Add electric forces one component at a time
You will be able to: Calculate a net force by adding two perpendicular force contributions.
How do several charges combine their pushes and pulls?
A test bead is pulled right by one charge and upward by another. A 3 N rightward force and a 4 N upward force give a 5 N diagonal result, not a 7 N force.
A useful starting point: Charge signs set direction; distance sets strength →
Words and symbols before equations
- Superposition
- Calculate each source contribution separately and add the vectors.
- Component
- The signed amount of a vector along a chosen x or y axis.
- Net force
- The vector sum of all forces on the selected object.
- Source charge
- A charge producing the interaction being calculated.
What this picture assumes
A fixed +1 μC target at the origin, with sources at (r,0) and (0,r). The diagram is force-component space, not a spatial map. Both axes use an equal N scale. Only forces on the target are summed.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Sources at (0.3,0) and (0,0.3) m: net F = (0.1, 0.1) N, magnitude 0.1414 N.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Choose the object whose force you want. Draw separate arrows for its interactions with the other charges; do not include forces exerted on those other objects in its own sum.
Use Coulomb’s law and a direction for each contribution. Then Fₓ = ΣFᵢₓ and Fᵧ = ΣFᵢᵧ. A negative component means a direction along the negative axis, not a negative magnitude.
After adding components, find |F| = √(Fₓ² + Fᵧ²). Use the signs to identify the quadrant before reporting an angle. In the model the +1 μC target is at the origin, with one source on each positive axis; source positions remain fixed.
A worked example, step by step
A +1 μC target is at the origin. A −1 μC source is at (0.30, 0) m and a −1 μC source at (0, 0.30) m. Find the net force.
- Each interaction has r = 0.30 m and attracts the target toward its source.
- Each magnitude is (9 × 10⁹)(10⁻⁶)²/(0.30)² = 0.10 N.
- Add components: F = (0.10, 0.10) N.
- |F| = 0.141 N, at 45° above +x. The scalar sum 0.20 N would be incorrect.
Add components before magnitudes. Forces on different objects do not belong in one free-body sum.
If the net force is zero, must every individual force be zero?
Compare with an explanation
No. Nonzero contributions can cancel vectorially.
Predict. Change one thing. Explain.
Start with two negative source charges. Reverse only the charge on the x axis. Predict which force component changes sign and which stays fixed.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Sources at (0.3,0) and (0,0.3) m: net F = (0.1, 0.1) N, magnitude 0.1414 N.
A fixed +1 μC target at the origin, with sources at (r,0) and (0,r). The diagram is force-component space, not a spatial map. Both axes use an equal N scale. Only forces on the target are summed.
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 questionIn the worked arrangement, replace the source at (0.30, 0) m with +2 μC. Keep the y-axis source −1 μC. Find the target’s net force components and magnitude.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: The x source repels the positive target left.
- 1 point: Fₓ = −0.20 N.
- 1 point: Fᵧ = +0.10 N.
- 1 point: |F| = √(0.20² + 0.10²) = 0.224 N, pointing upper-left.
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 1What does superposition add?
Vectors, component by component.
RECALL 2What stays fixed when one source reverses?
Contributions from unchanged sources.
RECALL 3When can magnitudes be added directly?
When all contributions point in the same direction.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Add electric forces one component at a time
- F_net = ΣFᵢ.
- Fₓ = ΣFᵢₓ; Fᵧ = ΣFᵢᵧ.
- |F| = √(Fₓ² + Fᵧ²).
Remember: Add components before magnitudes. Forces on different objects do not belong in one free-body sum.
Conditions: A fixed +1 μC target at the origin, with sources at (r,0) and (0,r). The diagram is force-component space, not a spatial map. Both axes use an equal N scale. Only forces on the target are summed.
Refresh Kid · AP Physics C: Electricity and Magnetism Unit 1 (official Unit 8) · Objectives 8.1.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 8.1, objectives 8.1.A. 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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