The Field Guide
The Mistake Museum
The book behind these diagnostics — 89 of the predictable ways students misunderstand physics, with the exact wording to drop and the one to use instead.
Electric potential is where a confident vocabulary does the most damage. A student can recite “the field is the slope of the potential,” put numbers into V = kq/r, and read an equipotential diagram without ever deciding what the field comes from, what the potential energy belongs to, or what “fifty volts” means before a reference is named. A single-sitting diagnostic that maps the exact misconceptions your students carry across potential and potential energy, the field-potential link, reference and sign, and the conductor at equilibrium. Heatmap delivered within 48 hours of class completion.
“The field is the slope of the potential,” “potential is energy,” “zero volts, zero field” are recited detached from their conditions — that the field comes from the change in the potential, not its value; that potential is energy per charge; that only differences are physical. The arithmetic works on routine problems; the picture underneath resurfaces in capacitance, circuits, and electromagnetism. These five are the most load-bearing.
At the midpoint between a positive charge and an equal negative charge the potential is zero, yet the field there is strong — the field comes from how fast the potential changes, not from its value. The converse traps too: inside a charged conductor the potential is large and constant while the field is exactly zero. The foundational discrimination the rest of the topic rests on.
A charge sits where the potential is V. Asked for its potential energy, many answer V; asked what the potential becomes if the charge is doubled, many double it too. But potential is energy per unit charge, fixed by the source charges; the energy of a charge placed there is qV. Doubling the charge doubles the energy it carries and leaves the potential, and the field, unchanged.
The field is the slope of the potential — but with a minus sign: it points from high potential to low. Asked to read the field off a potential-against-position graph, many keep the slope’s sign, so their field points uphill, toward increasing potential. The minus sign carries the physics, and dropping it inverts the field direction and the energy argument together.
A point is at a potential of fifty volts. Asked what that means physically, many treat it as an absolute fact about the point. But only potential differences are physical: the fifty volts is measured relative to a chosen zero, and moving the zero — to the other plate, to earth, to infinity — changes the number without changing any field, force, or motion. A potential can perfectly well be negative.
Across several items the same habit surfaces: a sign dropped or flipped — the field sent uphill, a pair’s negative potential energy made positive, or a charge sent the way the opposite sign would go. The diagnostic tracks a sign lost or inverted as a cross-cutting lens — the most populated lens by design, flagged where it does the most damage.
Twenty-two items map twelve bands across potential and potential energy, the field-potential link, reference and sign, and path, dielectrics, and conductors. One band is the operational core — FLD-1 (the value of the potential does not fix the field) — and the field bands build on it, with the sign discipline running across the family as the most populated lens. Three cross-cutting lenses (L1–L3) are surfaced from the option patterns, never scored as standalone bands. Every distractor is a documented student-reasoning pattern, so a wrong answer carries a name, not just a mark.
The potential belongs to the point, fixed by the source charges; the energy of a charge placed there is qV. Doubling the charge doubles the energy and leaves the potential unchanged.
Potential energy belongs to a configuration of charges, not to one charge alone; its sign is set by the interaction — negative for charges that attract, positive for charges that repel.
Contributions add as ordinary signed numbers with no direction, and the total does not depend on any test charge placed at the point. A single-item, lower-confidence band.
The keystone. The field comes from how fast the potential changes, not from its value: zero potential can sit in a strong field, a point of zero field need not be at zero potential, and a constant potential means zero field.
On an equipotential map the field is strong where the lines are close together and weak where they spread out — strength comes from the spacing, not the labelled value.
The field points down the potential, from high to low, and crosses the equipotentials at right angles, not along them.
The field is minus the slope of the potential, and the potential difference is minus the signed area under the field, taken in the direction of travel.
A potential value means nothing until a zero reference is named; moving the zero changes the number but not the physics, and potentials can be negative.
A negative charge moves opposite a positive one in the same field; the sign of the charge sets the sign of its energy, qV, and the direction it accelerates.
In a conservative field the potential has one value at each point, so the difference between two points depends only on the endpoints; the change around any closed loop is zero.
With the charge held fixed, a dielectric weakens the field in the gap and the voltage falls; there is no conservation of potential. A single-item, lower-confidence band.
At equilibrium the field inside is zero, so the potential is constant throughout the interior — constant, not necessarily zero. A single-item, lower-confidence band.
Potential treated as energy, or the scalar potential given a direction. A cross-cutting lens, surfaced from option-level signals and reported as a cohort percentage — never scored as a standalone band.
A constant-potential, reference, equilibrium, or fixed-charge result used with its condition or qualifier dropped. Surfaced from option-level signals.
A sign dropped or flipped in the field-potential link, the energy, or the motion. The most populated lens by design, most often paired with a flagged field band.
Within 48 hours of your class completing the diagnostic, we send you a complete misconception analysis — actionable, teacher-readable, and ready to use in your next lesson. Six PDFs per sitting, scored against the 22-question total.
Colour-coded class heatmap showing performance by question and by student performance band (A–D). Items grouped by misconception band so cluster patterns become visible at a glance; folded threads appear as annotations.
Teacher-readable summary: which bands hit hardest, what they mean, the cross-cutting lens readout, and the recommended order of work — for a head of department to act on without re-deriving anything.
A Mistake Museum (16 named exhibits across the 12 bands, the keystone doubled, plus the three cross-cutting lens entries), a parallel Words That Hurt language guide, a sectioned Remediation Worksheet (15 sections), and a Teacher Answer Key — keyed to the bands your class flagged.
What each performance band (A–D) means for your students, with specific teacher action items — from “structurally sound” to “foundations not yet secure,” with the single-item bands explicitly caveated as lower-confidence.
| Q# | Concept Tested | Overall | A (18–22) | B (14–17) | C (9–13) | D (0–8) | Band |
|---|---|---|---|---|---|---|---|
| Q01 | Potential energy belongs to a system | 68% | 90% | 76% | 53% | 42% | POT-2 |
| Q02 | Zero potential is not zero field | 44% | 66% | 52% | 29% | 18% | FLD-1 |
| Q03 | A negative charge moves against the field | 56% | 78% | 64% | 41% | 30% | SGN-1 |
| Q04 | Zero field is not zero potential | 40% | 62% | 48% | 25% | 14% | FLD-1 |
| Q05 | Potential is energy per charge, not energy | 64% | 86% | 72% | 49% | 38% | POT-1 |
| Q06 | The sign of a pair’s potential energy | 60% | 82% | 68% | 45% | 34% | POT-2 |
| Q07 | Potential difference is path-independent | 64% | 86% | 72% | 49% | 38% | PTH-1 |
| Q08 | Constant potential, zero field | 48% | 70% | 56% | 33% | 22% | FLD-1 |
| Q09 | The field runs down the potential | 52% | 74% | 60% | 37% | 26% | FLD-3 |
| Q10 | A longer path, the same difference | 60% | 82% | 68% | 45% | 34% | PTH-1 |
| Q11 | Field direction from the potential | 56% | 78% | 64% | 41% | 30% | FLD-3 |
| Q12 | Constant, not zero, inside a conductor | 56% | 78% | 64% | 41% | 30% | CON-1 |
| Q13 | The sign of the charge sets the energy | 48% | 70% | 56% | 33% | 22% | SGN-1 |
| Q14 | The field is minus the slope | 52% | 74% | 60% | 37% | 26% | FLD-4 |
| Q15 | Moving the zero changes the number, not the physics | 60% | 82% | 68% | 45% | 34% | REF-1 |
| Q16 | Doubling the charge, not the potential | 72% | 94% | 80% | 57% | 46% | POT-1 |
| Q17 | A dielectric with the charge fixed | 52% | 74% | 60% | 37% | 26% | CFG-2 |
| Q18 | Field strength from the spacing | 64% | 86% | 72% | 49% | 38% | FLD-2 |
| Q19 | A lone potential value needs a reference | 56% | 78% | 64% | 41% | 30% | REF-1 |
| Q20 | Reading field strength off a map | 60% | 82% | 68% | 45% | 34% | FLD-2 |
| Q21 | Minus the signed area for the difference | 48% | 70% | 56% | 33% | 22% | FLD-4 |
| Q22 | Potential is a scalar | 60% | 82% | 68% | 45% | 34% | POT-3 |
Q02, Q04, Q08 — Band FLD-1, the field-versus-potential keystone. Reading the field off the value of the potential sits among the lowest in the diagnostic, at 14% in Band D and 22–25% in Band C on the hardest items. Until what the field comes from is settled — the change in the potential, not its value — the bands that build on it cannot.
Q05, Q16 — Band POT-1, potential versus potential energy; Q09, Q11 — field direction from the potential. Potential collapsed into energy, and the field pointed up the potential rather than down it, fall through Bands C and D — this confusion is not confined to weaker students, and it carries into the energy and the sign.
The sign lens (L3); the lower-confidence single-item bands. Submissions that drop or flip a sign — in the field-potential link, the energy, or the motion — fire the cross-cutting sign lens, reported as a cohort percentage. The single-item bands (POT-3, CFG-2, CON-1) are read as directional, lower-confidence signals, never settled.
I carried out a pilot test of the Physics Misconceptions Diagnostics with my Grade 11 (lower 6th) International Baccalaureate classes, as part of their revision for end of year exams. The tests covered Motion Foundations, Forces and Free-Body Diagrams - topics that are fundamental to the IB course as well as A’ level courses.
The tests were all set up by FundaFirst - all I had to do was point the students to web links. The students found the questions easy to access and to carry out. The information that came back from FundaFirst was incredibly useful, identifying areas where the class and/or individuals were weaker. These areas would have been much harder to identify without the tests. FundaFirst then provided concrete examples of how to address the misconceptions, with work sheets targeting these areas.
I will not hesitate to use FundaFirst’s diagnostic testing with future cohorts!
Fill in the form below. The Electric Potential diagnostic suits classes partway through or just past the electric-potential unit, where the field-and-potential reasoning has had time to settle.
→You receive a class-specific diagnostic link and a short setup message you can paste directly to your students. No student logins needed.
→Share the link. The diagnostic takes about 25 minutes (22 questions, no calculator required, single sitting). In-class or take-home.
→Class heatmap, cohort summary, band profiles, and remediation toolkit emailed to you within 48 hours of class completion.
Share your details below and we'll set up the diagnostic link within 24 hours. No commitment — this is a free pilot designed for teacher use and classroom feedback.
The diagnostic is grounded in physics education research, including the work of Knight, Chabay & Sherwood, and Moore. A FundaFirst video on the early history of atomic theory was licensed by National Geographic Learning (Cengage) for a chemistry title.
The Electric Potential diagnostic is strongest after the electric-field work, where the field concept and the vector reasoning the gradient and equipotential items lean on have their footing. Within the electricity sequence it is best run partway through, or just past, the electric-potential material. It runs cleanly on its own too. Eight sister diagnostics are also available — Motion, Newton’s Laws, Energy, Momentum, Projectile & Circular, Oscillations & Waves, Static Electricity, and Electric Fields — same format, same 48-hour turnaround.
View the Motion Diagnostic → View the Newton's Laws Diagnostic → View the Energy Diagnostic → View the Momentum Diagnostic → View the Projectile & Circular Diagnostic → View the Oscillations & Waves Diagnostic → View the Static Electricity Diagnostic → View the Electric Fields Diagnostic →
The book behind these diagnostics — 89 of the predictable ways students misunderstand physics, with the exact wording to drop and the one to use instead.