Zero potential and zero field are different statements
You will be able to: Compare scalar potential superposition with vector field superposition.
Can V be zero where E is not?
At the midpoint between a positive and an equal negative charge, the two potentials cancel. The fields point in the same direction—from positive toward negative—and add. Zero potential does not mean no electrical influence.
A useful starting point: A volt is energy per charge, not energy itself →
Words and symbols before equations
- Scalar superposition
- Add signed potentials without resolving directions.
- Vector superposition
- Add field components, including direction.
- Reference
- The common zero used for every source contribution; here infinity.
- Gradient
- Spatial rate and direction of potential change; E is its negative.
What this picture assumes
Two fixed point sources at (−1,0) and (+1,0) m, zero potential at infinity. Probe stays on x = 0 away from source singularities. V adds scalars; E adds components.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Probe at (0,0) m: V = 0 V; E = (36,0) N/C. Zero potential and zero field are different conditions.
- 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 finite set of point sources with zero at infinity, V = ΣkQ_i/r_i. Distances are positive; charge signs supply the sign of each scalar contribution. No angle factor is needed in this sum.
For E, each contribution has a direction and must be added vectorially. Two equal positive charges give nonzero positive V but zero E at their midpoint. Equal opposite charges give zero V but nonzero E there.
A single point’s V value says nothing by itself about the local slope. Adding a constant to every potential changes those values without changing E. At a zero-field point, the potential may have a stationary value; that does not require it to be zero.
| At the midpoint | Equal positive sources | Equal opposite sources |
|---|---|---|
| Potential, zero at infinity | Positive contributions add | Signed contributions cancel |
| Electric field | Opposite vectors cancel | Both vectors point from + toward − |
| Lesson | E = 0 need not mean V = 0 | V = 0 need not mean E = 0 |
A worked example, step by step
Place +2 nC at x = −1 m and −2 nC at x = +1 m. Find V and E at the midpoint.
- Both source distances are 1 m.
- V = 18 + (−18) = 0 V.
- Each field has magnitude 18 N/C and points +x at the midpoint.
- E = +36 N/C along x. The zero scalar sum does not cancel the vector sum.
Use signed scalar addition for V and component addition for E. Neither zero condition implies the other.
For equal opposite sources, is the perpendicular bisector at zero V?
Compare with an explanation
Yes with zero at infinity; the equal-distance scalar terms cancel, while the field generally remains nonzero.
Predict. Change one thing. Explain.
Compare equal positive sources with equal opposite sources at a fixed midpoint. Then move the probe along the perpendicular bisector and compare V and both field components.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Probe at (0,0) m: V = 0 V; E = (36,0) N/C. Zero potential and zero field are different conditions.
Two fixed point sources at (−1,0) and (+1,0) m, zero potential at infinity. Probe stays on x = 0 away from source singularities. V adds scalars; E adds components.
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 questionTwo +1 nC charges sit at (−1,0) and (1,0) m. Find V and E at the origin, and explain the result.
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Compare with the answer and four-point rubric
- 1 point: Each charge contributes +9 V.
- 1 point: V_total = +18 V.
- 1 point: The fields are +9 and −9 N/C along x, so E = 0.
- 1 point: Potential adds scalars; the field cancels as a vector sum.
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 1Does zero V imply no force on a probe?
No. Force depends on E, the spatial variation of V.
RECALL 2When do positive potentials cancel?
They do not cancel one another; opposite signed contributions or a reference shift are needed.
RECALL 3What does E = 0 say about the gradient?
The local gradient of V is zero.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Zero potential and zero field are different statements
- V = ΣkQ_i/r_i.
- E = ΣE_i = −∇V.
- V = 0 at a point does not imply E = 0 there.
Remember: Use signed scalar addition for V and component addition for E. Neither zero condition implies the other.
Conditions: Two fixed point sources at (−1,0) and (+1,0) m, zero potential at infinity. Probe stays on x = 0 away from source singularities. V adds scalars; E adds components.
Refresh Kid · AP Physics C: Electricity and Magnetism Unit 2 (official Unit 9) · Objectives 9.2.A, 9.2.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 9.2, objectives 9.2.A, 9.2.B. 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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