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
November 1, 2005

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E & M TIPER Sets Overview
TIPERs tasks are instructional materials based on formats that are inspired by the insights provided by education research
into students’ reasoning. Good research tasks and questions often make good instructional materials. These TIPERs are
designed to target important concepts and reasoning skills in order to promote and establish a strong functional
understanding of physics. This understanding provides a base upon which physics students can solve problems with better
understanding. These tasks can be used as tools for learning and informative assessment. They are designed to provide
small incremental changes to teaching styles that teachers should find less stressful and more acceptable to utilize.
Students enter courses with beliefs about the way the world behaves. Some of these beliefs may be only partially
consistent with the physically correct perception. The goal of these tasks is to help students change their ideas when
necessary. In many cases, it is very difficult to modify the students’ thinking. There is some evidence that instructional
approaches which emphasize putting the students into confrontations with phenomena and their peers while debating
predictions, testing ideas, and explanations leads to more productive learning. One aspect of this approach is the
importance of asking questions in different ways and asking very similar questions that are interrelated. TIPERs provide
tasks that encourage using and support active learning and they require little learning on the part of students to handle the
task formats effectively.
TIPER formats in this book include: Ranking Tasks (RT); Working Backwards Tasks (WBT); What, if anything, is
Wrong Tasks (WWT); Troubleshooting Tasks (TT); Bar Chart Tasks (BCT); Conflicting Contentions Tasks (CCT);
Linked Multiple Choice Tasks (LMCT); Changing Representations Tasks (CRT); Predict and Explain Tasks (PET);
Qualitative Reasoning Tasks (QRT); and Comparison Tasks (CT). In a particular TIPER set, not all formats are used but
there usually are three or four different formats depending on the focus of the set. The sets are much broader in electricity
and much more focused in magnetism.
There are two major categories of tasks in this book: electricity (but not circuits) and magnetism. Within each category,
tasks are listed by task format. This was done in order to prevent students from readily recognizing tasks dealing with the
same question or issue. Each title task has a part that describes briefly the setup and a second part that indicates the target
aspect of the task such as force or field. Tasks with identical task setups often are part of the same set. Each task has a
short ID such as eT7-TT1 or mT2-QRT1 to allow for quick searches for a task. In the other part of this instructor’s guide,
a solution including answer and a short explanation to each task is provided with a special color indicating a solution. The
solution pages match the student edition.
Several common conventions are employed in these tasks. All electric currents are conventional currents unless otherwise
specified. A circle with a dot in the center is used to represent a vector pointing out of the page and a circle with an x in
the center is used to represent a vector pointing into the page. Uniform fields, electric or magnetic, will be constant both in
space and in time. There are no other forces or fields such as gravitation in these situations unless explicitly identified.
In this manual, there is an alternative table of contents in which the tasks are listed by the topics typically found in most
textbooks to help educators select tasks for their students. This alternative table also includes a task level where F
represents a Foundational Task level suitable for all students, I represents an Intermediate Task, and A represents an
Advanced Task level that may use calculus or other aspects such as flux.
One way of using the TIPERs is to have students work on TIPERs individually, then have them compare their work with
other students and finally have a class discussion on the issues. Students are encouraged to discuss what they did and the
rationale for their responses. It is the expectation that they will eventually come to a correct consensus viewpoint in their
group or class. Another way of using them is to place students in small groups where each person can work on a different
task from the same set and eventually the issues with each task can be discussed and resolved in the group. There are
several other ways to use them such as homework; each instructor needs to find a technique which is comfortable.
TIPERs are intended to be very flexible. Instructors can use individual tasks or any combination of tasks that they think
would be useful. While the tasks within a set are correlated, they do not need to be used together. The basic unit is the

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individual task. TIPERs can be used to introduce new material, to review previous material or ideas, to introduce lab
work, as test items, as homework, as group work in class, or as class discussion items. The various formats provide
alternative ways of focusing students on important or confusing ideas and concepts. We know that students’
understanding will be more robust if they deal with multiple representations or tasks on important issues.
TIPER Formats
Ranking Tasks (RT)
A Ranking Task is an exercise that presents students with a set of variations, ranging from four to eight, on a basic
physical situation. The variations differ in the values (numeric or symbolic) for the variables involved but also frequently
include variables that are not important to the task. The students’ task is to rank the variations on the basis of a specified
physical quantity. Students must also explain the reasoning for their ranking scheme and rate their confidence in their
ranking. These tasks require students to engage in a comparison-reasoning process that they seldom do.
For the Ranking Task format, there may be two, three or more of the variations that have equivalent values for the target
quantity. In these cases, answers need to explicitly show that they are tied either by putting tied answers in the same
answer blank or placing a circle surrounding the ones that are tied. Examples of these are found at the end of this
document. In addition, one of the options often available is the ranking for (whatever quantity is designated) cannot be
determined. With ranking tasks, it may not be possible to figure out specific values for a quantity, but you may still be
able to compare the situations to decide which is largest and so on and thus rank the situations.
Working Backwards Tasks (WBT)
Working Backwards Tasks, also referred to as “Physics Jeopardy” tasks (Van Heuvelen and Maloney, 1999), essentially
reverse the order of the problem steps. For example, the given information could be an equation with specific values for
all, or all but one, of the variables. The students then have to construct a physical situation for which the given equation
would apply. Such working backwards tasks require students to take numerical values, including units, and translate them
into physical variables. Working backwards problems also require students to reason about these situations in an unusual
way and often allow for more than one solution.
What, if anything, is Wrong Tasks (WWT)
What, if anything, is Wrong Tasks (Peters, 1982) require students to analyze a statement, or diagrammed situation, to
determine if it is correct or not. If everything is correct the student is asked to explain what is going on and why it works
as described. If something is incorrect the student has to identify the error and explain how to correct it. These are open-
ended exercises so they provide insights into students’ ideas since they will often have interesting reasons for accepting
incorrect situations and for rejecting legitimate situations; and often students’ responses provide ideas for generating new
items.
Troubleshooting Tasks (TT)
Troubleshooting Tasks are variations on the What, if anything, is Wrong Tasks. In these items, the students are explicitly
told that there is an error in the given situation. Their job is to determine what the error is and explain how to correct it.
These tasks can often produce interesting insights into students’ thinking because they will at times identify some correct
aspect of the situation as erroneous. Once again, this outcome helps develop new items.
Bar Chart Tasks (BCT)
Bar Chart Tasks have histograms for one or more quantities. Frequently histograms are given for before and after some
physical process with one bar left off. Students are asked to complete the bar chart by supplying the value for the missing
quantity. Requiring the students to translate between representations they are using and this one is usually quite
productive in developing a better understanding. These items can be especially useful since most students seem to adapt to
and understand bar chart representations relatively easily.
Conflicting Contentions Tasks (CCT)
Conflicting Contentions Tasks present students with two or three statements that disagree or conflict in some way. The
students have to decide which contention they agree with and explain why. These tasks are very useful for contrasting
alternate conceptions with physically accepted statements. This process is facilitated in these tasks because they can be
phrased as “which statement do you agree with and why” rather than asking which statement is correct or true. These
tasks compliment the WWTs.

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Linked Multiple Choice Tasks (LMCT)
Linked Multiple Choice Tasks have one set of answer possibilities that apply to a collection of questions about a related
set of cases. In these tasks, different variations of the situation are described and the students choose from a limited set of
possible outcomes. These items allow for the comparison of how students think about various aspects and/or variations of
a situation. These tasks have the nice feature that one gets both the student’s answer to a particular question and their
pattern of responses for the variations presented.
Predict and Explain Tasks (PET)
Predict and Explain Tasks describe a physical situation that is set up at a point where some event is about to occur.
Students have to predict what will happen in the situation and explain why they think that will occur. These tasks must
have situations with which the students are familiar, or have sufficient background information, to enable the students to
understand the situation. By doing this, it will make students feel comfortable enough to attempt to complete the task.
Changing Representations Tasks (CRT)
These tasks require students to translate from one representation (e.g., an electric field diagram) to another (e.g., an
equipotential curves or surfaces diagram). Students often learn how to cope with one representation without really
learning the role and value of representations and their relationship to problem solving. Getting students to go back and
forth between/among different representations forces them to develop a more robust understanding of each representation.
Among the representations that will be employed at times are mathematical relationships, so this task can serve at times as
a bridge between conceptual understanding and traditional problem solving.
Qualitative Reasoning Tasks (QRT)
These tasks can take a variety of forms, but what they have in common is that the analysis is qualitative. Frequently
students are presented with an initial and final situation and asked how some quantity, or aspect, will change. Qualitative
comparisons (e.g., the quantity increases, decreases, or stays the same) are often the appropriate answer. Qualitative
reasoning tasks can frequently contain elements found in some of the other task formats (e.g., different qualitative
representations and a prediction or explanation).
Comparison Tasks (CT)
These tasks require making a decision on whether a quantity in one situation is greater than, less than, or equal to that
quantity in a second situation along with the reasoning for the decision. These situations may be complicated or difficult
but they can be answered without detailed equations and computations. They are useful in eliciting student ideas about
underlying concepts. A sequence of related comparison tasks can help in connecting or bridging related concepts and
provide for information for assessing and/or guiding future instruction.

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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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Category mT4: Straight Current-Carrying Wire in a Uniform Magnetic Field
This set deals with only one question. This set deals with the force on a current-carrying wire segment when placed in a
magnetic field.
Category mT5: Magnetic Forces
This set probes an important aspect of the magnetic interactions between varieties of pairs of objects. Students are asked
about the relative magnitudes of the forces the two objects exert on each other.
Category mT6: Magnetic Field near Straight Current-Carrying Wire
This set focuses on the magnetic field associated with a long straight current carrying wire. Items ask about magnitude
and/or direction of the field at specified points.
Category mT7: Magnetic Field near a Current-Carrying Circular Loop
This set focuses on the magnetic field at the center of a circular current-carrying coil of wire. Again the questions in the
items ask about magnitude and/or direction of the field.
Category mT8: Magnetic Field near Three Parallel Current-Carrying Wires
This set deals with the vector superposition of magnetic fields due to three parallel long straight current-carrying wires.
Category mT9: Force on Parallel Current-Carrying Wires
This set deals with the force on a current-carrying wire near two other parallel current-carrying wires.
Category mT10: Energy of a Moving Charge in a Uniform Magnetic Field
This set focuses on the issue that a constant and uniform magnetic field does no work on a moving charge since the force
and velocity are always perpendicular to each other.
Category mT11: Flux or Flux Change in Loops in Uniform Magnetic Fields
This set deals with moving rectangular wire loops that travel into, through, and/or out of a region that contains a uniform
magnetic field. The issue targeted is the total flux or the change in flux passing through the loops in the different
situations.
Category mT12: Voltage Induced in Loops in Uniform Magnet Fields
The induced emf in a rectangular wire loop that is being moved into, through and/or out of a uniform magnetic field is the
focus of this set.
Category mT13: Induced Current or Current Changing in Wires near Coils with Bulbs
This set is a variation on the theme of mT12 set since the physical situation is the same (a rectangular wire loop being
moved into, through and/or out of a uniform magnetic field) but this time the question is about the current in the loop
instead of the induced emf. This set also has light bulbs in circular wire coils that are situated next to long straight current-
carrying wires. The currents in the wires are changing and the students are to predict, or explain, the comparative
brightness of the bulbs. In addition, this set has a physical situation where a circular loop of wire is outside and concentric
with a solenoid. The questions in the items focus on the current in the wire loop for changes in the current in the solenoid.
Category mT14: Magnetic Field or Induced Magnetic Field near a Loop in Uniform Magnetic Field
This set deals with rectangular wire loops that travel into, through, and/or out of a region that contains a uniform magnetic
field. The issue targeted is the total magnetic field at the center point or the induced magnetic field at the center point of
the loops in different situations.
Category mT15: Wire Coils and Moving Magnets
This set deals with a permanent magnet moving toward, or away, from a circular coil of wire that is suspended from a
string. The issue explored is how the induced magnetic field interacts with the changing field from the moving magnet.

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I eT5 TT2 Potential near Two Charges—Electric Field 133
I eT2 WBT6 Electric Potential x and y Graphs—Electric Field 143
Work-Energy Issues
A eT6 RT1 Three-Dimensional Locations in a Constant Electric Potential—Work 38
I eT6 RT2 Three Charge System—Electric Potential Energy 39
I eT6 RT3 Electron in Equipotential Surfaces—Kinetic Energy Change 40
A eT6 RT4 Charges and Equipotentials—Work 41
I eT6 CT1 Three Charge System—Electric Potential Energy and Work Done 60
I eT6 QRT1 Two Charged Objects—Work and Energy 76
I eT6 CCT3 Systems of Point Charges—Work to Assemble 102
I eT6 BCT1 Systems of Point Charges—Work to Assemble 117
I eT6 WWT1 Moving Charged Particle in an Electric Field—Potential Energy

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Electromagnetic Induction
F mT12 RT1 Moving Rectangular Loops in Uniform Magnetic Fields—Voltage 165
I mT13 RT1 Moving Rectangular Loops in Uniform Magnetic Fields—Current 166
I mT13 RT2 Changing Current—Bulb Brightness 167
I mT14 RT1 Wire on a Loop Moving in a Magnetic Field—Magnetic Field 168
I mT14 RT2 Loop Moving into a Uniform Magnetic Field—Magnetic Field 169
I mT14 RT3 Loops and Uniform Magnetic Fields—Magnetic Field 170
I mT14 RT4 Wire on a Loop Moving in a Magnetic Field—Induced Magnetic Field 171
I mT14 RT5 Loops and Uniform Magnetic Field—Induced Magnetic Field 172
A mT15 RT1 Wire Loops and Moving Magnets—Loop Motion 173
A mT13 CT2 Moving Rectangular Loops in Uniform Magnetic Fields—Current 175
I mT13 CT1 Moving Rectangular Loops in Uniform Magnetic Fields—Current

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Ranking Task Sample I
For a ranking task, each item will have a number of situations as illustrated. Your task will be to rank the items in a
specific order. After ranking them you will be asked to identify the basis you used for the ranking and the reasoning
behind your choice. It is extremely important that you are careful to write out the proper ranking once you have
determined what basis you are going to use, i.e., make sure all of the situations are ranked in the proper order according to
your basis. The sample below shows how to rank items and what your explanation should be like. NOTE: Although the
procedure for working the item is correct, the particular answer, which was chosen at random from actual student
responses, may not be correct.
Example:
Shown below are eight cars that are moving along horizontal roads at specified speeds. Also given are the masses of the
cars. All of the cars are the same size and shape, but they are carrying loads with different masses. All of these cars are
going to be stopped by plowing into barrel barriers. All of the cars are going to be stopped in the same distance.
Rank these situations from greatest to least on the basis of the strength of the forces that will be needed to stop the cars in
the same distance. That is, put first the car on which the strongest force will have to be applied to stop it in x meters, and
put last the car on which the weakest force will be applied to stop the car in the same distance.
A
m = 1200 kg
B
m = 1000 kg
C
8 m/s
m = 1600 kg
D
m = 1500 kg
5 m/s16 m/s12 m/s
E
m = 1200 kg
F
m = 1600 kg
G
5 m/s
m = 1500 kg
H
m = 1100 kg
10 m/s12 m/s9 m/s
Greatest 1 B 2 A F 3 4 H 5 E 6 C 7 D G 8 Least
Or, all cars require the same force. ________
Please carefully explain your reasoning.
Since acceleration is the change in velocity divided by the change in time and all the changes in times are the same, then I
used the change in velocity.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10
Notice in this example that two situations produced the same result for the ranking and that these were listed in the same
answer blank. Such a possibility exists for all items. In the same way, it is possible that all of the situations will give the
same result. If that occurs, and only if that occurs, the option of all equal, or all the same, should be chosen.

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Ranking Task Sample II
Each ranking task will have a number of situations, or variations of a situation, that have varying values for two or three
variables. Your task is to rank these variations on a specified basis. After ranking the items, you will be asked to explain
how you determined your ranking sequence and the reasoning behind the way you used the values of the variables to
reach your answer. An example of how to work the ranking tasks follows.
Example:
Shown below are six situations where a cart, which is initially moving to the right, has a force applied to it such that the
force will cause the cart to come to a stop. All of the carts have the same initial speed, but the masses of the carts vary, as
do the forces acting upon them.
Rank these situations, from greatest to least, on the basis of how long it will take each cart to stop.
A
60 g
B
40 g
C
60 g
D
75 g
E
50 g
F
40 g
60 N
60 N
48 N 48 N
40 N 40 N
Greatest 1___B___ 2___A___ 3___F____ 4___C __ 5___D____ 6____E____ Least
Or, all of these carts will require the same time to stop. _______
Please carefully explain your reasoning.
I think the time depends on the acceleration, so I divided the forces by the masses.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10
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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E & M TIPERs Key1
ELECTROSTATICS
RANKING T ASKS (RT)
ET1-RT1: CHARGED I NSULATING BLOCKS —CHARGE DENSITY
The block of insulating material shown at right has a volume V o . An overall
charge Qo is spread evenly throughout the volume of the block so that the block
has a uniform charge density
ρo .
Six additional charged insulating blocks are shown below. For each block, the
volume is given as well as either the charge or the charge density.
Vo
2Qo
2Vo
2Qo
2Vo
Qo
2Vo
ρo
2Vo
2
ρo
Block A Block B Block C
Vo
2
ρo
Block EBlock D Block F
Rank the charge densities of the six blocks.
Greatest 1 ___ AEF ____ 2 _______ 3 _______ 4 ___ BD ____ 5 _______ 6 ___ C ____ Least
OR, the charge density is the same for all six blocks. ____
OR, the ranking for the charge density cannot be determined. ____
Carefully explain your reasoning.
Charge density is defined as the ratio of total charge divided by volume, so you compute that for each
block if not already given.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10
Vo Qo
ρo

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E & M TIPERs Key2
ET1-RT2: B REAKING A C HARGED I NSULATING 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.
A B
C
O
h/3
2h/3
w/3
2w/3
Rank the charge densities of the original block O, piece A, piece B, and piece C.
Greatest 1 _____ 2 _____ 3 _____ 4 _____ Least
OR, the charge density is the same for all four pieces. __ X __
OR, the ranking for the charge densities cannot be determined. ____
Carefully explain your reasoning.
The charge density is not going to change because each block will have a charge proportional to its
volume since the charge is uniformly distributed.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10

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E & M TIPERs Key3
ET1-RT3: CHARGED I NSULATING BLOCKS —CHARGE
The block of insulating material shown at right has a volume V o . An overall
charge Qo is spread uniformly throughout the volume of the block so that the
block has a charge density
ρo .
Six additional charged insulating blocks are shown below. For each block, the volume is given as well as
either the charge or the charge density of the block.
Vo
2Qo
2Vo
2Qo
2Vo
Qo
2Vo
ρo
2Vo
2
ρo
Block A Block B Block C
Vo
2
ρo
Block EBlock D Block F
Rank the overall charge of the six blocks.
Greatest 1 ___ F ____ 2 ___ ABDE ____ 3 _______ 4 _______ 5 _______ 6 ___ C ____ Least
OR, the charge is the same for all six blocks. ____
OR, the ranking for the charge cannot be determined. ____
Carefully explain your reasoning.
To determine the total charge for the blocks where it is not given we need to multiply the charge density
by the volume and then rank the blocks.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10
Vo Qo
ρo

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E & M TIPERs Key4
ET1-RT4: PAIRS OF CONNECTED CHARGED CONDUCTORS —C HARGE
Three pairs of charged, isolated, conducting spheres are connected with wires and switches. The spheres
are very far apart. The large spheres have twice the radius of the small spheres. Each sphere on the left
has a charge of +20 nC and each sphere on the right has a charge of +70 nC before the switches are
closed.
+20 nC +70 nC
A B
+20 nC +70 nC
C D
+20 nC +70 nC
E F
Rank the electric charge of the spheres after all of the switches are closed.
Greatest 1 ___ D ____ 2 ___ ABEF ____ 3 _______ 4 _______ 5 _______ 6 ___ C ____ Least
OR, the electric charge is the same for all six spheres. _____
OR, the ranking of the electric charge cannot be determined. _____
Carefully explain your reasoning.
The charges will move until the potential of each sphere will be the same. Equal size spheres will
share the charge equally, but where the sizes differ the larger sphere will have the larger charge.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10

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E & M TIPERs Key5
ET1-RT5: COLLECTION OF SIX CHARGED CONNECTED CONDUCTORS —C HARGE
Six charged conducting spheres are connected with wires and switches. The large spheres have twice
the radius of the small spheres. Each sphere on the left has a charge of +20 nC and each sphere on the
right has a charge of +70 nC before the switches are closed.
+20 nC +70 nC
A B
+20 nC +70 nC
C D
+20 nC +70 nC
E F
Rank the electric charge of the spheres after all of the switches are closed.
Greatest 1 ___ ABD ____ 2 _______ 3 _______ 4 ___ CEF ____ 5 _______ 6 _______ Least
OR, the electric charge is the same for all six spheres. _____
OR, the ranking of the electric charge cannot be determined. _____
Carefully explain your reasoning.
The charges will move until the potential of each sphere is the same, so the larger spheres will all have
the same charge, as will the three smaller spheres.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10

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E & M TIPERs Key6
ET1-RT6: PAIRS OF OUTSIDE AND I NSIDE CONNECTED CHARGED CONDUCTORS —CHARGE
Two pairs of charged, hollow, spherical conducting shells are connected with wires and switches. The
system AB is very far from CD. The large shells have four times the radius of the small shells. Each pair
has a charge of +20 nC on the small shell and +60 nC on the large shell before the switches are closed.
+60 nC
A B
+20 nC
C
+20 nC
D
+60 nC
Rank the electric charge on the shells A-D after the switches are closed.
Greatest 1 ___ C ____ 2 ___ B ____ 3 ___ A ____ 4 ___ D ____ Least
OR, the electric charge is the same for all four shells. _____
OR, the ranking of the electric charge cannot be determined. _____
Carefully explain your reasoning.
The charge flows until the potential is the same of each sphere for A and B but all the charge on D
flows to the outside sphere since there is no charge inside a conducting object giving C the largest
charge.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10

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E & M TIPERs Key7
ET1-RT7: CHARGED ROD AND ELECTROSCOPE—EXCESS C HARGE
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.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10

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E & M TIPERs Key8
ET3-RT1: T HREE -DIMENSIONAL L OCATIONS IN A CONSTANT ELECTRIC POTENTIAL —F ORCE
The electric potential has a constant value of six volts everywhere in a three-dimensional region, part of
which is shown below.
x
y
z
A
B
C
E
F
D
G
H
Rank the strength (magnitude) of the electric force on a charge of +2 μC if it is placed at the labeled
points.
Greatest 1 ______ 2 ______ 3 ______ 4 ______ 5 ______ 6 ______ 7 ______ 8 ______ Least
OR, the electric force is the same but not zero for all of these points. ____
OR, the electric force is zero for all of these points. __ X __
OR, the ranking for the electric force cannot be determined for all of these points. ____
Carefully explain your reasoning.
The field is zero since the potential does not change, thus the force is zero.
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10

Loading page 24...

E & M TIPERs Key9
ET3-RT2: CHARGES ARRANGED IN A T RIANGLE—F ORCE
In each case below, three particles are fixed in place at the vertices of an equilateral triangle. The triangles
are all the same size. The particles are charged as shown. (In case C, the top particle has no charge.)
q2q
2q
A
2qq
2q
B
–q2q
0
C
–2qq
2q
D
2q2q
2q
E
–2q2q
2q
F
Rank the magnitude of the net electric force on the lower left particle.
Greatest 1 __ E ___ 2 __ A ___ 3 __ F ___ 4 __ B ___ 5 ___ CD __ 6 _____ Least
OR, the net electric force on the lower left particle is the same for all six cases. ____
OR, the ranking for the net electric force on the lower left particle cannot be determined. ____
Carefully explain your reasoning.
We apply Coulomb’s Law to the interaction between the lower left charge and the other two, taking
account of the vector process of adding the forces.
q2q
2q
A
2qq
2q
B
–q2q
0
C
–2qq
2q
D
2q2q
2q
E
–2q2q
2q
F
How sure were you of your ranking? (circle one)
Basically Guessed Sure Very Sure
1 2 3 4 5 6 7 8 9 10

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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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