Add forces as vectors
You will be able to: Find a net electric force by summing signed or perpendicular components.
What if more than one charge pulls on an object?
A small charged bead can be pushed right by one charge and upward by another. Adding their force magnitudes would lose the directions. Resolve the interactions one at a time, then combine components.
A useful starting point: Charge and force: size first, direction next →
Words and symbols before equations
- Superposition
- The net force is the vector sum of the individual forces.
- Component
- The signed part of a vector along a chosen axis.
- Net force
- All forces on one chosen object added together.
- Magnitude
- Vector length; for perpendicular components, F=√(F_x²+F_y²).
What this picture assumes
Positive +1 μC target, each source 0.30 m away along a perpendicular axis. Only electric forces shown. Component and resultant arrows share a scale of 500 drawing units/N. Source positions are listed separately from the force-vector diagram.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Net (0.3, 0.4) N; magnitude 0.5 N, angle 53.13° above +x. Components and resultant act on the same +1 μC target.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Draw only forces acting on the selected charge. For each source, use its separation and charge signs to determine magnitude and direction. Choose positive x right and positive y up before assigning signs.
Sum x-components separately from y-components. Two perpendicular forces of 0.03 N and 0.04 N give a 0.05 N resultant, not 0.07 N. The angle measured from +x obeys tan θ=F_y/F_x, with the correct quadrant.
A force pair between two different objects is not a cancellation on one object. Gravity or support forces must be included if a question asks for the total mechanical force rather than only the net electric force. Calculations here involve no more than four charges.
A worked example, step by step
A target experiences 0.03 N rightward and 0.04 N upward electric forces. Find the resultant.
- F_x=+0.03 N and F_y=+0.04 N.
- F=√(0.03²+0.04²)=0.05 N.
- θ=tan⁻¹(0.04/0.03)≈53° above +x.
- The result is one diagonal net force acting on the target.
Add components before taking the magnitude. Magnitudes alone are not a vector sum.
Can two nonzero electric forces give zero net force?
Compare with an explanation
Yes, if they are equal in magnitude and opposite on the same target.
Predict. Change one thing. Explain.
Two positive source charges sit left of and below a positive target. Change the sources independently. Observe the horizontal, vertical and resultant vectors on one common scale.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Net (0.3, 0.4) N; magnitude 0.5 N, angle 53.13° above +x. Components and resultant act on the same +1 μC target.
Positive +1 μC target, each source 0.30 m away along a perpendicular axis. Only electric forces shown. Component and resultant arrows share a scale of 500 drawing units/N. Source positions are listed separately from the force-vector diagram.
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 questionA target has electric components F_x=−0.06 N and F_y=+0.08 N. (a) Sketch directions. (b) Find magnitude. (c) Give angle relative to the negative x axis. (d) Explain why 0.14 N is incorrect.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: Leftward x component and upward y component.
- 1 point: Magnitude 0.10 N.
- 1 point: About 53° above the negative x axis.
- 1 point: 0.14 N adds magnitudes without their perpendicular directions.
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 1First step in superposition?
Choose the target object and axes.
RECALL 2What is added?
Signed vector components.
RECALL 3Are third-law partners on one free-body diagram?
No. They act on different objects.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Add forces as vectors
- F_net,x=ΣF_x; F_net,y=ΣF_y.
- F_net=√(F_net,x²+F_net,y²).
- State angle reference and quadrant.
Remember: Add components before taking the magnitude. Magnitudes alone are not a vector sum.
Conditions: Positive +1 μC target, each source 0.30 m away along a perpendicular axis. Only electric forces shown. Component and resultant arrows share a scale of 500 drawing units/N. Source positions are listed separately from the force-vector diagram.
Refresh Kid · AP Physics 2 Unit 2 (official Unit 10) · Objectives 10.1.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 10.1, objectives 10.1.A. 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.
Want to work through this with a tutor?
Bring your question about Add forces as vectors. Your explanation and answers remain free to access.