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Volume I · MMXXVI AP Physics C: Electricity and Magnetism
Library AP Physics C: Electricity and Magnetism Unit 13: Electromagnetic Induction
⁂   AP Physics C: Electricity and Magnetism · Unit 13

13. Electromagnetic Induction

10–20% of the AP exam. 12 key topics. 4 common errors analyzed.

10–20% exam weight

Unit 13: Electromagnetic Induction

Unit 13 (Electromagnetic Induction) is part of the calculus-based AP Physics C: E&M curriculum. Gauss's Law, line integrals, and differential equations appear throughout — set up integrals carefully before evaluating.

Key topics in this unit

  1. Magnetic flux: Φ_B = ∫B · dA
  2. Faraday's Law: EMF = –dΦ_B/dt
  3. Lenz's Law: direction of induced current opposes the change in flux
  4. Motional EMF: EMF = BLv (and generalisation to non-uniform fields via integration)
  5. Induced electric fields from time-varying magnetic flux (∮E · dL = –dΦ_B/dt)
  6. Self-inductance: L = NΦ/I; induced EMF = –L(dI/dt)
  7. Mutual inductance (qualitative and quantitative definition)
  8. Energy stored in an inductor: U = LI²/2
  9. LR circuit time-domain behavior: I(t) = (EMF/R)(1 – e^(–Rt/L)); time constant τ = L/R
  10. LC circuit oscillations: analogy to SHM, angular frequency ω = 1/√(LC)
  11. Maxwell's equations in integral form: Gauss's Law (E and B), Ampère-Maxwell Law (with displacement current), Faraday's Law
  12. Displacement current concept: ∂Φ_E/∂t term in Ampère-Maxwell Law

Common errors — what the rubric penalizes

These are the most frequently penalized mistakes on AP exam FRQs and MCQs. Review each before your next practice session.

Common error

Misapplying Lenz's Law direction — students identify that a current is induced but assign it the wrong direction, often by forgetting to ask 'what change is the induced current opposing?' rather than reasoning from the flux change alone; this is especially error-prone when the source is a moving conductor in a non-uniform field.

Common error

Omitting or mis-signing the negative sign in Faraday's Law (EMF = –dΦ_B/dt) when computing the magnitude of an induced EMF — students drop the sign and lose the physical meaning, producing wrong answers when the problem asks for the direction of induced current.

Common error

Confusing LR circuit initial/final conditions with RC circuit conventions — in an LR circuit, the inductor acts as an open circuit at t = 0 (if no prior current) and a short circuit at t → ∞, which is the opposite of the capacitor's behavior; students who memorise RC rules without understanding the underlying physics invert the limits.

Common error

Treating LC oscillation energy as non-conserved — students compute Q_max or I_max correctly but then fail to use energy conservation (U_E + U_B = constant) to relate charge and current at intermediate times, instead attempting to solve the differential equation from scratch each time.

Study checklist

  • Can you list all key topics from memory without this page?
  • Have you worked through at least one FRQ-style question per topic?
  • Can you explain each common error above — and why the correct answer differs?
  • Have you reviewed the relevant College Board CED section and formula sheet entries?
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