Electric Flux
▶︎ Watch it animatedinteractive step-through · ~3 min · optional ⚙︎ Open the appletFlux Lab · tilt the loop and watch which angle the cosine actually takesElectric flux measures how much field passes through a surface: $\Phi = \vec{E}\cdot\vec{A} = EA\cos\theta$ for a flat surface in a uniform field, and $\Phi = \int\vec{E}\cdot d\vec{A}$ when the field varies over it. The angle is measured to the surface NORMAL, so a surface held broadside to the field carries the maximum flux and one lying edge-on carries none. On a closed surface the outward normal fixes the sign, and the net flux counts field lines leaving minus field lines entering.
Two errors define this topic. The first is dropping the angle or measuring it to the surface instead of its normal, which turns a sheet parallel to the field, catching nothing, into the case of maximum flux. The second is reading zero net flux as zero field. A closed box in a uniform field has zero net flux with a strong field everywhere on it, because whatever enters also leaves; zero net flux says only that the ENCLOSED charge is zero. The mirror version, treating a strong field on a surface as proof of charge inside, fails for the same reason.
The work
3 ways in · any order
Lesson
Electric Flux
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Fixes the flux angle as the one measured to the surface normal, builds the flux integral for a field that varies across the surface, and separates zero net flux from zero field in both directions.
Diagnostic
10-item topic check
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Ten items spanning the failure modes of this topic: computing flux as E times A with no orientation, measuring the angle to the surface instead of its normal, reading zero net flux as a dead field, and treating a strong field on a closed surface as proof of enclosed charge. Take it cold to find which one is yours, or after the lesson to confirm it is not.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.