A volt is energy per charge, not energy itself
You will be able to: Distinguish source potential V from probe interaction energy U = qV.
How can the same location give different potential energies to different charges?
At a point with potential +12 V relative to a chosen zero, each positive coulomb has +12 J of interaction energy relative to that reference. A +2 μC probe has +24 μJ; a −2 μC probe has −24 μJ.
A useful starting point: Count each charge pair exactly once →
Words and symbols before equations
- Electric potential V
- Energy per small test charge for a specified source configuration and reference; measured in volts.
- Volt
- 1 V = 1 J/C.
- Probe charge q
- The small charge whose interaction energy is wanted; assumed not to rearrange fixed sources.
- Potential energy U
- For a probe and fixed sources, the interaction contribution qV, in joules.
What this picture assumes
Point source in vacuum; V = 0 at infinity. Probe does not rearrange the source. U is the probe-source interaction energy. Potential and energy use different units and separate scales.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Source potential V = 36 V; signed probe -3 μC has U = -108 μJ. V is independent of the probe.
- 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 a point source Q in vacuum and V(∞) = 0, V = kQ/r. Q is the source charge. The probe q does not appear in V; it appears in U = qV.
Potential is a signed scalar. It is not a vector, even though the electric field is. Positive potential means positive energy per positive probe charge relative to the chosen reference, not an automatic direction of motion.
The potential energy being discussed is the probe–source interaction energy. A fixed source configuration may also have its own constant internal energy. When q is small enough not to change the sources, ΔU = qΔV is a useful way to track the changing part.
| Property | Potential V | Potential energy U |
|---|---|---|
| Meaning | Energy per test charge in a specified source field | Energy of the charge-source configuration |
| Units | Volt = J/C | Joule |
| Test charge dependence | Independent of the small probe q | U = qV for a probe and fixed sources |
A worked example, step by step
A +2 nC source is 0.50 m from a point. Find V there and U for a −3 μC probe.
- Use V = kQ/r with zero at infinity.
- V = (9 × 10⁹)(2 × 10⁻⁹)/0.50 = +36 V.
- U = qV = (−3 × 10⁻⁶)(36) = −108 × 10⁻⁶ J.
- The probe interaction energy is −108 μJ. Changing q changes U but not the source’s 36 V potential.
Do not confuse source charge Q with probe charge q, or volts with joules.
If the probe is removed, does the source potential disappear?
Compare with an explanation
No. V describes the fixed sources and reference even without a probe.
Predict. Change one thing. Explain.
Keep Q and r fixed while changing q through zero. Compare the potential and energy readouts, then change Q to see both respond.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Source potential V = 36 V; signed probe -3 μC has U = -108 μJ. V is independent of the probe.
Point source in vacuum; V = 0 at infinity. Probe does not rearrange the source. U is the probe-source interaction energy. Potential and energy use different units and separate scales.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant potential, energy, work, field-gradient or line-integral 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 −1 nC source lies 0.30 m from a point. Calculate V and the energies of +2 μC and −2 μC probes there.
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Compare with the answer and four-point rubric
- 1 point: V = 9(−1)/0.30 = −30 V.
- 1 point: For +2 μC, U = −60 μJ.
- 1 point: For −2 μC, U = +60 μJ.
- 1 point: The source potential is the same for both; the probe sign changes its interaction energy.
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 one volt?
One joule per coulomb.
RECALL 2Is potential a vector?
No, it is a signed scalar.
RECALL 3What multiplies V to give probe energy?
The signed probe charge q.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
A volt is energy per charge, not energy itself
- V_point = kQ/r for V(∞) = 0.
- U_probe = qV; ΔU = qΔV.
- 1 V = 1 J/C; 1 μC × 1 V = 1 μJ.
Remember: Do not confuse source charge Q with probe charge q, or volts with joules.
Conditions: Point source in vacuum; V = 0 at infinity. Probe does not rearrange the source. U is the probe-source interaction energy. Potential and energy use different units and separate scales.
Refresh Kid · AP Physics C: Electricity and Magnetism Unit 2 (official Unit 9) · Objectives 9.2.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 9.2, objectives 9.2.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. This is E&M Unit 2: Electric Potential, numbered Unit 9 in the official combined Physics C sequence. Topics 9.1–9.3 retain their official identifiers. Models assume electrostatic fields and state whether source charges are fixed or free. Potential integrals use the specified rods, ring, arc and infinite line or cylinder. Infinite-line examples use a finite reference radius, not zero potential at infinity. The optional 3D equipotential surface uses height to represent volts, not a particle trajectory. 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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