Track charge through contact
You will be able to: Apply charge conservation and distinguish net charge from its distribution.
Where did the extra electrons come from?
Two identical metal spheres initially carry +6 nC and −2 nC. Connecting them allows charge to move. The combined charge is still +4 nC; redistribution does not create or destroy it.
A useful starting point: Separate charge without creating it →
Words and symbols before equations
- Net charge
- Algebraic sum of positive and negative charge.
- Isolated pair
- The selected pair exchanges no charge with its surroundings.
- Contact charging
- Charge transfers through a conducting connection.
- Identical-sphere model
- Far-separated equal spheres share net charge equally after connection in a symmetric environment.
What this picture assumes
Two identical conducting spheres, right sphere initially −2 nC, far apart with negligible mutual influence and no external source/ground. Connection permits equilibrium then disconnection. Equal sharing depends on the stated symmetry.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Initial total=4 nC; final total=2(2)=4 nC. Electrons enter the left sphere.
- 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 an isolated system, total charge stays constant. A single object’s net charge changes only when charge crosses its boundary. Rubbing transfers charge between materials; it does not manufacture charge.
Charge redistributes in connected conductors until electrostatic equilibrium and equal potential are reached. Identical far-separated spheres in a symmetric environment end with equal charges. Unequal shapes or nearby external charges can prevent equal sharing.
Negative mobile electrons moving one way correspond to positive-charge transfer in the opposite bookkeeping direction. Keep the chosen system boundary clear and sum signed charges, not magnitudes.
A worked example, step by step
Identical far-separated spheres start at +6 nC and −2 nC, are connected and then separated. Find final charges and the electron-transfer direction.
- Total Q=+6−2=+4 nC.
- Identical spheres share equally: q_final=+2 nC each.
- The initially positive sphere becomes less positive by 4 nC, so electrons enter it.
- Electrons move from the initially −2 nC sphere toward the +6 nC sphere.
Equal potential does not generally mean equal charge; equal sharing requires the stated symmetry.
Must each sphere keep its original charge?
Compare with an explanation
No. Only the isolated pair’s total is fixed; electrons can move between them.
Predict. Change one thing. Explain.
Vary the initial charge on one of two identical spheres. Compare before/after totals and predict electron direction before reading the explanation.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Initial total=4 nC; final total=2(2)=4 nC. Electrons enter the left sphere.
Two identical conducting spheres, right sphere initially −2 nC, far apart with negligible mutual influence and no external source/ground. Connection permits equilibrium then disconnection. Equal sharing depends on the stated symmetry.
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 identical isolated spheres have −6 nC and +2 nC. (a) Find total charge. (b) Find final charges after contact. (c) State which loses electrons. (d) Find the magnitude of charge transferred.
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Compare with the answer and four-point rubric
- 1 point: Total −4 nC.
- 1 point: Each ends at −2 nC.
- 1 point: The initially −6 nC sphere loses electrons.
- 1 point: 4 nC is transferred.
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 is conserved?
Total signed charge of an isolated system.
RECALL 2Does rubbing create charge?
No. It transfers charge between materials.
RECALL 3What do connected conductors equalize?
Electric potential, not generally charge.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Track charge through contact
- Q_total=Σq; isolated total charge is constant.
- Identical symmetric spheres: q_f=(q₁+q₂)/2.
- Electron count transferred = |Δq|/e.
Remember: Equal potential does not generally mean equal charge; equal sharing requires the stated symmetry.
Conditions: Two identical conducting spheres, right sphere initially −2 nC, far apart with negligible mutual influence and no external source/ground. Connection permits equilibrium then disconnection. Equal sharing depends on the stated symmetry.
Refresh Kid · AP Physics 2 Unit 2 (official Unit 10) · Objectives 10.2.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 10.2, objectives 10.2.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.
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