Volts: energy per unit charge
You will be able to: Calculate scalar potential and relate it to a test charge’s energy.
How is potential different from potential energy?
A location at +100 V gives a +2 μC test charge potential energy +0.0002 J relative to the chosen reference. A −2 μC test charge at the same location has negative potential energy. The location’s potential has not changed sign.
A useful starting point: Energy belongs to interacting charges →
Words and symbols before equations
- Potential V
- Electric potential energy per unit charge, in volts (1 V=1 J/C).
- Source contribution
- Point-source V=kQ/r with zero at infinity.
- Potential difference ΔV
- V_final−V_initial; it determines ΔU=qΔV.
- Scalar superposition
- Add signed source potentials without directional components.
What this picture assumes
Left source +1 nC and right source ±1 nC, each 0.50 m from the midpoint probe. Potential zero at infinity. Field is a vector and potential a scalar; their readouts use different units and no shared magnitude scale.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- V=36 V from scalar addition; E_x=0 N/C from vector addition. Equal positive potentials add while equal opposing fields cancel.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Potential depends on the source configuration and chosen reference, not the small test charge. Potential energy of a test-charge/source system depends on both: U=qV. Use signed q and V.
At the midpoint of equal positive sources, fields cancel but potentials add. At the midpoint of equal opposite sources, potentials cancel while fields reinforce. These examples separate scalar from vector addition.
Conductors connected together redistribute charge until they share potential at electrostatic equilibrium. Different sizes can then carry different charges. A battery can maintain a potential difference through chemical processes that separate charge; it is not merely a reservoir that creates charge.
| Quantity | Kind | Units |
|---|---|---|
| Force F | Vector on a charge | N |
| Field E | Vector at a location | N/C |
| Potential energy U | Scalar of a configuration | J |
| Potential V | Scalar energy per unit charge | J/C = V |
A worked example, step by step
Charges +1 nC and −2 nC are each 0.30 m from a point. Find potential there and U for a +3 nC test charge.
- V₁=kQ₁/r=30 V and V₂=−60 V.
- V_total=−30 V; potentials add as signed scalars.
- U=qV=(3×10⁻⁹)(−30)=−9×10⁻⁸ J.
- The result uses zero source potential at infinity and a nonperturbing test charge.
Zero potential does not imply zero field. Volts are J/C, not joules.
At the midpoint of equal positive charges, can E=0 while V is nonzero?
Compare with an explanation
Yes. Field vectors cancel but both scalar potentials are positive.
Predict. Change one thing. Explain.
Compare equal like charges with an opposite pair at the midpoint. Read potential and field together. Predict whether changing a test charge would change either source quantity.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
V=36 V from scalar addition; E_x=0 N/C from vector addition. Equal positive potentials add while equal opposing fields cancel.
Left source +1 nC and right source ±1 nC, each 0.50 m from the midpoint probe. Potential zero at infinity. Field is a vector and potential a scalar; their readouts use different units and no shared magnitude scale.
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 point is at +200 V. A test charge −4 nC is placed there. (a) Find U relative to the potential reference. (b) State the potential for a +4 nC test charge. (c) Find that positive charge’s U. (d) Explain the distinction.
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Compare with the answer and four-point rubric
- 1 point: U=−8×10⁻⁷ J.
- 1 point: V stays +200 V for unchanged sources.
- 1 point: U=+8×10⁻⁷ J.
- 1 point: Potential describes the source field location; energy also depends on test charge.
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 1Potential units?
Volts, J/C.
RECALL 2How are multiple potentials combined?
As signed scalars.
RECALL 3Equal potential implies equal charge?
No. Geometry affects conductor charge at a given potential.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Volts: energy per unit charge
- V=ΣkQ_i/r_i.
- U=qV; ΔU=qΔV.
- Connected conductors share potential at electrostatic equilibrium.
Remember: Zero potential does not imply zero field. Volts are J/C, not joules.
Conditions: Left source +1 nC and right source ±1 nC, each 0.50 m from the midpoint probe. Potential zero at infinity. Field is a vector and potential a scalar; their readouts use different units and no shared magnitude scale.
Refresh Kid · AP Physics 2 Unit 2 (official Unit 10) · Objectives 10.5.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 10.5, objectives 10.5.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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