The tool below drills the chain from your own derivations.
WeSolve+ reads the whole document and writes the questions for you
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Unit 13 flux derivatives, from your own notes
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Faraday's law is a derivative, so set up the flux first
Faraday's law reads emf as minus the rate of change of magnetic flux, so every problem starts by writing the flux as field times area times orientation and asking which factor carries the time dependence. A growing field, a shrinking loop and a rotating coil are the three canonical cases, and the graded step is the explicit derivative, not the memorised result.
Lenz's law is the sign, stated as opposition
Lenz's law gives the minus sign physical form: the induced current circulates to oppose the change in flux that created it, which is energy conservation in disguise. State the direction argument in words, flux increasing into the page, so induced current runs counterclockwise to push flux out, because free response scores the reasoning and not the arrow alone.
Motional emf: the rod on rails makes the derivative geometric
A conducting rod sliding on rails through a uniform field sweeps area at a rate set by its speed, so the flux derivative is B l v without limits or tables. The circuit then closes the loop: current, force on the rod opposing its motion by Lenz, and the external agent's power matching the resistor's dissipation. That energy audit, pull against magnetic drag, is the unit's favourite full derivation.
Inductance prices a circuit's self opposition
Inductance measures how much flux a coil threads through itself per ampere, so a changing current induces a back emf of L times the current's derivative. The solenoid's inductance follows from its geometry, and the stored energy, one half L I squared, sits in the magnetic field itself. Derivations that assemble these from Faraday's law rather than quoting them are the scored version.
LR circuits refuse sudden change, exponentially
An inductor cannot jump its current, so just after a switch closes it behaves as an open wire and long after as a plain conductor. Between the two, the LR circuit relaxes exponentially on the time constant L over R: write the loop rule, separate the differential equation, and check both limits against the two switch behaviours. The limit check is free credit and catches sign errors early.
What to photograph for Electromagnetic Induction
Your flux derivations and LR curves. Related: Unit 12, photo to quiz and pricing.
Sources used on this page
- College Board, AP Physics C: Electricity and Magnetism
- Faraday's law of induction
- Lenz's law
- Inductance
- RL circuit
- Active recall
- Spaced repetition
- Testing effect
- Forgetting curve
- Generation effect
- Judgment of learning
- Metacognition
- Desirable difficulty
- Distributed practice
- Formative assessment
- Flashcard
- Cloze test
- Multiple choice
- Test (assessment)
- Educational assessment
- Advanced Placement
- Curriculum
- Study skills
- Study guide
- Note-taking
- Overlearning
- Instructional scaffolding
- Item analysis
- Mastery learning
| Setup | What changes in the flux | The move |
|---|---|---|
| Growing field, fixed loop | B carries the derivative | Differentiate B, keep area |
| Rod on rails | Area grows at l v | emf is B l v, then the circuit |
| Rotating coil | Orientation oscillates | Differentiate the cosine |
| Switch just closed | Current cannot jump | Inductor as open wire |
| Long after closing | Nothing changes | Inductor as plain wire |
| Between the limits | Exponential relaxation | Time constant L over R |
What does AP Physics C E and M Unit 13 cover?
Electromagnetic induction at the calculus level: Faraday's and Lenz's laws, motional emf, self inductance, stored energy and LR circuits.
How do I start any induction problem?
Write the flux through the loop as field, area and orientation, identify which factor depends on time, and differentiate that factor explicitly.
What does Lenz's law actually fix?
The direction: induced current opposes the change in flux that created it, which keeps the bookkeeping consistent with energy conservation.
Why is the rod on rails so common on the exam?
It chains the whole unit: geometric flux derivative, induced current, opposing force, and an energy audit between the pulling agent and the resistor.
How do I handle an inductor at switch time?
Current cannot jump: just after switching the inductor is an open wire, long after it is a plain conductor, and the exponential bridges the two on L over R.
Can I build questions from my own Unit 13 notes?
Yes. Whatever you upload sets the boundary. Photograph the pages or send the chapter as a PDF and the questions stay inside it.
Last updated: 2026-08-15