AP Physics C E&M Full Mock Test 4 — Biot-Savart, Ampere's Law, and Magnetic Force FRQs
AP Physics C E&M Full Mock 4 focuses on magnetism: Biot-Savart integrals, Ampere's law derivations, and magnetic force FRQ problems across all E&M units.
About Full Mock 4
Full Mock 4 for AP Physics C: Electricity & Magnetism concentrates its most challenging questions on Unit 12 — magnetic fields and electromagnetism. The Biot-Savart law and Ampere's law are the magnetic analogues of Coulomb's law and Gauss's law, and AP-style FRQs testing these laws demand the same rigorous integral calculus setup that the electrostatics derivations require. Mock 4 builds this magnetism-specific calculus fluency.
Magnetism Topics Under Emphasis
Biot-Savart Law Calculations
The Biot-Savart law (dB = (μ₀/4π)(I dl × r̂)/r²) requires students to set up a vector integral for the magnetic field produced by a current-carrying conductor. Mock 4 includes FRQ problems requiring:
- Full Biot-Savart setup for a finite straight wire at a perpendicular distance: expressing dl in terms of an integration variable, computing the cross product magnitude, writing the integral with correct limits, and evaluating.
- Magnetic field along the axis of a circular current loop: justifying cancellation of transverse components and integrating the axial contribution.
- Comparing the on-axis B(x) field to the result at the centre (x = 0) and far from the loop (x >> R) using limiting cases.
Ampere's Law Integral Setup
Mock 4 tests Ampere's law (∮B·dl = μ₀I_enc) for three canonical geometries plus variations:
- Infinite straight wire — standard derivation giving B = μ₀I/(2πr)
- Solenoid — rectangular Amperian loop derivation giving B = μ₀nI inside, zero outside
- Toroid — circular Amperian loop giving B = μ₀NI/(2πr); comparison to solenoid result
- Thick wire with non-uniform current density J(r) — requiring ∫J·dA to find I_enc inside the conductor
Magnetic Force FRQs
FRQ problems in Mock 4 extend magnetic force analysis beyond the basic F = qv × B formula. Problems include: the force per unit length between two parallel current-carrying wires (derived using Ampere's law for one wire then F = IL × B for the second), the trajectory of a charged particle entering a region of combined E and B fields, and the net force and torque on a current loop in a non-uniform magnetic field.
MCQ Distribution in Mock 4
Approximately 45% of MCQ items draw primarily from Unit 12, with the remainder balanced across Units 8–11 and 13. The Unit 13 (induction) MCQs in Mock 4 preview the connection between the magnetic field derivations of Unit 12 and the Faraday's law calculations of Unit 13 — specifically testing how a known B field (derived via Ampere's law or Biot-Savart) determines the flux and hence the induced EMF.
Skill-Building Value of Mock 4
Completing Mock 4 builds the magnetic field derivation skills that are directly required in Unit 13. Students who can set up a Biot-Savart integral and evaluate an Ampere's law loop in Mock 4 will find the flux integral in Faraday's law — which uses the B field as an input — significantly more tractable. Mock 4 therefore serves as both standalone magnetism practice and preparation for the induction-focused Mock 7.