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CED objectives

Electric Fields

▶︎  Watch it animatedinteractive step-through · ~3 min · optional ⚙︎  Open the appletField and Path Lab · launch a charge sideways and watch it leave its own field line

The electric field is force per unit positive test charge, $\vec{E} = \vec{F}/q_0$, defined at every point in space and independent of whatever charge is used to probe it. A point charge sources $E = k|q|/r^2$ directed radially, away from positive and toward negative, and several sources superpose as VECTORS: each contribution gets an arrow and a set of components before anything is added. Field lines draw that vector field, with the tangent giving direction and the line density giving magnitude.

Three errors dominate. Reading a field line as a path, so a charge released on a curved line is expected to follow it, when the line fixes only the direction of the acceleration and any velocity across it makes the trajectory diverge. Reading blank space between drawn lines as zero field, when the drawing is a finite sample of a continuous field. And adding contributions by magnitude: cancelling at the midpoint of a $+q$ and $-q$ pair where the two arrows actually point the same way and add to $8kq/d^2$, or summing three $3000$ N/C contributions from different directions into $9000$ N/C without ever resolving a component.

same midpoint, opposite outcomes: draw the two arrows before adding + + arrows OPPOSE E = 0 + − arrows AGREE E = 8kq / d² the memorized outcome is worthless without the pair it belongs to away from +, toward −: at the midpoint of the dipole both point the same way
Like charges cancel at the midpoint, unlike charges reinforce there. Draw each arrow at the field point and the two cases separate themselves.
a field line gives the direction of the ACCELERATION, not the path field line released from rest actual path a here v here v carries the old direction while a turns: the path falls behind the line and stays behind it
Release from rest and the first instant of motion is along the line. After that the velocity points where the line used to go, so the path separates from it and never comes back.

The work

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Lesson
Electric Fields ›

Defines the field as force per unit positive test charge, drills superposition through components rather than magnitudes, and separates a field line from a trajectory in the curved case where the two are most often confused.

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

Ten items spanning the failure modes of this topic: tracing a released charge along its field line, reading blank space between lines as zero field, cancelling a dipole midpoint that actually reinforces, and summing angled contributions without components. 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