Unit 13 · Electromagnetic Induction
The Complete AP Physics C: Electricity and Magnetism Guide · AP Physics C: Electricity and MagnetismUnit 13 · Electromagnetic Induction
- The Complete AP Physics C: Electricity and Magnetism Guide
- AP Physics C: Electricity and Magnetism
- 6 sections
Unit 13: Electromagnetic Induction accounts for 10–20% of AP Physics C: Electricity and Magnetism multiple-choice content. Section I has 42 multiple-choice questions in 85 minutes and contributes 50% of the score. For Section II's 4 free-response questions in 95 minutes (50%), be ready to carry the same unit skills and representations into a complete solution. Magnetic flux combines field, oriented area, and angle. Faraday's law differentiates signed flux, and Lenz's law fixes the opposing current direction. For a moving loop, mark entry, full-overlap, and exit intervals before taking the slope.
- How AP Physics C: Electricity and Magnetism assesses this 10–20% of the multiple-choice section · Section I: 42 MCQs in 85 min, 50% · Section II: 4 FRQs in 95 min, 50% · show the model with oriented loop and area vector, flux-versus-time graph, RL transient and energy diagram
- Key skills Apply Faraday and Lenz laws, Analyze motional emf, Reason about inductance RL circuits and magnetic energy
- How to study for Unit 13 This page turns oriented loop and area vector, flux-versus-time graph, RL transient and energy diagram into one route: choose the loop normal and state whether field area or angle changes.
- The organizing decision define loop orientation and determine how magnetic flux changes before assigning induced emf or current
What AP Physics C: Electricity and Magnetism Unit 13 covers
Use this map to connect each assessed skill to the relationship or representation that makes it visible.
Apply Faraday and Lenz laws
oriented loop and area vector; Faraday's law gives emf as the negative time derivative of magnetic fluxAPPHYSICSCEM-U13-S2Analyze motional emf
flux-versus-time graph; Lenz's law opposes the change in flux rather than the original fieldAPPHYSICSCEM-U13-S3Reason about inductance RL circuits and magnetic energy
RL transient and energy diagram; Inductors resist changes in current and store magnetic energyUnit 13: Electromagnetic Induction accounts for 10–20% of AP Physics C: Electricity and Magnetism multiple-choice content.
Official unit name and weighting: College Board course and exam description.
Build signed flux before differentiating
Connect the published share to the unit model
Magnetic flux combines field, oriented area, and angle. Faraday's law differentiates signed flux, and Lenz's law fixes the opposing current direction. For a moving loop, mark entry, full-overlap, and exit intervals before taking the slope.
Self-inductance audit — An inductor opposes current change: induced emf = −L dI/dt, stored energy U_L = LI^2/2, and a long solenoid has L = mu_core N^2 A/ell. Use a specified linear inductor; ideal connecting wires are modeled with zero inductance. Its current cannot jump under finite voltage.
LR drill — With a 12.0 V source, R = 3.00 ohms, and L = 0.600 H in series, tau = L/R = 0.200 s (H/ohm = s) and I_final = E/R = 4.00 A. From I(0) = 0, I(0.400 s) = 4.00[1 − exp(−0.400/0.200)] A = 3.46 A. At one tau a rise reaches 63%, a source-free decay retains 37%, and at long time an ideal inductor is a wire.
LC drill — An ideal source-free, resistance-free LC loop obeys d^2q/dt^2 = −q/(LC), so omega = 1/sqrt(LC) and electric energy trades with magnetic energy. For L = 20.0 mH, C = 5.00 microfarads, and Q0 = 30.0 microcoulombs, sqrt(LC) = 3.162 × 10^-4 s, omega = 3.16 × 10^3 rad/s, T = 2pi/omega = 1.99 ms, and I_max = Q0/sqrt(LC) = 94.9 mA because C/s = A. Nonzero resistance makes the oscillation damped.
The decision that organizes this unit
Define the system and choose the route before calculating
define loop orientation and determine how magnetic flux changes before assigning induced emf or current
choose the loop normal and state whether field area or angle changes
Mechanism route and repair branches
Relationships to preserve
- Faraday's law gives emf as the negative time derivative of magnetic flux
- Lenz's law opposes the change in flux rather than the original field
- Inductors resist changes in current and store magnetic energy
Representations to read
- oriented loop and area vector
- flux-versus-time graph
- RL transient and energy diagram
Branches to reject
- opposing the field instead of its change
- changing both loop orientation and sign mid-solution
- using motional-emf formulas when geometry or velocity is not perpendicular
| Key concept | Why it's hard | What scores |
|---|---|---|
| Construct signed flux | Overlap and field orientation can change by interval. | A piecewise area relation with correct signs and breakpoints. |
| Differentiate to emf | Flux magnitude can be mistaken for induced emf. | A visible time or position derivative followed by resistance and direction. |
| Model LR and LC states | Current continuity and ideal-oscillation assumptions can be skipped. | Initial state, asymptote or energy exchange, time scale, and a unit-checked numerical value. |
How AP Physics C: Electricity and Magnetism assesses Electromagnetic Induction
What a complete response must make visible
Match the task to evidence that a reader can audit, then check the most likely reasoning failure before finalizing the response.
| Task | Evidence to show | Hurdle |
|---|---|---|
| Apply Faraday and Lenz laws | oriented loop and area vector; Faraday's law gives emf as the negative time derivative of magnetic flux | opposing the field instead of its change |
| Analyze motional emf | flux-versus-time graph; Lenz's law opposes the change in flux rather than the original field | changing both loop orientation and sign mid-solution |
| Reason about inductance RL circuits and magnetic energy | RL transient and energy diagram; Inductors resist changes in current and store magnetic energy | using motional-emf formulas when geometry or velocity is not perpendicular |
Resolve the Electromagnetic Induction evidence conflict
Carry the model from prompt to check
- Step 1Choose one loop normal and positive circulation direction before assigning signs.
- Step 2While crossing a field boundary, write flux as B times the changing overlap area.
- Step 3Use emf=-B dA_overlap/dt; for a rectangular loop of transverse width ell moving at speed v, the magnitude is B ell v.
- Step 4The overlap-area derivative reverses sign on exit, so induced emf and current reverse; they are zero while overlap is constant.
Key terms for Unit 13: Electromagnetic Induction
Models, uses, and boundaries
- Apply Faraday's and Lenz's Laws
- Faraday's law gives emf as the negative time rate of magnetic flux Choose this formula when the prompt asks you to apply faraday's and lenz's laws and the declared system, frame, source, geometry, and process match the model. A Apply Faraday's and Lenz's Laws solution must stop if it substitutes values before declaring the system, direction or sign convention, units, and stated model conditions.
- Calculate Motional EMF
- A rod moving orthogonally through a uniform field has motional emf B ell v Choose this formula when the prompt asks you to calculate motional emf and the declared system, frame, source, geometry, and process match the model. A Calculate Motional EMF solution must stop if it substitutes values before declaring the system, direction or sign convention, units, and stated model conditions.
- Analyze Self-Induction
- An inductor's self-induced emf opposes the current change Choose this formula when the prompt asks you to analyze self-induction and the declared system, frame, source, geometry, and process match the model. A Analyze Self-Induction solution must stop if it substitutes values before declaring the system, direction or sign convention, units, and stated model conditions.
- Calculate Magnetic Energy in an Inductor
- Magnetic energy stored in an ideal inductor is one half L I squared Choose this formula when the prompt asks you to calculate magnetic energy in an inductor and the declared system, frame, source, geometry, and process match the model. A Calculate Magnetic Energy in an Inductor solution must stop if it substitutes values before declaring the system, direction or sign convention, units, and stated model conditions.
AP Physics C: Electricity and Magnetism Unit 13 FAQ
How much of AP Physics C: Electricity and Magnetism does Unit 13 carry?
Unit 13: Electromagnetic Induction accounts for 10–20% of AP Physics C: Electricity and Magnetism multiple-choice content.
What is the first move on a Electromagnetic Induction problem?
choose the loop normal and state whether field area or angle changes
Which relationships should I preserve?
Faraday's law gives emf as the negative time derivative of magnetic flux Lenz's law opposes the change in flux rather than the original field Inductors resist changes in current and store magnetic energy
Which representations should I practice?
Practice moving among oriented loop and area vector, flux-versus-time graph, RL transient and energy diagram.
What error should I check before submitting an answer?
Check for opposing the field instead of its change; changing both loop orientation and sign mid-solution; using motional-emf formulas when geometry or velocity is not perpendicular.
Evidence workshop
Continue from the free model into complete practice
The full unit guide continues with the chapter’s worked examples, figures, scoring tables, and answer checks.
- Carry motional emf through current, force, and speed
- Carry motional emf through current, force, and speed (continued)
- Differentiate rotating flux, then square current for power
- Differentiate rotating flux, then square current for power (continued)
- Convert overlap geometry into flux, current, and power
- Convert overlap geometry into flux, current, and power (continued)
Full unit practice. Open the complete guide for the full evidence workshop and synthesis.
Related AP Physics C: Electricity and Magnetism unit guides
AP Physics C: Electricity and Magnetism Exam Guide & Review
The whole exam and its official unit sequence.08Electric Charges, Fields, and Gauss’s Law
15–25% of the multiple-choice section09Electric Potential
10–20% of the multiple-choice section10Conductors and Capacitors
10–15% of the multiple-choice section11Electric Circuits
15–25% of the multiple-choice section12Magnetic Fields and Electromagnetism
10–20% of the multiple-choice sectionHow to study AP Physics C: Electricity and Magnetism Unit 13
Start with the organizing decision
Before solving, restate the decision in operational terms: define loop orientation and determine how magnetic flux changes before assigning induced emf or current. Your first written move should be to choose the loop normal and state whether field area or angle changes.
Practice the same idea in several representations
Rotate through oriented loop and area vector, flux-versus-time graph, RL transient and energy diagram. Use each representation to practice Apply Faraday and Lenz laws, Analyze motional emf, Reason about inductance RL circuits and magnetic energy, and explain what stays invariant when the surface form changes.
Turn each error into a repair check
After every attempt, audit the response for opposing the field instead of its change; changing both loop orientation and sign mid-solution; using motional-emf formulas when geometry or velocity is not perpendicular. Then redo only the first step that made the reasoning diverge, keeping units, direction, and model conditions visible.
Confirm current course details in the official College Board course and exam description for the May 2027 administration.
