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.
The electric field is where a confident vocabulary does the most damage. A student can recite “sigma over two epsilon-nought,” quote “zero inside a conductor,” and write Gauss’s law without ever deciding whether the plane’s field fades with distance, what actually cancels the field inside the metal, or when Gauss’s law can deliver a field at all. A single-sitting diagnostic that maps the exact misconceptions your students carry across field construction, magnitude and falloff, the capacitor, conductors, and Gauss’s law. Heatmap delivered within 48 hours of class completion.
“Sigma over two epsilon-nought,” “zero inside a conductor,” “Gauss’s law gives the field” are recited detached from their conditions — that the uniform plane field is the infinite idealisation, that the interior is zero by cancellation, that Gauss’s law delivers a field only with enough symmetry. The arithmetic works on routine problems; the picture underneath resurfaces in every later topic that leans on the field model. These five are the most load-bearing.
Close to a large charged plate the field is σ/(2ε₀). Asked what it is twice as far away, many students fade it with distance — fields weaken as you back off. But an infinite plane’s field is uniform: it does not depend on distance, and it reverses direction across the plane. A finite sheet’s field does fall off — and the single word “infinite” is what separates them. The first keystone.
Gauss’s law always holds, for any closed surface. Asked to find a point charge’s field with a cube drawn around it, many students expect the law to deliver it. But Gauss’s law is always valid and only sometimes useful: solving it for the field needs enough symmetry to take the field outside the flux integral. A sphere gives the field; a cube gives a correct flux statement and no field. The second keystone.
The field inside a conductor is zero. Asked why, many students say the metal blocks it — the conductor stops the field getting in. But nothing blocks or uses up a field: fields superpose. The interior is zero because the conductor’s own charges rearrange until their field exactly cancels the external one inside. The architecture keystone — fields add, nothing blocks.
To find the field of a charged rod or disc, many students reach for a remembered formula, or treat the whole object as a point charge at its centre. But an extended source has to be built: slice it into pieces, write each piece’s charge as a density times an element, cancel components in pairs by symmetry, and add the contributions. The governing difficulty is knowing what to integrate, not the calculus itself.
Across several items the same habit surfaces: a clean result quoted with its condition stripped off — the infinite-plane field used for a finite sheet, “zero inside a shell” applied to a solid sphere or without the words “its own charge,” the capacitor gap taken as uniform without the symmetry argument that makes it so. The diagnostic tracks this condition-stripping as a cross-cutting lens, surfaced from the option patterns.
Thirty items map sixteen bands across field construction and superposition, magnitude and falloff, the parallel-plate capacitor, conductors and charged shells, Gauss’s law in its integral and differential forms, and field representation. Two bands are the operational core — RES-1 (the infinite-plane idealisation) and GAU-1 (Gauss’s law as valid but only sometimes useful) — with CON-1, screening as superposition, as the architecture keystone. 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.
An extended source is built from its pieces — each piece’s charge written as a density times an element, dq = λ dx, and the contributions integrated; any sub-object whose field is known can serve as the piece.
Keep the surviving field component and let the cancelling one drop out by symmetry; an on-axis result does not transfer off-axis.
Cutting a uniformly charged sheet into unequal pieces leaves the surface density unchanged. A single-item, lower-confidence band.
The keystone. An infinite plane’s field is uniform — it does not weaken with distance, and it reverses direction across the plane; distance-independence is the infinite idealisation, and a finite sheet’s field does fall off.
Not every source falls off as 1/r² — the geometry sets the falloff. A single-item, lower-confidence band.
Outside a sphere the field is measured from the centre and is not strongest at the centre; a shell’s interior is zero for its own field, while a solid sphere’s interior field rises with r.
A single charged plate gives half the gap field; the two plate fields add in the gap and cancel outside.
The gap field is uniform only by the symmetry argument; a small fringe field remains at the edges. A single-item, lower-confidence band.
The architecture keystone. One charge does not block or use up another’s field; a conductor’s zero interior is its own induced charges cancelling the external one — fields add, nothing blocks.
Zero field inside from its own charge, but an external charge’s field still reaches in; the nearest surface charges do not dominate inside — the rest of the shell cancels them by symmetry.
The field just outside a conductor’s surface is half from the local patch and half from the rest of the surface; field components are continuous across a charge-free boundary.
The keystone. Gauss’s law is always true, but the field factors out of the flux integral only with enough symmetry — the cube non-example: drawing any surface does not yield the field.
An external charge gives a field on the surface but zero net flux through it; the angle between field and surface matters.
div E = ρ/ε₀ is a pointwise, local statement, not the enclosed-charge integral; divergence is a scalar, and a strong uniform field can have zero divergence. HL and AP-C only.
The divergence operator carries a geometric term, not a bare derivative; an axial field (from an axis) is not a radial one (from a point). HL and AP-C only.
A field arrow is a scaled vector at a point; the field exists in the spaces off the arrows too. A single-item, lower-confidence band.
A closed form reached for instead of building the field. A cross-cutting lens, surfaced from option-level signals and reported as a cohort percentage — never scored as a standalone band.
A clean result quoted with its condition stripped off — the infinite-plane field for a finite sheet, “zero inside a shell” without its conditions. The lens most often paired with a flagged RES-1 or CON band.
A field pulled from Gauss’s law or a divergence without checking that the symmetry permits it. A cross-cutting lens, surfaced from option-level signals.
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 30-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 (20 named exhibits across the 16 bands and the three cross-cutting lenses), a parallel Words That Hurt language guide, a sectioned Remediation Worksheet (19 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 (25–30) | B (19–24) | C (13–18) | D (0–12) | Band |
|---|---|---|---|---|---|---|---|
| Q01 | Build a charged rod’s field; convert dq to a density times an element | 66% | 88% | 74% | 51% | 40% | SET-1 |
| Q02 | A distribution can be built from any sub-object whose field is known | 58% | 80% | 66% | 43% | 32% | SET-1 |
| Q03 | Keep the surviving component; the cancelling one drops out | 64% | 86% | 72% | 49% | 38% | SET-3 |
| Q04 | Cutting a charged sheet leaves the surface density unchanged | 62% | 84% | 70% | 47% | 36% | SET-5 |
| Q05 | An on-axis result does not transfer off-axis | 54% | 76% | 62% | 39% | 28% | SET-3 |
| Q06 | The infinite-plane field is uniform; it does not weaken with distance | 46% | 68% | 54% | 31% | 20% | RES-1 |
| Q07 | The field reverses direction across the plane | 50% | 72% | 58% | 35% | 24% | RES-1 |
| Q08 | Distance-independence is the infinite idealisation, not a universal rule | 42% | 64% | 50% | 27% | 16% | RES-1 |
| Q09 | Not every source falls off as 1/r² | 56% | 78% | 64% | 41% | 30% | RES-2 |
| Q10 | Exterior field from the centre; not strongest at the centre | 60% | 82% | 68% | 45% | 34% | RES-3 |
| Q11 | Shell interior zero for its own field; solid interior rises with r | 50% | 72% | 58% | 35% | 24% | RES-3 |
| Q12 | A lone plate gives half the gap field | 62% | 84% | 70% | 47% | 36% | CAP-1 |
| Q13 | The two plate fields add in the gap and cancel outside | 52% | 74% | 60% | 37% | 26% | CAP-1 |
| Q14 | The gap is uniform only by symmetry; the fringe is small but nonzero | 58% | 80% | 66% | 43% | 32% | CAP-3 |
| Q15 | One charge does not block or use up another’s field | 50% | 72% | 58% | 35% | 24% | CON-1 |
| Q16 | A conductor’s zero interior is cancellation, not the metal stopping the field | 46% | 68% | 54% | 31% | 20% | CON-1 |
| Q17 | A fixed-charge shell: zero own-field inside, external charge reaches in | 48% | 70% | 56% | 33% | 22% | CON-2 |
| Q18 | The nearest surface charges do not dominate inside | 54% | 76% | 62% | 39% | 28% | CON-2 |
| Q19 | The surface field is half local patch, half the rest of the surface | 50% | 72% | 58% | 35% | 24% | CON-3 |
| Q20 | Field components are continuous across a charge-free boundary | 58% | 80% | 66% | 43% | 32% | CON-3 |
| Q21 | Always true, but the field factors out only with enough symmetry | 44% | 66% | 52% | 29% | 18% | GAU-1 |
| Q22 | The cube non-example: any surface does not yield the field | 42% | 64% | 50% | 27% | 16% | GAU-1 |
| Q23 | What enough symmetry actually buys you | 54% | 76% | 62% | 39% | 28% | GAU-1 |
| Q24 | An external charge gives field on the surface but zero net flux | 60% | 82% | 68% | 45% | 34% | GAU-2 |
| Q25 | Flux is not field times area; the angle matters | 54% | 76% | 62% | 39% | 28% | GAU-2 |
| Q26 | The differential form is pointwise (local), not the enclosed-charge form | 48% | 70% | 56% | 33% | 22% | GAU-U1 |
| Q27 | Divergence is a scalar; a strong uniform field can have zero divergence | 44% | 66% | 52% | 29% | 18% | GAU-U1 |
| Q28 | The divergence operator carries a geometric term, not a bare derivative | 46% | 68% | 54% | 31% | 20% | GAU-U2 |
| Q29 | Axial (from an axis) is not radial (from a point) | 42% | 64% | 50% | 27% | 16% | GAU-U2 |
| Q30 | An arrow is a scaled vector at a point; the field exists off the arrows | 64% | 86% | 72% | 49% | 38% | REP-1 |
Q06, Q07, Q08 — Band RES-1, the infinite-plane-versus-finite-sheet keystone. Whether the uniform σ/(2ε₀) result belongs to the infinite idealisation, and a finite sheet’s field falls off, sits among the lowest in the diagnostic — 42% overall on the hardest item, and lower still through Bands C and D. Until the idealisation is settled, the capacitor and Gauss bands that reuse it cannot.
Q21, Q22, Q23 — Band GAU-1, the valid-but-only-sometimes-useful keystone; Q15, Q16 — Band CON-1, screening as superposition. Gauss’s law read as always usable (the cube non-example) and the conductor read as blocking rather than cancelling fall through Bands C and D together — the two ideas the differential-form and shell bands build on.
The condition-lens (L2) and symmetry-lens (L3); the lower-confidence single-item bands. Submissions that apply a result outside its condition, or extract a field without the symmetry check, fire the cross-cutting lenses, each reported as a cohort percentage. The single-item bands (SET-5, RES-2, CAP-3, REP-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 Fields diagnostic suits classes partway through or just past the electric-fields unit, where the field-construction 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 30 minutes (30 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 Fields diagnostic is strongest after the Static Electricity diagnostic — the electrostatics conceptual prerequisite, where charge, force, and the field concept have their footing — and after the kinematics and forces work. Within the electricity unit it is best run partway through, or just past, the electric-fields 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 Potential — 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 Potential 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.