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CED objectives

Electric Potential Energy

▶︎  Watch it animatedinteractive step-through · ~3 min · optional ⚙︎  Open the appletAssembly Ledger · list the pairs before computing, then total the same triangle the four ways it actually gets totalled and watch the doubling and the missing term appear

The electric potential energy of a pair of point charges is $U = kq_1q_2/r$ with both signs kept, measured from zero at infinite separation. A negative $U$ marks a bound pair, so separating a proton and an electron raises $U$ toward zero, while a like pair carries positive $U$ and converts it to kinetic energy as it flies apart. The distance enters as $1/r$, one rung down from the inverse-square force. For several charges the total is a sum over distinct pairs, three for three charges and six for four, or equivalently one half of the sum of $q_iV_i$ over the charges.

Two errors dominate. Dropping the charge signs, which is the correct habit for the force magnitude and the wrong one here, so every pair comes out positive and separation questions run backward. And totalling a configuration charge by charge rather than pair by pair, which either counts each interaction twice by omitting the factor of one half, or pairs a newly added charge with only one of the charges already present.

U = kq₁q₂ / r, with the signs kept U r 0 like pair: U > 0 flies apart on its own, spending U as kinetic energy unlike pair: U < 0, BOUND separating it raises U toward zero, which costs energy dropping the signs collapses both curves onto the upper one
The sign is the whole diagnosis. Below the axis the pair is held together; above it, the pair is waiting to fly apart.
one term per connecting line, never one term per charge 1 2 3 3 charges → 3 pairs 4 charges → 6 pairs n(n−1)/2. The charge-by-charge qᵢVᵢ route walks each line twice, so it needs a factor of one half
Drawing the connections first makes both errors visible: a missing line, or a line walked from both ends.

The work

3 ways in · any order
Lesson
Electric Potential Energy ›

Keeps the charge signs so a bound pair reads negative, drills the 1/r scaling against the force's inverse square, and counts a configuration's energy pair by pair.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the failure modes of this topic: dropping the charge signs so every pair comes out positive, running separation questions backward, and totalling a configuration charge by charge so interactions are double counted or missed. Take it cold to find which one is yours, or after the lesson to confirm it is not.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

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.

Take the diagnostic to identify your misconceptions
Diagnostic first