Charge signs set direction; distance sets strength
You will be able to: Calculate a two-charge force and distinguish charge sign from force direction.
Why can two charged objects attract or repel?
Two small charged beads can push apart without touching. Give one bead the opposite sign and the force becomes attractive. Doubling their separation makes either force one quarter as strong.
A useful starting point: Scalars, vectors and direction →
Words and symbols before equations
- Charge q
- A signed scalar measured in coulombs (C); an electron has −e, a proton +e and a neutron zero charge.
- Elementary charge e
- About 1.60 × 10⁻¹⁹ C; ordinary isolated net charge is an integer multiple of e.
- Point charge
- An approximation when object size is negligible compared with the relevant distances.
- Coulomb constant k
- About 9.0 × 10⁹ N·m²/C² in vacuum; use this rounded value throughout this unit.
What this picture assumes
Two stationary point charges in vacuum; +x is right. F_right is the force on the right charge. Finite bead size, radiation and motion are not modeled. k = 9.0 × 10⁹ N·m²/C².
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Force on right charge: -0.6 N along x; on left: 0.6 N. Magnitude 0.6 N. Attractive.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
For two stationary point charges in vacuum, the force magnitude is k|q₁q₂|/r². First calculate a positive magnitude; then use like-sign repulsion or opposite-sign attraction to draw the direction along the line between charges.
Each object feels an equal-magnitude opposite force even if the charges or masses differ. Their accelerations can differ because acceleration also depends on mass. A negative charge does not automatically experience a leftward force.
Gravity between positive masses is always attractive, whereas electric forces can attract or repel. Both point-source forces vary as 1/r². Electric forces between elementary charged particles are much stronger than their mutual gravity, but large nearly neutral systems can have very little net electrical interaction. Microscopic electrical interactions also underlie everyday contact forces.
| Property | Electric | Gravitational |
|---|---|---|
| Source property | Signed charge | Positive mass |
| Direction | Attractive or repulsive | Attractive |
| Distance scaling | 1/r² for point charges | 1/r² for point masses |
A worked example, step by step
A +2 μC bead and a −3 μC bead are 0.30 m apart in vacuum. Find the force magnitude on each bead.
- Convert: 2 μC = 2 × 10⁻⁶ C and 3 μC = 3 × 10⁻⁶ C; r² = 0.090 m².
- Use F = k|q₁q₂|/r² because the beads are modeled as stationary point charges.
- F = (9.0 × 10⁹)(6 × 10⁻¹²)/0.090 = 0.60 N.
- Each bead feels 0.60 N toward the other. Increasing r to 0.60 m would give 0.15 N.
Charge is a signed scalar; force is a vector. Charge sign alone does not specify an axis direction.
Does the larger charge feel the larger force?
Compare with an explanation
No. The two interaction forces have equal magnitudes and opposite directions.
Predict. Change one thing. Explain.
Double the separation while keeping both charges fixed. Predict the factor of change. Reverse one charge and distinguish a direction change from a magnitude change.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Force on right charge: -0.6 N along x; on left: 0.6 N. Magnitude 0.6 N. Attractive.
Two stationary point charges in vacuum; +x is right. F_right is the force on the right charge. Finite bead size, radiation and motion are not modeled. k = 9.0 × 10⁹ N·m²/C².
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant charge, vector superposition, electric field, flux or symmetry 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 +1 μC point charges are 0.20 m apart. Find both force magnitudes and directions, then predict the force at 0.40 m.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: F = (9 × 10⁹)(10⁻⁶)²/(0.20)².
- 1 point: F = 0.225 N on each.
- 1 point: Forces point away from one another and have equal magnitude.
- 1 point: At twice the distance F = 0.05625 N, one quarter as large.
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 1Is charge a vector?
No. It is a signed scalar.
RECALL 2Why can accelerations differ when forces are equal?
The objects can have different masses.
RECALL 3Why can gravity matter for large neutral objects?
Positive and negative electrical contributions largely cancel, while gravitational attractions add.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Charge signs set direction; distance sets strength
- F = k|q₁q₂|/r² for stationary point charges in vacuum.
- 1 μC = 10⁻⁶ C; q = Ne for signed integer N.
- Gravity: Gm₁m₂/r², always attractive for positive masses.
Remember: Charge is a signed scalar; force is a vector. Charge sign alone does not specify an axis direction.
Conditions: Two stationary point charges in vacuum; +x is right. F_right is the force on the right charge. Finite bead size, radiation and motion are not modeled. k = 9.0 × 10⁹ N·m²/C².
Refresh Kid · AP Physics C: Electricity and Magnetism Unit 1 (official Unit 8) · Objectives 8.1.A, 8.1.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 8.1, objectives 8.1.A, 8.1.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. This is E&M Unit 1: Electric Charges, Fields, and Gauss’s Law, numbered Unit 8 in the official combined Physics C sequence. Topics 8.1–8.6 retain their official identifiers. Quantitative force examples use at most four point charges. Field integrals use the specified rods, ring, arc and infinite wire; Gauss-law field calculations use spherical, cylindrical or planar symmetry. Optional projected 3D views clarify area normals and geometry; camera rotation never changes the physics. Checked with the Fall 2026 clarifications. 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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