Field215ImT12CRT1Magnetic Flux vs Time Graph—Emf vs Time Graph219ImT13CRT1Moving Rectangular Loops in Uniform Magnetic Fields—Current220ImT13WWT1Changing Current—Bulb Brightness227FmT14WWT1Moving Loop in Uniform Magnetic Field—Induced Magnetic Field228ImT14WWT2Loop Moving into a Uniform Magnetic Field—Induced Magnetic Field228AmT12TT1Moving Rectangular Loops in Uniform Magnetic Fields—Voltage232ImT13TT1Changing Current—Bulb Brightness232ImT14TT1Moving Loops in Uniform Magnetic Fields—Magnetic Field233ImT13PET1Circular Loops within a Solenoid—Ammeter235ImT12WBT1Moving Rectangular Loops in Uniform Magnetic Fields—Situation242

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xivRanking Task Sample IFor a ranking task, each item will have a number of situations as illustrated. Your task will be to rank the items in aspecific order. After ranking them you will be asked to identify the basis you used for the ranking and the reasoningbehind your choice. It is extremely important that you are careful to write out the proper ranking once you havedetermined what basis you are going to use, i.e., make sure all of the situations are ranked in the proper order according toyour basis. The sample below shows how to rank items and what your explanation should be like.NOTE: Although theprocedure for working the item is correct, the particular answer, which was chosen at random from actual studentresponses, 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 thecars. All of the cars are the same size and shape, but they are carrying loads with different masses. All of these cars aregoing 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 inthe same distance. That is, put first the car on which the strongest force will have to be applied to stop it in x meters, andput last the car on which the weakest force will be applied to stop the car in the same distance.Am = 1200 kgBm = 1000 kgC8 m/sm = 1600 kgDm = 1500 kg5 m/s16 m/s12 m/sEm = 1200 kgFm = 1600 kgG5 m/sm = 1500 kgHm = 1100 kg10 m/s12 m/s9 m/sGreatest1B2A F34H5E6 C7 D G8LeastOr, 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 Iused the change in velocity.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910Notice in this example that two situations produced the same result for the ranking and that these were listed in the sameanswer blank. Such a possibility exists for all items. In the same way, it is possible that all of the situations will give thesame 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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xvRanking Task Sample IIEach ranking task will have a number of situations, or variations of a situation, that have varying values for two or threevariables. Your task is to rank these variations on a specified basis. After ranking the items, you will be asked to explainhow you determined your ranking sequence and the reasoning behind the way you used the values of the variables toreach 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 theforce 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, asdo 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.A60 gB40 gC60 gD75 gE50 gF40 g60 N60 N48 N48 N40 N40 NGreatest 1___B___ 2___A___ 3___F____ 4___C __ 5___D____ 6____E____ LeastOr, 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 GuessedSureVery Sure12345678910Notice in this example that in one instance, two of the situations produced the same value of the ratio used to determinethe ranking, and that the letters for the ones that tied are circled showing they were ranked equally (A and F). In anotherinstance, three of the remaining situations have the same ranking and they are circled together (C and D and E), showingthis result. In the same way, it is possible that all of the arrangements will give the same result for a particular basis. If thatoccurs, and only if that occurs, the option of all equal, or all the same, should be chosen.

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E & M TIPERs Key1ELECTROSTATICSRANKINGTASKS(RT)ET1-RT1:CHARGEDINSULATINGBLOCKS—CHARGEDENSITYThe block of insulating material shown at right has a volumeVo.An overallchargeQois spread evenly throughout the volume of the block so that the blockhas a uniform charge densityρo.Six additional charged insulating blocks are shown below. For each block, thevolume is given as well aseitherthe charge or the charge density.Vo2Qo2Vo2Qo2VoQo2Voρo2Vo2ρoBlock ABlock BBlock CVo2ρoBlock EBlock DBlock FRank the charge densities of the six blocks.Greatest 1 ___AEF____ 2 _______ 3 _______ 4 ___BD____ 5 _______ 6 ___C____ LeastOR, 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 eachblock if not already given.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910VoQoρo

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E & M TIPERs Key2ET1-RT2: BREAKING ACHARGEDINSULATINGBLOCK—CHARGEDENSITYA block of insulating material (labeled O in the diagram) with a widthw,heighth,and thicknessthas apositive charge+Qodistributed uniformly throughout its volume. The block is then broken into threepieces, A, B, and C, as shown.ABCOh/32h/3w/32w/3Rank the charge densities of the original block O, piece A, piece B, and piece C.Greatest 1 _____ 2 _____ 3 _____ 4 _____ LeastOR, 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 itsvolume since the charge is uniformly distributed.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key3ET1-RT3:CHARGEDINSULATINGBLOCKS—CHARGEThe block of insulating material shown at right has a volumeVo.An overallchargeQois spread uniformly throughout the volume of the block so that theblock has a charge densityρo.Six additional charged insulating blocks are shown below. For each block, the volume is given as well aseitherthe charge or the charge density of the block.Vo2Qo2Vo2Qo2VoQo2Voρo2Vo2ρoBlock ABlock BBlock CVo2ρoBlock EBlock DBlock FRank the overall charge of the six blocks.Greatest 1 ___F____ 2 ___ABDE____ 3 _______ 4 _______ 5 _______ 6 ___C____ LeastOR, 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 densityby the volume and then rank the blocks.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910VoQoρo

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E & M TIPERs Key4ET1-RT4:PAIRS OFCONNECTEDCHARGEDCONDUCTORS—CHARGEThree pairs of charged, isolated, conducting spheres are connected with wires and switches. The spheresare very far apart. The large spheres have twice the radius of the small spheres. Each sphere on the lefthas a charge of +20 nC and each sphere on the right has a charge of +70 nC before the switches areclosed.+20 nC+70 nCAB+20 nC+70 nCCD+20 nC+70 nCEFRank the electric charge of the spheres after all of the switches are closed.Greatest 1 ___D____ 2 ___ABEF____ 3 _______ 4 _______ 5 _______ 6 ___C____ LeastOR, 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 willshare 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)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key5ET1-RT5:COLLECTION OFSIXCHARGEDCONNECTEDCONDUCTORS—CHARGESix charged conducting spheres are connected with wires and switches. The large spheres have twicethe radius of the small spheres. Each sphere on the left has a charge of +20 nC and each sphere on theright has a charge of +70 nC before the switches are closed.+20 nC+70 nCAB+20 nC+70 nCCD+20 nC+70 nCEFRank the electric charge of the spheres after all of the switches are closed.Greatest 1 ___ABD____ 2 _______ 3 _______ 4 ___CEF____ 5 _______ 6 _______ LeastOR, 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 havethe same charge, as will the three smaller spheres.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key6ET1-RT6:PAIRS OFOUTSIDE ANDINSIDECONNECTEDCHARGEDCONDUCTORS—CHARGETwo pairs of charged, hollow, spherical conducting shells are connected with wires and switches. Thesystem AB is very far from CD. The large shells have four times the radius of the small shells. Each pairhas a charge of +20 nC on the small shell and +60 nC on the large shell before the switches are closed.+60 nCAB+20 nCC+20 nCD+60 nCRank the electric charge on the shells A-D after the switches are closed.Greatest 1 ___C____ 2 ___B____ 3 ___A____ 4 ___D____ LeastOR, 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 Dflows to the outside sphere since there is no charge inside a conducting object giving C the largestcharge.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key7ET1-RT7:CHARGEDROD ANDELECTROSCOPE—EXCESSCHARGEIn each of the four cases below, a charged rod is brought close to an electroscope that is initiallyuncharged. In cases A and B, the rod is positively charged; in cases C and D, the rod is negativelycharged. In cases A and C, the leaf of the electroscope is deflected the same amount, which is more than itis deflected in cases B and D.ABCDRank the net charge on the electroscope while the charged rod is near.(This will be a negativevalue if there is more negative than positive charge on the electroscope.)Greatest positive 1 _______ 2 _______ 3 _______ 4 _______ Greatest negativeOR, 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 sinceno charge is transferred.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key8ET3-RT1:THREE-DIMENSIONALLOCATIONS IN ACONSTANTELECTRICPOTENTIAL—FORCEThe electric potential has a constant value of six volts everywhere in a three-dimensional region, part ofwhich is shown below.xyzABCEFDGHRank the strength (magnitude) of the electric force on a charge of +2 μC if it is placed at the labeledpoints.Greatest 1 ______ 2 ______ 3 ______ 4 ______ 5 ______ 6 ______ 7 ______ 8 ______ LeastOR, 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)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key9ET3-RT2:CHARGESARRANGED IN ATRIANGLE—FORCEIn each case below, three particles are fixed in place at the vertices of an equilateral triangle. The trianglesare all the same size. The particles are charged as shown. (In case C, the top particle has no charge.)q2q2qA2qq2qB–q2q0C–2qq2qD2q2q2qE–2q2q2qFRank the magnitude of the net electric force on the lower left particle.Greatest 1 __E___ 2 __A___ 3 __F___ 4 __B___ 5 ___CD__ 6 _____ LeastOR, 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, takingaccount of the vector process of adding the forces.q2q2qA2qq2qB–q2q0C–2qq2qD2q2q2qE–2q2q2qFHow sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key10ET3-RT3:CHARGES IN APLANE—FORCEIn each case shown below, small charged particles are fixed on grids having the same spacing.Eachchargeqis identical, and all other charges have a magnitude that is an integer multiple ofQ.ABCDEFGHqq+2Q–2Q+4Qq–4Qq–Q+2Q+8Q+8Qq+2Qq–2Q+2Qqq–2QRank the magnitude of the electric force on the charge labeledqdue to the other charges.Greatest 1 __ADEH_ 2 ______ 3 ______ 4 ______ 5 _F___ 6 ___G___ 7 ___B__ 8 ___C___ LeastOR, 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 sumwhen more than one charge is involved.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key11ET3-RT4:TWOCHARGES—FORCEIn each case shown below, small charged particles are fixed on grids having the same spacing.Eachchargeqis identical, and all the other charges have a magnitude that is an integer multiple ofq.ACEBDFq–8qq–4qq+2q+16q+4q+8qqqqRank the magnitude of the electric force on the charge labeledqdue to the other charge.Greatest 1 __ACDE___ 2 _____ 3 _____ 4 _____ 5 __F___ 6 __B___ LeastOR, the electric force on q is the same but not zero for all six cases. ____OR, the electric force on q is zero for all six cases. ____OR, the ranking for the electric force on q cannot be determined. ____Carefully explain your reasoning.The force (Coulomb’s Law) is proportional to the product of the charges and inversely proportional tothe square of the distance between them. The larger charges and the closer charges are ranked higher.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key12ET3-RT5:TWO ANDTHREECHARGES IN ALINE—FORCEIn each case shown below, small charged particles are fixed on grids having the same spacing.Eachchargeqis identical, and all the other charges have a magnitude that is an integer multiple ofq.A–4qqBCDEF–2qq+2qq–qq+2qq+2q+2qq–2q–2qRank the magnitude of the electric force on the charge labeledqdue to the other charges.Greatest 1 __ADE___ 2 _____ 3 _____ 4 __BF___ 5 _____ 6 __C___ LeastOR, the electric force on q is the same but not zero for all six cases. ____OR, the electric force on q is zero for all six cases. ____OR, the ranking for the electric force on q cannot be determined. ____Carefully explain your reasoning.In cases A, B and F the net force on q is found simply using Coulomb’s Law. In C, D and E, useCoulomb’s law to find the magnitude of the forces on q by each of the other two charges. Then, takinginto consideration the direction of these forces, add them vectorially to find the magnitude of the netforce on q.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key13ET3-RT6:CHARGEDRODS ANDPOINTCHARGES—FORCEIn each case A-D, a point charge+qis fixed in place as well as someother point charges or charged rods.The charged insulating rod in case A has a lengthxand a charge+2Qdistributed uniformly along it. The charged insulating rod in case D isan arc of radiusy,and has a charge +2Qdistributed uniformly along it.Rank the magnitude of the electric force on +qdue to the othercharges in each case.Greatest 1 __C___ 2 __D___ 3 __A___ 4 __B___ LeastOR, the electric force on +q is the same for all four cases. ____OR, the ranking for the electric force on +q cannot be determined.____Carefully explain your reasoning.C has greatest force since total charge 2Q is concentrated in one spotat distance y. B is least since charge is split in half and each half isfarther away and greatest angle. A and D are both smaller than C since the charge is spread out, butlarger than B since more of the charge is closer to q and closer to being on the same vertical line. D isgreater than A since the charge in D is never farther than the distance y, whereas in A, the charge atthe ends of the line is farther away than y.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910+2Q+qθyθy+2Q+qDCy+q+2Q+qBAy+Qθθxx+Qyθθ

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E & M TIPERs Key14ET3-RT7:CHARGEDCURVEDROD—FORCEA point charge+qis placed near a curved, charged, insulating rod as shown at left below.The charge isplaced at the center of curvature of the curved rod. For each of the five cases A-E, the charge density onthe rod varies according to the graphs, but the total charge is the same.θ0°–20°–40°–60°20° 40° 60°θCharge densityA0°–20°–40°–60°20° 40° 60°θCharge densityB0°–20°–40°–60°20° 40° 60°θCharge densityD0°–20°–40°–60°20° 40° 60°θCharge densityC0°–20°–40°–60°20° 40° 60°θCharge densityECharge densityvaries alongrodd+qRank the magnitude of the electric force on+qdue to the charge in the curved rod in each case.Greatest 1 ___D____ 2 ___A____ 3 ___C____ 4 ___B____ 5 ___E____ LeastOR, the electric force on +q is the same (but not zero) for all five cases. ____OR, the electric force on +q is zero for all five cases. ____OR, the ranking for the electric force on +q cannot be determined. ____Carefully explain your reasoning.Vector addition or integration yields that more concentrated charge distribution gives larger forcesince the x-components cancel due to symmetry. The largest will be the one where the y-componentsare larger. This will occur when the charge is concentrated nearθ=0.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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E & M TIPERs Key15ET3-RT8:THREE-DIMENSIONALLOCATIONS NEAR APOINTCHARGE—ELECTRICFORCEThere is a positive point charge+qlocated at (0, 3, 0) as shown in the three-dimensional region below.Within that region are points located on the corners of two cubes as shown below. The small cube hasedges of 1 centimeter length and the larger cube has edges of 3 centimeter length.xzABCEFDGHy+qRank the strength (magnitude) of the electric force on a +3qpoint charge if it is placed at the labeledpoints.Greatest 1 ___C___ 2 __D___ 3 __BG__ 4 ______ 5 _AFH__ 6 ______ 7 ______ 8 __E___ LeastOR, the electric force is the same but not zero for all these points. ____OR, the electric force is zero for all these points. ____OR, the ranking for the electric force cannot be determined for all these points. ____Carefully explain your reasoning.The force between two point charges decreases as the distance between those charges increases.How sure were you of your ranking? (circle one)Basically GuessedSureVery Sure12345678910

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