Compare electric and gravitational interactions
You will be able to: Compare inverse-square force laws without assuming one interaction always dominates.
Why does gravity matter for nearly neutral objects?
Two everyday objects contain enormous numbers of charges, but their positive and negative charges nearly cancel. Their masses do not cancel in that way. This explains why gravity remains important for large, nearly neutral systems.
A useful starting point: Add forces as vectors →
Words and symbols before equations
- Gravitational constant G
- 6.67×10⁻¹¹ N·m²/kg² in these examples.
- Electric force F_E
- Can attract or repel; depends on charge signs.
- Gravitational force F_g
- Attractive between ordinary masses; F_g=Gm₁m₂/r².
- Force ratio
- A dimensionless comparison obtained by dividing magnitudes.
What this picture assumes
Two 1 kg pointlike masses each with the same positive net charge; vacuum, k=9×10⁹ and G=6.67×10⁻¹¹ in SI. Graph uses force ratio, not unscaled force arrows. Real extended neutral-body polarization is outside this point model.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Electric repulsion 9e-9 N; gravitational attraction 6.67e-11 N. Ratio=134.9 for these two masses and charges; changing separation alone leaves it unchanged.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Both point-object laws decrease as 1/r². Their ratio is F_E/F_g=k|q₁q₂|/(Gm₁m₂), so separation cancels when comparing the same two objects.
Electric interactions between charged elementary particles commonly exceed gravity by a vast factor. This does not mean any weakly charged macroscopic pair must be dominated by electricity: the masses and net charges determine the ratio.
At large scales, positive and negative charges often nearly balance while gravitational attraction accumulates. A neutral object can still polarize in a nonuniform electric field; treating net charge as zero in a point-charge formula does not describe every extended-body interaction.
A worked example, step by step
Two 1 kg pointlike objects each carry +1 μC and are 1 m apart. Compare force magnitudes.
- F_E=9×10⁹(10⁻⁶)²/1²=0.009 N, repulsive.
- F_g=6.67×10⁻¹¹ N, attractive.
- F_E/F_g≈1.35×10⁸.
- Doubling their separation quarters both forces, leaving the ratio unchanged.
Neutrality cancels net charge, not mass. Do not infer the force ratio without specifying both.
Does changing r change their force ratio?
Compare with an explanation
Not for these two inverse-square point-object models with fixed masses and charges.
Predict. Change one thing. Explain.
Change the common separation for two fixed masses and charges. Compare the two force readouts and their ratio. Then vary charge to see why the ratio is not a universal constant.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Electric repulsion 9e-9 N; gravitational attraction 6.67e-11 N. Ratio=134.9 for these two masses and charges; changing separation alone leaves it unchanged.
Two 1 kg pointlike masses each with the same positive net charge; vacuum, k=9×10⁹ and G=6.67×10⁻¹¹ in SI. Graph uses force ratio, not unscaled force arrows. Real extended neutral-body polarization is outside this point model.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant charge, field or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionTwo fixed masses with nonzero charges have F_E/F_g=100 at distance r. (a) Find the ratio at 3r. (b) Give each force’s scale factor. (c) Predict the ratio if one charge halves. (d) Explain why large nearly neutral systems can be gravity-dominated.
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Compare with the answer and four-point rubric
- 1 point: The ratio remains 100.
- 1 point: Each force becomes 1/9 its previous magnitude.
- 1 point: The ratio becomes 50.
- 1 point: Net electric charges nearly cancel while masses continue to attract.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Shared distance dependence?
Inverse square for the point-object models.
RECALL 2Does the ratio depend on separation?
No, when comparing the same objects under these laws.
RECALL 3Why can gravity dominate macroscopically?
Net charge can nearly cancel while mass does not.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Compare electric and gravitational interactions
- F_g=Gm₁m₂/r².
- F_E/F_g=k|q₁q₂|/(Gm₁m₂).
- Electric forces can repel; gravitational forces between ordinary masses attract.
Remember: Neutrality cancels net charge, not mass. Do not infer the force ratio without specifying both.
Conditions: Two 1 kg pointlike masses each with the same positive net charge; vacuum, k=9×10⁹ and G=6.67×10⁻¹¹ in SI. Graph uses force ratio, not unscaled force arrows. Real extended neutral-body polarization is outside this point model.
Refresh Kid · AP Physics 2 Unit 2 (official Unit 10) · Objectives 10.1.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 10.1, objectives 10.1.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the second AP Physics 2 unit; College Board numbers it Unit 10; the first unit in this course is official Unit 9. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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