Electric Charge and Electric Force
▶︎ Watch it animatedinteractive step-through · ~3 min · optional ⚙︎ Open the appletCoulomb Bench · commit to a direction before the arrows appear, read the signed product that cannot explain either of them, and run the gravity comparison once per pair and once in bulkCharge comes in two signs, is conserved by every charging process, and is quantized in units of $e$. The force between two point charges has magnitude $F = k|q_1||q_2|/r^2$ and lies along the line joining them, toward each other for unlike charges and apart for like ones. The absolute value bars are deliberate, because the sign of a charge product is a number rather than a direction. Both charges appear symmetrically, so the pair always shares one force magnitude and differs only in acceleration.
Four errors dominate. Reading a direction off the signed product instead of off the arrangement, which scrambles as soon as a third charge joins. Scaling the force as $1/r$ rather than $1/r^2$, so doubling the separation halves instead of quarters. Handing the larger charge the larger force, when the formula is symmetric in the two charges. And extending the enormous per-pair strength of the electric force to planets and stars, when bulk matter is neutral enough that nothing electric survives at that scale.
The work
3 ways in · any order
Lesson
Electric Charge and Electric Force
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Separates the magnitude of Coulomb's law from its direction, drills the inverse-square scaling against the 1/r forms that come later, and settles why the larger charge does not exert the larger force.
Diagnostic
10-item topic check
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Ten items spanning the failure modes of this topic: reading a direction off a signed charge product, scaling the force as 1/r, handing the bigger charge the bigger force, and carrying the per-pair strength of electricity up to astronomical scale. 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.