AP Physics C E&M Full Mock Test 7 — Faraday's Law, RL Circuits, and Inductance FRQs
AP Physics C E&M Full Mock 7 targets electromagnetic induction: Faraday's law FRQs, Lenz's law direction problems, RL circuit ODE derivations, and inductance calculations.
About Full Mock 7
Full Mock 7 for AP Physics C: Electricity & Magnetism places its most challenging questions on Unit 13 — electromagnetic induction. Faraday's law (EMF = −dΦ_B/dt), Lenz's law, motional EMF, self-inductance, and RL circuit differential equations are the most conceptually rich topics in AP Physics C E&M. They combine the magnetic field concepts of Unit 12 with the differential equation techniques of Unit 11, making Unit 13 the natural climax of the E&M course. Mock 7 provides the focused practice this unit demands.
Electromagnetic Induction Topics Under Emphasis
Faraday's Law Applications
Mock 7 FRQs test Faraday's law in all three scenarios where flux changes:
- Changing B at constant area: A solenoid with time-varying current produces a changing B; a loop around the solenoid has EMF = −d(BA)/dt = −A·dB/dt. The dB/dt term requires knowing how B depends on solenoid current (B = μ₀nI), then differentiating with respect to time.
- Changing area (motional EMF): A conducting rod sliding on rails in a uniform B field — area increases at rate Lv, giving EMF = BLv. FRQ sub-parts extend this to the current, power dissipated in the circuit resistance, and the retarding force on the rod.
- Changing orientation: A rotating loop in a uniform B field — Φ = BA cosωt, giving EMF = BAω sinωt. AP-style questions ask for the maximum EMF and the time at which it occurs.
Lenz's Law Direction Problems
Mock 7 includes several problems specifically targeting Lenz's law direction determination. Students must: identify whether flux through a loop is increasing or decreasing, determine the direction of induced current to oppose the change, and verify this is consistent with the negative sign in Faraday's law. These problems test conceptual understanding that MCQ format probes efficiently.
RL Circuit Differential Equations
Mirroring the RC circuit FRQs of Mock 3, Mock 7 FRQs require full RL circuit ODE derivation:
- Writing KVL for an RL circuit: ε − IR − L(dI/dt) = 0
- Rearranging and solving by separation of variables to obtain I(t) = (ε/R)(1 − e^(−t/τ_L)) with τ_L = L/R
- Computing the energy stored in the inductor at steady state: U = ½LI² = ½L(ε/R)²
- Comparing τ_L = L/R to τ = RC and noting that larger L slows the circuit while larger R speeds it up, opposite to RC behaviour
Self-Inductance Derivations
Mock 7 includes FRQ sub-parts requiring derivation of self-inductance for a solenoid: using B = μ₀nI, computing Φ_B = BA = μ₀nIA, multiplying by the number of turns N = nℓ, and obtaining L = μ₀n²Aℓ. Students must show each step explicitly.
How Mock 7 Reinforces Units 12 and 13 Together
Because Faraday's law requires knowledge of B (from Unit 12) to compute flux, Mock 7 FRQs inevitably draw on Biot-Savart and Ampere's law results as inputs. This cross-unit structure means that strong performance on Mock 7 simultaneously confirms Unit 12 mastery. Errors in Mock 7 flux calculations should be traced back to whether the B field input was incorrect (Unit 12 gap) or the dΦ/dt differentiation was incorrect (Unit 13 gap).