Physics — Algebra and Trigonometry · 35 minutes
Suggested grades 11–12 · Unit 3: Fields and Collision Design · Lesson 1 of 2
Predict an Electric-Force Ratio
Use a relative inverse-square model without building or handling electrical devices.
Mr. S Teaches · Original starter lesson · HS-PHYS-05 · Grade range is planning guidance.Watch, notice, discuss
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Coulomb's law | Physics | Khan Academy
By Khan Academy
Use the inverse-square dependence to predict ratios while keeping charge signs separate from force magnitude.
Open on YouTube: Coulomb's law | Physics | Khan Academy (opens a new tab) ↗Coulomb's Law - Net Electric Force & Point Charges
By The Organic Chemistry Tutor
Preview the two-charge algebra examples; the later multi-charge cases extend beyond this ratio lesson.
Open on YouTube: Coulomb's Law - Net Electric Force & Point Charges (opens a new tab) ↗What idea from the video helps you calculate three force ratios and explain both magnitude and direction under a point-charge model? Identify one useful example and one limit of the video's model or explanation.
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Learning objective
Calculate three force ratios and explain both magnitude and direction under a point-charge model.
Before you begin
- Use squares, ratios and signs.
Gather your materials
- Paper or notebook
- Pencil; calculator optional for numerical work; all task data supplied below
Language to know
- point charge
- An idealized charge concentrated at one mathematical location.
- inverse-square relationship
- A dependence proportional to one divided by the square of distance.
- electric field model
- A representation of interactions associated with electric charges.
Understand the concept
Paper model: For two point charges at separation r, force magnitude is F=k|q1q2|/r². Like charges repel and opposite charges attract. Compare cases using ratios, so k need not be evaluated. Doubling separation while keeping charges unchanged gives F/4; doubling one charge at unchanged separation gives 2F. These idealized rules do not describe every extended charge distribution. This lesson uses symbols and supplied data only: no batteries, outlets or charged equipment.
Teach it step by step
- Read the formula and identify which quantities affect magnitude and which signs affect direction.
- Draw a baseline pair with force arrows; reverse one charge and redraw the interaction direction.
- Calculate changed-case ratios rather than repeatedly substituting an unspecified constant.
- Use a precise model detail to identify why “twice as far means half the force” is incorrect.
Make the thinking visible
Worked example or model response
If one charge doubles and separation triples, Fnew/Fold=2/3²=2/9. If a charge changes from positive to negative with the same magnitude, the magnitude can stay unchanged while the interaction switches between repulsion and attraction.
Guided practice
Together find the ratio when both charge magnitudes double at the original distance.
Independent practice
Calculate ratios for unchanged charges at half the separation and for one charge tripled at twice the separation. Draw directions for an opposite-sign pair and identify a model boundary.
Quick assessment
Would replacing r with 2r in the denominator multiply force by two or divide it by four?
Answer key & assessment criteria
Answers and teaching guidance
- Guided: The numerator becomes four times larger, so the magnitude is 4F.
- Independent: Half separation gives 4F; triple one charge at double separation gives 3F/4. Opposite signs attract. Point-like geometry or ideal isolation is a valid boundary.
- Quick check: It divides magnitude by four because the entire separation is squared.
Look for: Assess the stated objective using the concrete criteria and explanations in the answer key. Invite an alternative supported solution; distinguish a model’s prediction from an established observation.
Make it work for your learner
More support
Use a ratio grid showing charge multiplier and squared-distance multiplier separately.
Extension challenge
Compare the algebraic structure with a gravitational inverse-square model while explaining the distinction between charge signs and positive mass values.
Verified references · Selected contributions
Standards connections
Selected NGSS high school-band contribution; full performance requires additional evidence and instruction.
Subject-content standards
These records identify the part of a subject standard practiced here. Course placement is instructional guidance; the source’s category or band remains authoritative.
Contributes to NGSS performance expectation
HS-PS2-4
NGSS · High school band
Use inverse-square force models for interacting charges or masses.
Read the official performance expectation ↗This selected mathematical representation addresses idealized electrostatic interactions. Gravitation, extended distributions and empirical force measurements are outside the core task.
Verified 2026-11-04. Selected contribution, not full attainment.
Supporting literacy connections
These records apply to the specified reading, writing or communication task. They do not establish subject-content alignment.
Supporting Common Core literacy connection
RST.11-12.1
Common Core · Grades 11–12
Analyze technical details, distinctions and gaps using textual evidence.
Read the official standard ↗The activity explicitly analyzes the provided technical text, table or model. It contributes selected literacy practice rather than complete grade-band reading coverage or independent subject-content alignment.
Verified 2026-11-04. Selected contribution, not full attainment.