Diagnostic · Superposition & Gauss
Electric Fields Diagnostic
Maps how your students build the field: superposition, falloff set by geometry, screening, and Gauss inside its conditions. It shows which band to address first.
IB DP · AP · A-Level · GCSE / IGCSE
1
Forms
30
Questions
~30
Minutes
16 + 3 lenses
Bands
FundaFirst HS diagnostics have run in classrooms at 10 schools · 9 countries · 3 continents
The wrong ideas come from physics education research, which has recorded them since the 1970s: Viennot, Trowbridge & McDermott, Arons, Hestenes, Maloney. The physics comes from Arons, Knight, Moore, and Chabay & Sherwood.
What it maps
Sixteen misconception bands across six families, plus three cross-cutting lenses.
SET-1
Build the Field by Superposition
An extended source is built from its pieces. Each piece’s charge is written as a density times an element, dq = λ dx, and the contributions are integrated. Any sub-object whose field is known can serve as the piece.
SET-3
Symmetry and the Distance Reference
Keep the field component that survives and let the cancelling one drop out by symmetry. An on-axis result does not carry over off the axis.
SET-5
Surface Charge Density Is Intensive
Cutting a uniformly charged sheet into unequal pieces leaves the surface density unchanged. Asked once, so a lower-confidence band.
RES-1
A Plane Is Uniform, a Finite Sheet Falls Off
The core band. An infinite plane’s field is uniform. It does not weaken with distance, and it reverses direction across the plane. The independence from distance is the infinite idealisation, and a finite sheet’s field does fall off.
RES-2
Falloff Is Set by Geometry
Not every source falls off as 1/r². The geometry sets the falloff. Asked once, so a lower-confidence band.
RES-3
Sphere and Shell
Outside a sphere the field is measured from the centre and is not strongest at the centre. Inside a uniformly charged shell, the shell’s own field is zero. Inside a uniformly charged nonconducting sphere, the field grows in proportion to the distance from the centre.
CAP-1
The Factor of Two
A single charged plate gives half the gap field. The two plate fields add in the gap and cancel outside.
CAP-3
The Gap Is Uniform Only by Symmetry
The gap field is uniform only by the symmetry argument. A small fringe field remains at the edges. Asked once, so a lower-confidence band.
CON-1
Screening Is Superposition
The core band for conductors. One charge does not block or use up another’s field. A conductor’s zero interior is its own induced charges cancelling the external field. Fields add and nothing blocks.
CON-2
The Fixed-Charge Shell
Zero field inside from its own charge, but an external charge’s field still reaches in. The nearest surface charges do not dominate inside, because the rest of the shell cancels them by symmetry.
CON-3
The Surface-Field Split and Continuity
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 boundary that carries no charge.
GAU-1
Always Valid, Only Sometimes Useful
The core band for Gauss’s law. The law is always true, but the field comes out of the flux integral only with enough symmetry. The cube is the standard non-example. Drawing any surface does not give the field.
GAU-2
Flux Is Not Field Times Area
An external charge gives a field on the surface but zero net flux through it. The angle between the field and the surface matters.
GAU-U1
The Differential Form Is Pointwise and Scalar
div E = ρ/ε₀ is a local statement at a point, and not the enclosed-charge integral. Divergence is a scalar, and a strong uniform field can have zero divergence. HL and AP-C only.
GAU-U2
Divergence Carries Geometric Terms
The divergence operator carries a geometric term. It is not a bare derivative. A field directed away from a line and one directed away from a point have different geometric terms in their divergence. HL and AP-C only.
REP-1
An Arrow Is a Scaled Vector at a Point
A field arrow is a scaled vector at a point. The field exists in the spaces off the arrows too. Asked once, so a lower-confidence band.
L1
A Remembered Form for the Construction
A remembered formula is used instead of building the field. A cross-cutting lens, read from the pattern of options chosen and reported as a percentage of the class. It is never scored as a band.
L2
A Result Outside Its Condition
A clean result quoted with its condition stripped off, such as the infinite-plane field for a finite sheet, or zero inside a shell without its conditions. The lens most often paired with a flagged RES-1 or CON band.
L3
A Field Without the Symmetry Check
A field pulled from Gauss’s law or a divergence without checking that the symmetry permits it. A cross-cutting lens, read from the pattern of options chosen.
A question from it
Students can quote every field result and still hold these ideas.
The plane’s field fades with distance
Close to a large charged plate the field is σ/(2ε₀). Asked what it is twice as far away, many students make it weaker, because fields fade as you back off. 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. The single word infinite separates the two cases.
Draw any surface and Gauss hands you the field
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. The 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 true statement about flux and no field.
The metal blocks the field
The field inside a conductor is zero. Asked why, many students say the metal blocks it, so the field cannot get in. Nothing blocks or uses up a field. The interior is zero because the conductor’s own charges rearrange until their field cancels the external one inside. Fields add and nothing blocks. That is the third core idea.
Look up the field instead of building it
To find the field of a charged rod or disc, many students reach for a remembered formula. Others treat the whole object as a point charge at its centre. 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 hard part is knowing what to integrate.
Use the result outside its condition
Across several questions the same habit shows: 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 as a cross-cutting lens, read from the pattern of options chosen.
How it runs
Students use one shared link and need no logins.
30 questions, about 30 minutes, no calculator required, single sitting.
The report arrives within 48 hours of your class finishing.
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Knight documents the misconceptions. Moore and Chabay & Sherwood supply the physics treatment.