Electric Fields
▶︎ Watch it animatedinteractive step-through · ~3 min · optional ⚙︎ Open the appletField Bench · traced field lines with a probe that reports its distance from the nearest one, a launched charge whose parabola crosses them, and a sphere that asks about its material firstThe electric field at a point is set by the source charges around it, $\vec{E} = \vec{F}/q$, so the test charge divides out and the field belongs to the location. The force on a charge placed there is $\vec{F} = q\vec{E}$ with the sign kept, so a positive charge is pushed along the field and a negative charge opposite to it. Field lines give the direction of that push, their density carries the strength, and contributions from several sources add as vectors. In a conductor at equilibrium the excess charge sits on the surface and the interior field is zero; a charged insulator keeps charge throughout its volume and has a field inside.
Six errors dominate. Reading $E = F/q$ as though a larger probe produced a larger field. Copying the field arrow onto a negative charge instead of reversing it. Treating a field line as the path a moving charge will follow. Reporting zero field at a point that merely falls between two drawn lines. Adding or cancelling field magnitudes without drawing the two arrows, which swaps the like-charge and unlike-charge midpoints. And carrying the conductor's zero interior field over to a charged insulator, where the charge stays where it was put.
The work
3 ways in · any order
Lesson
Electric Fields
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Divides the test charge out of the field definition, reverses the force on a negative charge, reads a field-line map without treating lines as trajectories, and superposes contributions as vectors.
Diagnostic
10-item topic check
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Ten items spanning the failure modes of this topic: making the field depend on the test charge, pushing a negative charge along the field, reading a field line as a path, calling blank space zero field, adding field magnitudes without arrows, and giving a charged insulator a conductor's empty interior. 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.