HS-PS3-5: Modeling Forces and Energy for Two Objects in a Field
In plain English: HS-PS3-5 is the NGSS high school performance expectation that asks students to develop and use a model of two objects interacting through an electric or magnetic field. The model shows the equal and opposite forces on the objects and how their energy changes as energy stored in the field changes. It is usually taught in Physics or Physical Science.
Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction.
Clarification Statement: Examples of models could include drawings, diagrams, and texts, such as drawings of what happens when two charges of opposite polarity are near each other, including an explanation of how the change in energy of the objects is related to the change in energy of the field.
Assessment Boundary: Assessment is limited to systems containing two objects.
Next Generation Science Standards · Disciplinary Core Idea: Energy · Official standard
Students build and use models of two objects that interact through an electric or magnetic field: two charged spheres, two magnets, a particle and a nucleus. Each model has three parts: field lines, an equal and opposite force pair, and energy bars that show how the kinetic energy of the objects changes as the energy stored in the field changes. Students test the models against invented data from carts, magnets and simulations.
The NGSS Clarification Statement says: "Examples of models could include drawings, diagrams, and texts, such as drawings of what happens when two charges of opposite polarity are near each other, including an explanation of how the change in energy of the objects is related to the change in energy of the field." The Assessment Boundary says: "Assessment is limited to systems containing two objects." Every system on this page has exactly two objects. All data sets are invented for teaching, and the lesson uses k = 8.99 × 10⁹ N·m²/C², e = 1.602 × 10⁻¹⁹ C and g = 9.8 N/kg.
Learning Objectives
By the end of this lesson, students will be able to:
Draw a model of two charges or two magnets that shows the field, with lines that never cross
Show that the forces on the two objects are equal in size and opposite in direction, and find their size for two small charged spheres
Use energy bars and U = kq1q2/r to explain how the kinetic energy of the objects changes when the energy stored in the field changes
Use data from carts, magnets or simulations to test and revise a model of a two-object interaction
Critique a classmate's model and correct errors in its field, forces or energy accounting
Prior Knowledge Required
Students should already be comfortable with:
Evidence that fields exist between objects that exert forces at a distance MS-PS2-5
How the arrangement of interacting objects changes stored energy MS-PS3-2
Kinetic energy, KE = ½mv², and conservation of energy in a closed system
Newton's third law: interaction forces come in equal and opposite pairs
Hang two inflated balloons from threads so they nearly touch. Rub both on a wool scarf or hair, then let them hang. They swing apart and stay apart. Hold one balloon still and slowly push the other toward it by hand, then let go.
Warm-Up Prompt
"When you pushed the balloons closer, you had to keep pushing. When you let go, the balloon swung away and sped up. Where did the energy for that motion come from, and where was it while you held the balloons close together? Draw a quick sketch that shows your idea."
Collect two or three sketches. Some students say the energy was in the balloon or in the hand; others say it was "in the charge." Keep the sketches: in the closure students redraw them with field lines, force arrows and energy bars.
Direct Instruction15-20 minutes
A model with three parts. Two charged objects (or two magnets) interact through the field between them. A complete model of the interaction shows (1) the field, drawn as lines that start on positive charges and end on negative charges (or run from north to south outside a magnet) and never cross; (2) the forces, drawn as one arrow on each object, equal in size and opposite in direction; and (3) the energy, drawn as bars for the kinetic energy of the objects and the energy stored in the field, before and after a change.
The rule that links forces and energy: when the objects move in the direction of the forces the field exerts on them (opposite charges moving together, like charges moving apart), the energy stored in the field decreases and the objects gain the same amount of kinetic energy. When something outside the system pushes them against those forces, it does work, and the energy stored in the field increases. For two small charged spheres the stored energy is U = kq1q2/r and the force has size F = k|q1q2|/r², with k = 8.99 × 10⁹ N·m²/C². A negative U means energy must be added to pull the pair apart. Diagram 1 shows the field and forces for Example 1, and Diagram 2 shows U against r for that pair.
Opposite charges: forces and energy
Sphere A (+4.0 nC) and sphere B (-4.0 nC), each 1.0 cm across, are held 6.0 cm apart on an insulating table and then released. They slide toward each other; friction is negligible.
Result: F = (8.99 × 10⁹)(4.0 × 10⁻⁹)²/(0.060)² ≈ 4.0 × 10⁻⁵ N on each sphere, toward the other. U at 6.0 cm = -2.40 × 10⁻⁶ J; U at 3.0 cm = -4.79 × 10⁻⁶ J. The field energy drops by 2.40 × 10⁻⁶ J, so the two spheres together gain 2.40 × 10⁻⁶ J of kinetic energy.
Like charges released
Two 2.0 g foam pucks on an air table each carry a +6.0 nC sphere 2.0 cm across. They are held with centers 4.0 cm apart and released.
Result: U = (8.99 × 10⁹)(6.0 × 10⁻⁹)²/0.040 = 8.09 × 10⁻⁶ J. When the pucks are far apart, U is close to 0, so the pair has gained 8.09 × 10⁻⁶ J of kinetic energy, shared equally: 4.05 × 10⁻⁶ J each, a final speed of about 0.064 m/s.
Two particles: closest approach
An alpha particle (charge +2e) with 5.0 MeV (8.01 × 10⁻¹³ J) of kinetic energy heads straight at a gold nucleus (charge +79e). Treat the nucleus as fixed, and use e = 1.602 × 10⁻¹⁹ C.
Result: At the closest point all the kinetic energy is stored in the field: k(2e)(79e)/r = 8.01 × 10⁻¹³ J gives r ≈ 4.6 × 10⁻¹⁴ m. The repulsive force there is about 18 N on each particle, and the alpha particle is pushed back the way it came.
Magnetic bumper
A 0.50 kg cart with a ring magnet rolls at 0.40 m/s toward a magnet fixed to the end of the track, like poles facing. It stops 1.5 cm from the fixed magnet, then rolls back at 0.38 m/s.
Result: KE before = ½(0.50)(0.40)² = 0.040 J. At the stop, about 0.040 J is stored in the magnetic field. KE after = ½(0.50)(0.38)² = 0.036 J, so about 0.004 J went to thermal energy and sound through friction.
After each example, ask students to point to the part of the model that shows the force pair and the part that shows the energy change. Stress two ideas: the force on the small charge is as large as the force on the large one, and energy is transferred between the field and the objects, never created.
Guided Practice15 minutes
Pairs complete a model of a new two-object system: a +1.0 nC sphere and a -7.0 nC sphere, each 1.2 cm across, at four separations. They fill in the table, then draw field lines, a force pair and energy bars for the move from 8.0 cm to 2.0 cm.
Guided practice: +1.0 nC and -7.0 nC spheres (values from the model F = k|q₁q₂|/r² and U = kq₁q₂/r)
Separation r (cm)
Force on each sphere (N)
Energy in the field U (J)
2.0
1.57 × 10⁻⁴
?
4.0
3.93 × 10⁻⁵
?
6.0
?
-1.05 × 10⁻⁶
8.0
?
-7.9 × 10⁻⁷
Fill in the blanks. Key: U = -3.15 × 10⁻⁶ J at 2.0 cm and -1.57 × 10⁻⁶ J at 4.0 cm; F = 1.75 × 10⁻⁵ N at 6.0 cm and 9.8 × 10⁻⁶ N at 8.0 cm.
Check the pattern: when r doubles from 2.0 to 4.0 cm, the force falls to one fourth and the energy moves halfway toward zero.
Draw the force pair. The arrow on the +1.0 nC sphere is the same length as the arrow on the -7.0 nC sphere.
Draw energy bars for the move from 8.0 cm to 2.0 cm. The field energy falls by about 2.4 × 10⁻⁶ J, and the kinetic energy of the spheres rises by the same amount.
Independent Practice10-15 minutes
Each student uses a model to analyze invented simulation data. A +2.0 nC bead 1.0 cm across (mass 1.0 g) is released with its center 2.0 cm from the center of a fixed +8.0 nC sphere 2.0 cm across. It slides along a frictionless track, straight away from the sphere.
Independent practice data (invented simulation output)
Separation r (cm)
2.0
4.0
8.0
16.0
Bead speed v (m/s)
0
0.085
0.104
0.112
Students compute the kinetic energy ½mv² and the field energy U = kq1q2/r at each separation, show that KE + U stays at about 7.2 × 10⁻⁶ J, and write a paragraph that uses the model to explain why the bead speeds up quickly at first and then hardly at all.
Closure5 minutes
Students return to their warm-up balloon sketches and redraw them as a three-part model: field lines between the balloons, a force pair, and energy bars for "held close" and "just released." Exit ticket: "Two magnets are pulled apart by hand, north pole facing south pole. Does the energy stored in the field increase or decrease? What supplied the energy?"
Differentiation Strategies
For Struggling Students
Give a model template with three labeled boxes (field, forces, energy) and a word bank: field line, force pair, kinetic energy, field energy, work
Start with magnets and balloons, which students can feel and see, before calculations with charged spheres
Provide energy bar charts with the total already drawn so students only split it between kinetic energy and field energy
For Advanced Students
Ask students to find how fast each sphere in Example 1 moves at 3.0 cm if each has a mass of 1.0 g, sharing the kinetic energy equally
Have students explain why U is negative for opposite charges and what the choice of U = 0 at a very large separation means
Ask students to use the area under the force-gap graph in Activity 3 to estimate the kinetic energy of the magnets if they were released
Assessment Guidance
What to Look For
Check that every model has both a force pair and an energy account, not only one of the two. Look for force arrows of equal length even when the charges or magnets differ, field lines that start and end in the right places without crossing, and energy bars in which every increase is matched by a decrease or by work from outside. Listen for students who say energy is "created" by the force or "used up" by the charges.
02
Classroom Activities
3 Activities
1
Magnetic Bumper Cart Lab
25 minGroups of 3-4
Groups send a cart carrying a ring magnet toward a second magnet fixed to the end of a track, with like poles facing. They measure the speed before and after the interaction and the closest gap, then build energy bar models of the two-magnet system.
Procedure
Tape a ceramic ring magnet to the front of a dynamics cart (total mass 0.50 kg on a balance). Tape a second ring magnet to the end stop so that like poles face each other.
Record video at 60 frames per second with a meter stick along the track. Give the cart a gentle push and find its speed over the last 20 cm before the magnets interact, the smallest gap between the magnets, and the speed over the first 20 cm after.
Repeat at three different starting speeds.
Safety: wear goggles, because ceramic magnets can chip if they snap together. Keep strong magnets away from phones, cards with magnetic stripes and anyone with a pacemaker, and never let two magnets snap together on a finger.
Sample Data (invented)
Speed before: 0.25, 0.35, 0.45 m/s. Closest gap: 2.8, 2.0, 1.4 cm. Speed after: 0.24, 0.33, 0.43 m/s. Students compute the kinetic energy before and after each trial and the energy stored in the field at the closest gap.
Discussion Questions
The faster the cart, the smaller the closest gap. Use your energy bars to explain why.
In every trial the cart comes back with 89% to 92% of its kinetic energy. Where did the rest go? Is it still in the system of two magnets?
Draw the force pair at the moment of closest approach. Which magnet pushes harder?
Modification for Distance Learning
Students analyze the sample data in a spreadsheet and build the energy bar models on a shared slide, then compare with a video of the cart posted by the teacher.
2
Model Storyboards and Gallery Critique
20 minGroups of 3
Each group draws a four-panel storyboard for one two-object interaction and then critiques another group's storyboard with a checklist. The storyboards are the models the standard asks for: drawings plus a short text that link forces to energy changes.
Scenario Cards
Card 1: a positive and a negative charged sphere are released from rest and move toward each other.
Card 2: two positive charged spheres are released from rest and move apart.
Card 3: a student's hands push two positive charged spheres closer together, slowly.
Card 4: a student pulls two magnets apart, north pole facing south pole.
Each storyboard shows the system before and after, with field lines, a force pair on the objects, and energy bars for kinetic energy, field energy and work done from outside.
Critique Checklist
Field lines never cross, and they start and end in the right places.
The two force arrows have the same length and point in opposite directions.
The energy bars balance: any increase in one bar is matched by a decrease in another or by work from outside the system.
The text explains how the change in the objects' energy is related to the change in the field's energy.
Discussion Questions
In which scenarios does the energy stored in the field increase, and what do those scenarios have in common?
Card 1 and Card 2 have forces in opposite directions. Why do both end with more kinetic energy?
Challenge Variation
Groups add a fifth card of their own design (for example, a steel ball rolling toward a magnet) and trade it with another group, who must build the model.
3
Pull-Apart Energy from a Force Graph
25 minPairs
Pairs measure the force between two attracting ceramic magnets at several gaps with a digital scale, graph force against gap, and use the area under the graph to find how much energy is stored in the field when the magnets are pulled apart.
Procedure
Tape one magnet on top of a 10 cm wooden block on a digital scale (the block keeps the magnet away from the scale's electronics) and tare the scale.
Clamp the second magnet to a ring stand above it, attracting side down, and lower it to set gaps from 0.5 cm to 3.0 cm using plastic spacers to measure each gap.
The scale reading drops as the upper magnet pulls up on the lower one. Convert the drop in grams to newtons: F = (reading drop in kg) × 9.8 N/kg.
Safety: goggles on, and keep fingers out of the gap.
Sample Data (invented)
Gap 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 cm; attractive force 2.40, 1.30, 0.75, 0.45, 0.28, 0.18 N. Students graph F against gap and add up trapezoid areas (average force × 0.005 m for each step) to estimate the energy that must be supplied to pull the magnets from 0.5 cm to 3.0 cm: about 0.020 J.
Discussion Questions
Most of the area lies between 0.5 cm and 1.5 cm. What does that say about where the energy change happens?
If the magnets were released at 3.0 cm, how much kinetic energy would they have just before the gap closed to 0.5 cm, ignoring friction? Where did it come from?
Modification for Distance Learning
Students use the sample data in a spreadsheet, compute the trapezoid areas in a column, and compare their estimate with a partner's.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Field and Force Model for Two Opposite Charges
Model of Example 1: a +4.0 nC sphere and a -4.0 nC sphere 6.0 cm apart. The field lines were computed from the two charges and drawn to scale. Each sphere feels an attractive force of about 4.0 × 10⁻⁵ N, shown by arrows of equal length.
Diagram 2: Energy Stored in the Field Against Separation
U = kq1q2/r for two 4.0 nC spheres, computed and drawn to scale. For the opposite pair (solid) U falls as the spheres get closer, so the field gives energy to the spheres. For the like pair (dashed) U rises as they get closer, so energy must be supplied by pushing.
04
Homework Assignment
~30 min
HS-PS3-5 Homework: Modeling Forces and Energy in Fields
Directions: Every system has exactly two objects, and all data are invented for practice. Use k = 8.99 × 10⁹ N·m²/C² and e = 1.602 × 10⁻¹⁹ C. For each problem, draw a model with field lines, a force pair and energy bars where they apply, and show calculations with units.
Part 1: Forces in the Model (Problems 1-2)
A +2.0 nC sphere and a -8.0 nC sphere, each 2.0 cm across, sit with centers 5.0 cm apart. (a) Find the size of the force on each sphere. (b) Draw the field lines and the force pair. (c) A classmate says, "The -8.0 nC sphere pulls harder because it has more charge." Use your model to answer the classmate.
Two long, straight, parallel wires lie 1 cm apart on a table and carry currents in the same direction. (a) Sketch the magnetic field around each wire and state whether the wires attract or repel. (b) Draw the force pair. (c) Predict what changes when the current in one wire is reversed, and explain which part of your model shows it.
Part 2: Energy in the Model (Problems 3-4)
Two +5.0 nC beads, each 1.2 cm across, hang on insulating threads. A student slowly pushes them from 10.0 cm to 2.5 cm apart. (a) Find the energy stored in the field at each separation. (b) How much work did the student do? (c) If the beads are released and fly far apart, how much kinetic energy do they have in total? (d) Draw energy bars for "start," "pushed together" and "far apart."
A 0.40 kg cart with a magnet rolls toward a fixed magnet, like poles facing. Video gives: gap 6.0, 4.0, 3.0, 2.0, 1.2 cm and cart speed 0.50, 0.49, 0.46, 0.36, 0 m/s. (a) Find the kinetic energy at each gap. (b) Find the energy stored in the field at each gap, taking it as zero at 6.0 cm. (c) Where does the energy change fastest? Explain with the model.
Part 3: Critique and Plan (Problems 5-6)
A student models two bar magnets placed end to end, north pole facing south pole, 3 cm apart. The drawing shows (i) field lines going from the south pole to the north pole in the gap, (ii) two field lines crossing in the middle, (iii) a long force arrow on the larger magnet and a short one on the smaller magnet, both pointing away from the gap. (a) Identify every error. (b) Redraw the model correctly. (c) The magnets are released and snap together. Describe the energy change of the field and of the magnets.
Plan an investigation with a charge simulation to test the claim that the energy stored in the field of two opposite charges is proportional to 1/r. (a) Name the independent, dependent and controlled variables. (b) Invented results for +4.0 nC and -5.0 nC: r = 3.0, 4.0, 5.0, 10.0 cm gives U = -5.99, -4.50, -3.60, -1.80 × 10⁻⁶ J. Show that U × r is constant. (c) Use the model to predict the kinetic energy the pair gains when the separation shrinks from 10.0 cm to 3.0 cm.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Field and Force Model
Field lines drawn correctly (right direction, never crossing) and an equal and opposite force pair
Field or forces drawn, with one error in direction or size
Energy Accounting
Energy stored in the field and kinetic energy computed with units, and every change balanced by another change or by outside work
Energies computed, but one transfer missing or a sign error
Using the Model
Claims and critiques cite a specific part of the model (a force arrow, a bar, a value of U)
Claim stated without pointing to the model
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Every system has two objects, and all data are invented. Charged spheres are small and about 2 cm across unless stated. Use k = 8.99 × 10⁹ N·m²/C². Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Two small spheres with opposite charges are held apart and then released, and they speed up toward each other. Which energy statement about this two-object system is correct?
Answer: A
As opposite charges move together, the field energy falls and the spheres gain that same amount of kinetic energy. Choice B would mean energy appears from nowhere. Choice C treats a force as a source of energy; a force transfers energy, it does not make it. Choice D is wrong because the charges do not change during the motion.
Question 2 of 20 · Multiple Choice
A +2.0 nC sphere and a -10.0 nC sphere are 4.0 cm apart. How does the force on the +2.0 nC sphere compare with the force on the -10.0 nC sphere?
Answer: C
The two forces are an interaction pair: equal in size and opposite in direction, whatever the two charges are. Choice A is the error of thinking the larger charge pulls harder. Choice D would make both spheres move the same way, which an attraction cannot do.
Question 3 of 20 · Multiple Choice
Two +3.0 nC spheres have centers 3.0 cm apart. What is the electric force on each sphere?
Answer: D
F = (8.99 × 10⁹)(3.0 × 10⁻⁹)²/(0.030)² = 9.0 × 10⁻⁵ N, and like charges repel. Choice A divides by r instead of r² (that expression gives energy in joules, not force). Choice B has the right size but the wrong direction. Choice C forgets to divide by r².
Question 4 of 20 · Multiple Choice
The distance between two charged spheres is tripled and nothing else changes. What happens to the force on each sphere?
Answer: B
The force depends on 1/r², so tripling r divides the force by 3² = 9. Choice A uses 1/r, which is how the stored energy changes, not the force. Choices C and D have the relationship upside down.
Question 5 of 20 · Multiple Choice
A student's hands slowly push two positive charged spheres from 6.0 cm apart to 2.0 cm apart and hold them there. Which statement about the energy is correct?
Answer: A
The hands push against the repulsion, so they do work, and that energy is stored in the field. Choice B applies the rule for opposite charges to like charges. Choice C ignores the work done. Choice D is wrong because the spheres are moved slowly and end at rest.
Question 6 of 20 · Multiple Choice
A student draws a model of the field around a positive and a negative charge. Which feature shows that the model is wrong?
Answer: C
Field lines point away from positive charges and toward negative charges, so this drawing has every arrow reversed. Choice A is correct, because lines crowd together where the field is strong. Choice B is correct, because the forces are an equal and opposite pair. Choice D is correct, because the field fills the space around the charges, not only the gap between them.
Question 7 of 20 · Multiple Choice
In one magnetic bumper trial on a level track, a group records a cart arriving at 0.30 m/s and leaving at 0.34 m/s. Which conclusion does the two-magnet model support?
Answer: B
The field only stores the kinetic energy the cart brings in and returns it, minus what friction turns into thermal energy, so the cart cannot leave faster on a level track unless something outside the system (a push, a tilt) added energy or a measurement is off. Choices A and D break energy conservation. Choice C has no physical basis: the mass does not change.
Question 8 of 20 · Multiple Choice
Two bar magnets lie on a table with the north pole of one facing the north pole of the other. Which statement describes the forces?
Answer: D
Like poles repel, and the two forces are an equal and opposite pair. Choice A reverses the rule for like poles. Choice B denies the interaction pair. Choice C ignores the field, which acts across the gap.
Question 9 of 20 · Multiple Choice
A +2.0 nC sphere and a -5.0 nC sphere move from 10.0 cm apart to 5.0 cm apart, and only the electric force acts. How much kinetic energy does the pair gain?
Answer: A
U = kq1q2/r goes from -8.99 × 10⁻⁷ J to -1.80 × 10⁻⁶ J, a drop of 9.0 × 10⁻⁷ J, and the kinetic energy rises by that amount. Choice B gives the change in field energy, not in kinetic energy. Choice C uses only the final value of U. Choice D uses 1/r², the force formula, instead of 1/r.
Question 10 of 20 · Multiple Choice
A steel paper clip lies on a smooth table and is pulled toward a magnet, speeding up as it goes. Which energy statement is correct for the system of the clip and the magnet?
Answer: C
The clip moves in the direction of the magnetic force, so field energy is transferred to the clip as kinetic energy. Choice A has the direction of the transfer backward. Choice B breaks energy conservation. Choice D is wrong because a magnet is not used up when it pulls a clip.
Question 11 of 20 · Multiple Choice
In a graph of stored energy U against separation r for two opposite charges, U becomes more negative as r gets smaller. What does this model predict about pulling the two charges farther apart?
Answer: B
Moving up the curve (toward U = 0) raises the field energy, and that energy must come from outside the system, such as a hand. Choice A reads the graph backward. Choice C would need a push away from each other, which opposite charges do not give. Choice D confuses the direction of the force with the energy cost.
Question 12 of 20 · Multiple Choice
A proton with 2.0 MeV of kinetic energy (1 MeV = 1.602 × 10⁻¹³ J) is fired straight at a fixed lead nucleus (charge +82e, e = 1.602 × 10⁻¹⁹ C). How close does it get before it stops and turns back?
Answer: D
At the turning point all the kinetic energy is stored in the field: k(e)(82e)/r = 3.2 × 10⁻¹³ J, so r = 5.9 × 10⁻¹⁴ m. Choice A leaves out the factor 82 for the nucleus. Choice B uses only half the kinetic energy. Choice C forgets to convert MeV to joules.
Question 13 of 20 · Multiple Choice
Invented data for two charged spheres: at 2.0 cm the force is 20 × 10⁻⁵ N, at 4.0 cm it is 5.1 × 10⁻⁵ N, and at 8.0 cm it is 1.3 × 10⁻⁵ N. Which claim do the data support?
Answer: B
Each doubling of r cuts the force to about one fourth (20 to 5.1, then 5.1 to 1.3), the pattern of 1/r². Choice A would give 10 and 5 × 10⁻⁵ N at 4.0 and 8.0 cm. Choices C and D do not match a force that falls quickly with distance.
Question 14 of 20 · Multiple Choice
A +5.0 nC sphere and a +2.0 nC sphere are released from rest with centers 3.0 cm apart and fly apart. How much kinetic energy do they have in total when they are very far apart?
Answer: C
All the stored energy, U = (8.99 × 10⁹)(5.0 × 10⁻⁹)(2.0 × 10⁻⁹)/0.030 = 3.0 × 10⁻⁶ J, becomes kinetic energy. Choice A gives only one sphere's share, but the question asks for the total. Choice B divides by r² instead of r. Choice D wrongly assumes the energy disappears when the force becomes tiny.
Question 15 of 20 · Short Answer
A +5.0 nC sphere and a -5.0 nC sphere have centers 10.0 cm apart. Find the size and direction of the force on each sphere, and describe the force arrows in a correct model.
F = (8.99 × 10⁹)(5.0 × 10⁻⁹)²/(0.100)² = 2.2 × 10⁻⁵ N on each sphere, attractive. The model shows two arrows of the same length, one on each sphere, pointing toward the other sphere.
Question 16 of 20 · Short Answer
A 0.60 kg cart with a magnet rolls at 0.30 m/s toward a fixed magnet, like poles facing, stops for an instant and rolls back at 0.28 m/s. How much energy was stored in the magnetic field at the stop, and how much was transferred out of the two-magnet system?
KE before = ½(0.60)(0.30)² = 0.027 J, so about 0.027 J was stored in the field at the stop. KE after = ½(0.60)(0.28)² = 0.0235 J, so about 0.0035 J left the system as thermal energy and sound through friction.
Question 17 of 20 · Short Answer
A balloon is rubbed on a wool scarf. The balloon becomes negatively charged and the scarf positively charged. A student then slowly pulls the balloon 30 cm away from the scarf. Describe a three-part model of this interaction: field, forces and energy.
Field: lines start on the positive scarf and end on the negative balloon, without crossing. Forces: the scarf pulls the balloon toward it and the balloon pulls the scarf toward it, with forces of the same size. Energy: the student pulls against the attraction and does work, so the energy stored in the field increases; the objects end at rest, so their kinetic energy does not change.
Question 18 of 20 · Short Answer
A +3.0 nC sphere and a +5.0 nC sphere are pushed slowly from 5.0 cm apart to 2.5 cm apart. How much work must be done?
U goes from (8.99 × 10⁹)(1.5 × 10⁻¹⁷)/0.050 = 2.7 × 10⁻⁶ J to 5.4 × 10⁻⁶ J, so the work is 2.7 × 10⁻⁶ J, now stored in the field.
Question 19 of 20 · Short Answer
A classmate says, "When a positive and a negative charge rush toward each other, the electric force creates energy." Use a model of the two-charge system to respond.
The claim is wrong. In the model, the energy stored in the field decreases as the charges move together, and the kinetic energy of the charges increases by the same amount. The force transfers energy from the field to the charges; the total energy of the system stays the same.
Question 20 of 20 · Short Answer
Two ceramic magnets repel. Invented scale data give a force of 0.45 N when the gap is 1.5 cm and 0.12 N when the gap is 3.0 cm. At which gap is more energy stored in the field, and how many times larger is the force at 1.5 cm than at 3.0 cm?
More energy is stored at the 1.5 cm gap, because work against the repulsion is needed to push the magnets from 3.0 cm to 1.5 cm. The force is 0.45 ÷ 0.12 = 3.75 times larger at 1.5 cm.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HS-PS3-5 mean?
HS-PS3-5 asks students to build and use a model of two objects that interact through an electric or magnetic field, showing both the forces on the objects and the energy changes caused by the interaction. The code means High School, Physical Science, core idea 3 (Energy), performance expectation 5. The practice is modeling: drawings, diagrams and text, often with numbers.
Is HS-PS3-5 taught in physics or chemistry?
It is usually taught in a Physics or Physical Science course, in the electricity and magnetism unit. Chemistry courses use the same idea when they explain why energy is released as oppositely charged particles come together, but the performance expectation belongs to the energy strand of physical science.
What is the assessment boundary for HS-PS3-5?
The official Assessment Boundary is: "Assessment is limited to systems containing two objects." Every model, problem and quiz item on this page has exactly two interacting objects. Systems of three or more charges, and adding fields from several sources, are beyond this standard.
What counts as a model for HS-PS3-5?
A model is a drawing, diagram or text that explains the interaction, and the Clarification Statement gives the example of a drawing of two opposite charges near each other that also explains how the change in energy of the objects is related to the change in energy of the field. A strong model has field lines, an equal and opposite force pair and energy bars before and after a change.
Where is the energy stored when two charges are held apart?
It is stored in the electric field of the two-charge system, not in either charge. The amount depends on the separation and on the signs of the charges, which is why a model needs energy bars for the field as well as for the objects. Diagram 2 shows the stored energy against separation for a like pair and an opposite pair.
Why can't field lines cross?
The field at each point has only one direction, and a field line shows that direction. If two lines crossed, the field at the crossing would point two ways at once. Lines that cross are a quick sign that a student's model needs another look.
Do students need Coulomb's law for HS-PS3-5?
Not always, since a qualitative model can meet the standard. Many teachers add F = k|q1q2|/r² and U = kq1q2/r so students can put numbers on the forces and energy bars. Using the force law to describe and predict forces is also the focus of HS-PS2-4.
Can the model use magnets instead of charges?
Yes. The standard says electric or magnetic fields. Two magnets, a magnet and a steel object, or two wires carrying current all work, as long as the model shows the force pair and the energy transfer between the field and the objects. Magnet carts and force-against-gap data are low-cost ways to get numbers.
What mistakes do students make with forces between two charges?
A common error is to think the object with more charge, or the bigger magnet, pushes or pulls harder. The forces on the two objects are always equal in size and opposite in direction. Another error is drawing field lines as arrows from one object to the other only, with no field around the rest of the space.
How is HS-PS3-5 different from HS-PS3-2?
HS-PS3-2 is about modeling energy at the macroscopic scale as motion of particles or as energy stored in fields in general. HS-PS3-5 narrows this to one interaction between two objects through an electric or magnetic field and asks for the forces as well as the energy changes.
07
Related Standards
6 standards
These standards connect to HS-PS3-5: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-PS2-5Prerequisite
Investigate evidence that fields exist between objects exerting forces at a distance
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