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CED objectives

Electromagnetic Induction

▶︎  Watch it animatedinteractive step-through · ~3 min · optional ⚙︎  Open the appletLenz Bench · park the cursor on a flux graph and commit to the induced current's sense before the slope is revealed

Faraday's law, $\varepsilon = -N\,d\Phi_B/dt$, makes the induced EMF a rate of change and never a size, so on a flux-versus-time graph the EMF is the slope. Lenz's law, carried by the minus sign, aims the induced current at the change in flux: a growing flux is opposed, a shrinking flux is propped up. Three levers can move the flux, since $\Phi_B = BA\cos\theta$, which is why a bar sliding on rails in a perfectly constant field still generates $|\varepsilon| = BLv$. The field doing the pushing, $\oint \vec{E}\cdot d\vec{\ell} = -d\Phi_B/dt$, is non-conservative and has no potential function.

The failure modes are specific. Aiming Lenz's law at the field rather than at the change, which gets every withdrawal and every collapsing field backward. Ranking induction by the size of the flux, which reports a large EMF for a magnet resting inside a coil and puts the EMF peak where the flux peaks instead of a quarter cycle away. Reading the height of a flux graph where the slope belongs. Declaring no induction whenever $dB/dt = 0$, missing the area and rotation terms. And applying “work around a closed path is zero” to an induced field whose whole point is that it is not.

same field direction, opposite induced currents B into the page, GROWING × × × × × × × × × induced current COUNTERCLOCKWISE field OUT of the page: it fights the growth B into the page, SHRINKING × × × × × × × × × induced current CLOCKWISE field INTO the page: it fights the loss
The external field points the same way in both panels. What flipped the current is the sign of the rate of change, which is the only thing Lenz's law consults.
the EMF is the SLOPE of the flux, never its height Φ rising flat, and this is the MAXIMUM flux falling, steeply EMF small, steady ZERO where the flux is largest large, reversed t
The flat top is where students place the maximum EMF. It is the one interval where the EMF is exactly zero, and the short steep drop, where the flux is on its way to nothing, is where the EMF is biggest.

The work

3 ways in · any order
Lesson
Electromagnetic Induction ›

Makes the induced EMF a rate rather than a size, aims Lenz's law at the change in flux instead of at the field, works the area and rotation levers alongside the field lever, and separates the induced electric field from every electrostatic one.

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

Ten items spanning the failure modes of this topic: opposing the field instead of the change in flux, inducing an EMF from the size of the flux, reading a flux graph's height where its slope belongs, declaring no induction whenever the field is constant, and treating the induced electric field as conservative. 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